{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Principal Component Analysis (PCA) is frequently applied in machine learning as a sort of black box dimensionality reduction technique. PCA can be arrived at as an expression of a best fit probability distribution for our data. Treating PCA as a probability distribution opens up all sorts of fruitful avenues, we can draw new examples from the learned distribution and/or evaluate the likelihood of samples as we observe them to detect outliers. \n",
    "\n",
    "<!-- TEASER_END -->\n",
    "\n",
    "This post is part of a series of posts about the uses of PCA such as <a href=\"http://asymptoticlabs.com/blog/posts/other_uses_for_PCA_part1.html\"> decorrelation, semantic factor discovery, empirical noise modeling, </a> and <a href=\"http://asymptoticlabs.com/blog/posts/other_use_for_PCA_part2.html\"> data imputation/noise reduction </a>. \n",
    "Again we will be using the same faces dataset as in the earlier posts."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Probabilistic Interpretation of PCA\n",
    "\n",
    "Stop to consider for a moment what you might do if I asked you to make a simple probability model for a bunch of data I handed to you as a data matrix X in tidy format with samples being rows and columns being features. The model doesn't have to be very accurate it is more important that it is easy to compute given the data and easy to handle during analysis.\n",
    "\n",
    "Given it a moments thought? If you are like me then you might have answered something like treat each column as an independent normal distribution with width equal to its root mean square variation. That model is about as simple as you can get while still capturing something of the underlying distribution of the data. But the assumption that the different columns are independent could come back to bite us if the columns end up having lots of correlational structure. If you have read my other posts on PCA you might remember that PCA acts as a rotation which guarantees zero correlation between columns after its application. If you apply that rotation first and then model the (now guaranteed uncorrelated) columns as independent normal distributions the result is actually a very useful and fairly general probability distribution. \n",
    "\n",
    "The definition above of rotating our data to decorrelate our columns and then treating each column as an independent normal is actually exactly equivalent to modeling our data as being distributed like a multivariate normal distribution with a covariance matrix equal to our data covariance matrix. \n",
    "\n",
    "$$\n",
    "p(x) \\sim \\mathcal{N}(x, \\mu, \\Sigma)\n",
    "$$\n",
    "\n",
    "Lets tie this back to the usual definition of PCA as the low rank decomposition,\n",
    "\n",
    "$$\n",
    "X = WH\n",
    "$$\n",
    "\n",
    "Where W is a n_samples by k matrix and H is a k by n_features matrix. If H is a complete basis of the column space of X then we will always be able to perfectly reconstruct X by picking the correct corresponding W coefficients. But there are some choices of basis H which have better properties than others and in PCA we choose a basis H such that the rows of H are the eigenvectors of the data covariance matrix $\\Sigma = \\frac{1}{N}X^TX$. By the properties of eigenvectors the basis H is orthonormal and so $H^TH = HH^T = I$. \n",
    "\n",
    "We said above that PCA amounts to modeling our data like a multivariate normal probability distribution with a covariance matrix equal to our data covariance matrix. Lets evaluate the data covariance matrix in terms of $W$ and $H$ and see if we can see anything interesting. For convenience I'm going to evaluate N times the data covariance matrix instead so that I can drop the factor fo $\\frac{1}{N}$ from out front of my calculations.\n",
    "\n",
    "$$\n",
    "X^TX = H^TW^TWH\n",
    "$$\n",
    "\n",
    "How can we evaluate the product in the middle $W^TW$? Because of the orthonormality and completeness properties of H that we noted above putting any factor of $H^TH$ or $HH^T$ anywhere in our matrix expressions is just like putting an identity matrix into the expression, hitting our data matrix on the right with $H^TH$ we can find an expression for W in terms of H and X.\n",
    "\n",
    "$$\n",
    "X = X H^T H = WH \n",
    "$$\n",
    "\n",
    "Therefore,\n",
    "\n",
    "$$\n",
    "W = XH^T\n",
    "$$\n",
    "\n",
    "and so,\n",
    "\n",
    "$$\n",
    "W^TW = HX^TXH^T\n",
    "$$\n",
    "\n",
    "That may not look like a simpler equation than we had but remember that we said that the rows of H were the eigenvectors of the covariance matrix $\\frac{1}{N}X^TX$ that means that the product $X^TXH^T$ just gives us back the matrix $H^T$ with the eigenvalues multiplied into each column. Furthermore because of the orthonormality of H we can now see that the product $W^TW$ will be a diagonal matrix with the eigenvalues $v_i$ of $X^TX$ along the diagonal.\n",
    "\n",
    "This alows us to rewrite the expression above in terms of a sum over the eigenvalues $v_i$ like so,\n",
    "\n",
    "$$\n",
    "X^TX = \\sum_i^k v_i H_i^TH_i\n",
    "$$\n",
    "\n",
    "If we bring the factor of $\\frac{1}{N}$ that we dropped at the beginning of this calculation back in then the matrix product becomes the data coviriance matrix and the eigenvalues $v_i$ become the variance $\\sigma_i^2$ of the data projected along the principal vector $H_i$. Nothing else changes however and so we need only do the replacement $v_i$ -> $\\sigma_i^2$ and we have found the very interesting expression of the full data covariance matrix in terms of a sum over the principal vectors,\n",
    "\n",
    "$$\n",
    "\\Sigma_k = \\sum_i^k \\sigma_i^2 H_i^TH_i\n",
    "$$\n",
    "\n",
    "If we carry out the sum over the full number of dimensions of our input space so that k=D then there is no need for the subscript k above. The covariance matrix of our data $\\Sigma$ is equal to the full sum. However we now have the option of stopping short and using just the first few principal components instead of going all the way up to the full dimensionality of the column space of X. Adding the subscript k indicates that we may have taken only a partial sum in that expansion and chosen only the first fiew directions of highest variance over which to evaluate the sum.\n",
    "\n",
    "If D = k then the covariance matrix is equal to the full data covariance matrix and the PCA probability model is equal to the multivariate normal distribution with mean and covariance equal to our data. For a little extra intuition you can think of this as a two step process as we described above, rotate the data into a decorrelated space (that is $W$ with $H^T$ being the rotation matrix since $W = XH^T$) and then model the columns in the rotated space as independent normal distributions.\n",
    "\n",
    "## Why?\n",
    "\n",
    "You may be wondering why I just dragged you through all that linear algebra.\n",
    "So far we haven't done anything really amazing, all we have done is rewritten the data covariance matrix into some crazy format involving eigenvectors. It is interesting to note that PCA has this connection to the multivariate normal distribution but we don't need to know about that connection in order to build a probabilistic model for our data. \n",
    "\n",
    "Thats fair enough and if you are dealing with a smallish number of dimensions (say tens to hundreds) and you have scads of data with which to evaluate the full covariance matrix then by all means carry on. You don't need to know about this mathematical machinery you can use the standard statistical packages to either draw samples from your multivariate normal and/or evaluate the likelihood etc. But when we are dealing with high dimensional spaces such that D is several thousand or more it becomes extremely computationally expensive to calculate or store the full covariance matrix $\\Sigma$. Since the covariance matrix $\\Sigma_k$ is of the same dimension storing it as a proper matrix and/or carrying out any matrix multiplications will be just as expensive as using the full matrix. However because of our nice expansion above in terms of the outer product of the eigenvectors and eigenvalues $\\sigma_i^2 H_i^TH_i$ we don't have to keep around the whole matrix. By just keeping the most important few dimensions k << D we can still use this probabilistic formalism to operate in very high numbers of dimensions simply by replacing the full covariance matrix $\\Sigma$ by its best k dimensional approximation $\\Sigma_k$. Instead of evaluating the matrix $\\Sigma_k$ explicitly anywhere it would be required we can evaluate the equivalent expression in terms of the identity above which is much more computationally friendly. As a result we can deal with probabilistic models of the form, $p(x) \\sim \\mathcal{N}(x, \\mu, \\Sigma_k)$\n",
    "even when the dimension D is far too large to compute the full covariance matrix $\\Sigma$. \n",
    "\n",
    "There is a subtlety here with respect to the normalization of the probability distribution. The normalization constant for a multivariate normal is proportional to the inverse of the determinant of the covariance matrix. If the rank k is less than the full dimension that will mean that $\\sigma_k$ is singular and so has determinant 0. Thus the probability density $\\mathcal{N}(x, \\mu, \\Sigma_k)$ is not normalizable and is technically an improper likelihood. This is an important point but one we are going to gloss over until later in this post. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Example Generation\n",
    "\n",
    "Since we now have an idea of how to interpret PCA as a probability distribution lets start doing things that you can only really do with distributions. The first thing we might want to be able to do is to draw samples from our distribution. So lets fit a PCA expansion to a dataset and draw some random samples from the implied distribution. Generating examples directly from a PCA model gives useful insight into what the structure of our model is like and is often much more informative than simply looking at the principal components in isolation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import scipy\n",
    "import scipy.ndimage\n",
    "import sklearn\n",
    "import sklearn.datasets\n",
    "import sklearn.decomposition\n",
    "\n",
    "import scipy.stats"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "plt.rcParams.update(\n",
    "    {\n",
    "        \"figure.figsize\":(10,6),\n",
    "        \"font.size\":16,\n",
    "        \"image.cmap\":\"afmhot\",\n",
    "        \"image.interpolation\":\"nearest\",\n",
    "        \"image.aspect\":\"auto\",\n",
    "    }\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Lets copy some utility functions over from the earlier posts"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "faces_ds = sklearn.datasets.fetch_olivetti_faces()\n",
    "\n",
    "faces = faces_ds[\"data\"]\n",
    "#divide by the global standard deviation\n",
    "faces /= np.std(faces)\n",
    "\n",
    "subject_ids = faces_ds[\"target\"]\n",
    "\n",
    "im_shape = (64, 64)\n",
    "\n",
    "def as_image(arr):\n",
    "    return arr.reshape(im_shape)\n",
    "    \n",
    "def view_as_image(arr, ax=None, cmap=\"binary_r\", **imshow_kwargs):\n",
    "    if ax is None:\n",
    "        fig, ax = plt.subplots()\n",
    "    ax.axis(\"off\")\n",
    "    im = ax.imshow(as_image(arr), cmap=cmap, **imshow_kwargs)\n",
    "    return im\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "So how can we sample from the normal distribution $\\mathcal{N}(., \\mu, \\Sigma_K)$ when we can't explicitly evaluate the covariance matrix? The trick is to generate the random samples in PCA space $W$ where the variables are uncorrelated and then form the matrix product with $H$ to transform back to the full feature space. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "def sample_from_pca_distribution(pca, n_samples, n_dims=None):\n",
    "    full_dims = len(pca.explained_variance_)\n",
    "    #if no dimensionality is given assume we want to use all the dimensions\n",
    "    if n_dims is None:\n",
    "        n_dims = len(pca.explained_variance_)\n",
    "    \n",
    "    #generate uncorrelated white noise\n",
    "    noise_sample = np.random.normal(size=(n_samples, full_dims))\n",
    "    \n",
    "    #scale the noise to have the appropriate variance in each dimension\n",
    "    standard_deviations = np.zeros((n_samples, full_dims))\n",
    "    standard_deviations[:, :n_dims] = np.sqrt(pca.explained_variance_[:n_dims])\n",
    "    noise_sample *= standard_deviations\n",
    "    \n",
    "    #transform the noise back into data space\n",
    "    samples = pca.inverse_transform(noise_sample)\n",
    "    return samples"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Imagined Faces\n",
    "\n",
    "Now that we have all the theory out of the way lets have some fun and draw some samples from the learned distribution over face like images!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fbb2eeeb080>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fbb2e8736a0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fbb2e83b048>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fbb2e7f5a58>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fbb2e79ff60>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.decomposition import PCA\n",
    "\n",
    "pca = PCA(n_components=400)\n",
    "pca.fit(faces)\n",
    "\n",
    "np.random.seed(1234)\n",
    "imagined_faces = sample_from_pca_distribution(pca, n_samples=5)\n",
    "\n",
    "for im_face in imagined_faces:\n",
    "    view_as_image(im_face)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Sampling from this distribution is a fantastic way to interrogate our PCA model to see if it makes sense or not. If we had drawn samples which were unrecognizable as faces that would indicate that the covariance and mean of our data alone are not enough to describe it. For this data set we know that there are lots of non-linear effects within the data. For example the effect on the image of someone wearing glasses is an on/off effect you either have glasses on or you don't there is no way to linearly transition from not having glasses to having them on. Looking at the images you can see that all of the images seem to have ghostly rings around their eyes where glasses would go, none of the imagined faces seem to clearly be wearing glasses instead all of them are in some 1/2 glasses wearing limbo. \n",
    "\n",
    "The randomly generated faces are a little blurrier than the training images and clearly not all of the accessible parameter space correspond to realistic faces. However, the randomly generated faces are all clearly identifiable as a face and the diversity and quality of the samples is suprisingly high given the simplicity of the underlying probabilistic model. The fact that these imagined faces look pretty good is a decent indicator that treating the faces in this data set as being roughly normally distributed with covariance matrix $\\Sigma_K$ is a reasonably good approximation. \n",
    "\n",
    "As a side note there is a strong analogy to be drawn between the \"hallucinated faces\" in part 2 where we (ab)used \"denoising\" to turn random white noise images into face like images. Those faces had much less diversity and were also much less realistic looking. Why do these images look better? In the hallucinated faces case since we generated noise images in the image space and then transformed into PCA space the variance of the $W$ coefficients were not at all well matched to the typical level of variance present in the image data. Now that we are doing things right and generating the noise in PCA space and then transforming back to an image we get better matched results."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Statistics and Anomaly Detection\n",
    "\n",
    "Now that we have sampling from the PCA distribution under our belts lets turn to using the PCA expansion to calculate the likelihood of samples generated in some other way and think about how we might recognize anomalous outliers.\n",
    "\n",
    "Dealing with probability distributions on high dimensional spaces can be difficult and deciding when a point should be considered unusual or not is no exception. When we are dealing with a one dimensional probability distribution it is relatively easy to determine when a given value has a very low probability of happening and should therefore be considered \"anomalous\". However when we are dealing with a high dimensional probability distribution the probability density is spread out over a large high-dimensional \"volume\" the higher the number of dimensions the larger this effective volume and the lower the typical magnitude of the probability density is. As a result of this \"typical\" points in the high dimensional space have very low occurence probabilities. That is to say every point in this high dimensional space is remarkable in some sense even the most likely volumes are themselves very unlikely.\n",
    "\n",
    "For a more down to earth analog of this surprising fact consider a well shuffled deck of cards. Every configuration has a just one in 52 factorial chance of occurring. That is a chance of just 1 in roughly $8x10^{67}$. For comparison the chance of any given lottery number winning are something like 1 in $10^7$ (specifically one in 13,983,816 for a 6-49 game where one picks 6 unique numbers ranging from 1 to 49). So every time we shuffle a deck of cards and happen to find out that just one of the 52 factorial possibilities has happened to occur is a rare event indeed, roughly the equivalent of winning the lottery 9 times in a row! An event so rare that probably no deck of cards has ever had exactly that same configuration.\n",
    "\n",
    "So why then is no one surprised to see any given random shuffle? The answer of course is that none of these different configurations was any more or any less likely than any other and one of them had to happen. Because no particular configuration is more or less likely than any other the likelihood that we pick a configuration that is at least as rare as 1 in $10^{67}$ will occur with probability 1. Therefore a deck that happens to come out in one particular deck configuration cannot be seen as remarkable no matter how unlikely that cofiguration was in an absolute sense. \n",
    "\n",
    "An anomaly is an event that we should be surprised to see happen. As the example with a deck of cards shows very low absolute probability is not enough to make an event surprising. The key to detecting anomalies is to divide the space of possibilities up in to bins in such a way that the overwhelming majority of all possibilities lie in the \"normal\" bucket and a vanishingly small fraction $\\epsilon$ lie outside. Because the probability of landing outide of the normal bucket is at most \"epsilon\" we can meaningfully label any points that don't meet our normal criterion as anomalies.\n",
    "\n",
    "To return to the example of a shuffled deck of cards if we partition the set of all possible configurations into categories such that a very different number of deck configurations land in each one then a particular shuffled deck could indeed be considered anomalous. For example the configurations that result in all cards of the same suit being next to each other in the deck or perhaps more poignantly the configurations that would give you a royal flush and me a full house in a game of poker. These events could be considered \"anomalous\" because the overhwelming majority of all deck configurations do not result in them. But of course we must always have explicitly laid out where the boundaries between normal and anomalous lie before looking at any event, otherwise we will be back to concluding that every shuffle is miraculous in some way."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## $\\chi^2$ distribution\n",
    "\n",
    "The way that the division between normal and anomalous is usually done is to pick some statistic for which we can calculate the cumulative distribution function and to then call points \"normal\" if they lie below a $1-\\epsilon$ threshold. A convenient statistic distribution to use is the $\\chi^2$ distribution. The $\\chi^2$ distribution with D degrees of freedom may be defined as the distribution of the sum of the squared magnitude of the coordinates of a point drawn from a D dimensional spherical normal distribution. \n",
    "\n",
    "Because PCA decorrelates the input features we can treat each column in $W$ as an independent normal distributed variable with variance $\\sigma_i^2$. After dividing each column in $W$ by $\\sigma$ we can treat each column as independent unit normal distributions and therefore can reason about the distribution of distances of our points from the mean using the $\\chi^2$ distribution. \n",
    "\n",
    "Furthermore since we are treating each column in $W$ as independent of the others we can pick any combination of columns and analyze their squared sum as a $\\chi^2$ distribution with a number of dimensions equal to the number of columns we picked. We will start by looking at each column individually and compare it against a $\\chi^2$ distribution with 1 degree of freedom and then start looking at combinations as a $\\chi^2$ distribution with k degrees of freedom.\n",
    "\n",
    "Conveniently we can easily calculate the distribution functions for $chi^2$ using the scipy.stats package. As a helpful rule of thumb the $\\chi^2$ distribution approximates a normal distribution with mean $\\mu=D$ and variance $\\sigma^2 = D$ with the approximation becoming better for higher numbers of dimensions D."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5,0,'$\\\\chi$')"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fbb2d414390>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "chi2_grid = np.linspace(0, 30, 201)\n",
    "chi_grid = np.sqrt(chi2_grid)\n",
    "example_dims = [1, 2, 4, 8, 16]\n",
    "fig, axes = plt.subplots(len(example_dims), 2, figsize=(10, 10))\n",
    "\n",
    "for idx, n_dims in enumerate(example_dims):\n",
    "    axes[idx, 0].plot(chi2_grid, scipy.stats.chi2.pdf(chi2_grid, n_dims), c=\"b\", lw=2)\n",
    "    axes[idx, 0].set_yticks([])\n",
    "    axes[idx, 0].set_ylabel(\"D={}\".format(n_dims), fontsize=18)\n",
    "    \n",
    "    axes[idx, 1].plot(chi_grid, scipy.stats.chi.pdf(chi_grid, n_dims), c=\"b\", lw=2)\n",
    "    axes[idx, 1].set_yticks([])\n",
    "    \n",
    "axes[0, 0].set_title(\"$\\chi^2$ distribution\")\n",
    "axes[0, 1].set_title(\"$\\chi$ distribution\")\n",
    "axes[-1, 0].set_xlabel(\"$\\chi^2$\", fontsize=20)\n",
    "axes[-1, 1].set_xlabel(\"$\\chi$\", fontsize=20)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can easily divide the space of events into \"anomalous\" and \"normal\" categories by choosing a cut off $\\chi^2$ above which we label points as anomalies. However with the exact form of the cumulative $\\chi^2$ distribution at our disposal we can even go one better and ask the question \"what is the chance of a randomly occuring event having a $\\chi^2$ at least as high as observed?\". That way we not only get just the two categories of \"normal\" and \"anomalous\" but have some indication of the strength of our conviction. If a point is an outlier at a 1 in a 1000 level that is a world of difference from being an outlier at a level of one in a trillion although potentially both could be considered outliers by some definition. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Anomalous Images?\n",
    "\n",
    "That is more than enough theory without application lets try to answer the question of whether or not any of the faces in the data set are anomalous in a $\\chi^2$ sense. We will begin by looking at the distribution of each column in $W$ separately then as a sum and finally we will consider how to deal with variations outside of the subspace learned by PCA.\n",
    "\n",
    "When calculating the $\\chi^2$ values we have to be careful not to use an image both for calculating the PCA expansion and evaluting the $\\chi^2$ for that image. Consider the case in which we have just 2 images the normalized difference between the first and second image becomes our first (and only) principal component and the magnitude of that difference becomes our estimated RMS variance. Therefore we would always end up with a $\\chi^2$ of 1 no matter what the two images looked like. To avoid these sorts of effects we need to apply some sort of cross validation technique to ensure that if we use an image to generate a PCA expansion we do not also use that PCA expansion to evaluate a $\\chi^2$ value."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "#make a cross validation split\n",
    "n_folds = 10\n",
    "\n",
    "fold_indexes = np.random.random(len(faces)).argsort() % n_folds\n",
    "\n",
    "pca_expansions = []\n",
    "\n",
    "max_components = 350\n",
    "\n",
    "for fold_idx in range(n_folds):\n",
    "    train_faces = faces[fold_indexes != fold_idx]\n",
    "    fold_pca = PCA(n_components=max_components)\n",
    "    fold_pca.fit(faces[np.arange(len(faces)) != fold_idx])\n",
    "    pca_expansions.append(fold_pca)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now that we have a set of PCA expansions trained on 90% of the data we can go back and find out how strange in a $\\chi^2$ sense each image is compared to the training set that left that image out. First we project the images into PCA space and collect the variance associated with each dimension and collect the results for each fold."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "projected_coeffs = np.zeros((len(faces), max_components))\n",
    "projection_variances = np.zeros(projected_coeffs.shape)\n",
    "\n",
    "for fold_idx in range(n_folds):\n",
    "    cur_pca = pca_expansions[fold_idx]\n",
    "    fold_mask = fold_indexes == fold_idx\n",
    "    \n",
    "    lof_transform = cur_pca.transform(faces[fold_mask])\n",
    "    transformed_variances = cur_pca.explained_variance_\n",
    "    \n",
    "    projected_coeffs[fold_mask] = lof_transform\n",
    "    projection_variances[fold_mask] = transformed_variances"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The projected PCA coefficients represent how far from the mean we are along a direction in the high dimensional image space corresponding to each principal vector. Meanwhile the corresponding variances which have been fit by the PCA expansions for each direction indicate what the typical scale of variation is normal. We can transform the PCA coefficients into a $\\chi^2$ term by taking the square of the coefficients (that will be the squared distance from the mean along the direction of the corresponding principal vector) and dividing that by the variance. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "chi2_per_dimension = projected_coeffs**2/projection_variances"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## $\\chi$ distributions for 1 degree of freedom\n",
    "\n",
    "If our data distribution is really distributed like a multi variate normal then we should expect the $\\chi^2$ for each dimension alone to be distributed like a theoretical $\\chi^2$ distribution of one degree of freedom (abbreviated as D.o.F.). We can compare a normalized histogram of the resulting $\\chi^2$ values with what we would expect based on integrating the theoretical $\\chi^2$ distribution over the bins of our data. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "def distribution_comparison_plot(\n",
    "    x,\n",
    "    distribution,\n",
    "    hist_kwargs=None,\n",
    "    ax = None,\n",
    "):\n",
    "    if ax is None:\n",
    "        fig, ax = plt.subplots()\n",
    "    \n",
    "    if hist_kwargs is None:\n",
    "        hist_kwargs = {}\n",
    "    \n",
    "    hvals, hbins, patches = ax.hist(x, normed=True, histtype=\"step\", lw=3, **hist_kwargs)\n",
    "    \n",
    "    #integrate the probability distribution over the histogram bins\n",
    "    bin_integrals = np.diff(distribution.cdf(hbins))\n",
    "    bin_centers = 0.5*(hbins[1:]+hbins[:-1])\n",
    "    bin_dx = np.diff(hbins)\n",
    "    \n",
    "    ax.plot(bin_centers, bin_integrals/bin_dx, lw=3, alpha=0.7)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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YDxARU4GXA8dl5suADwGvqia8Dtc8cXBYMydJklqvbDK3GbC88flpwKasWfXhz8BOLY6rO/Q218yZzEmSpNYrm8zdBuzX+Pxi4MrMvKtxPAN4qOwXRsSOEfHFiLg0Ih6KiIyI2SXv7YmIEyJicUQ8EhF/i4iXlf3utnNJL0mSVLGyydz3gI9FxLnA8cB3ms79A3DdBL5zN+AoYBnwuwncB3AKcBLwJYqk8jLghxFx2ASf0x69LuklSZKqVWo5L4oE6hHgAIrBEJ9pOrcf8MMJfOdvM3NbgIh4M/DCMjdFxDbA+4DTMvNTjeKLImK3Rky/mEAM7WHNnCRJqljZtVn7gY+Ocu6lE/nCzFzXCdcOBTZiaK0gjeNvRMQumbloHZ9djR77zEmSpGp10qTBewMrgeuHlS9o7PdqbzgluJyXJEmqWNlJgzeKiI9ExNWNQQv9w7Z2TKI2E7gvM4evA3tv0/m1RMSxETE/IuYvXbq00gDX0lwz59QkkiSpAmX7zH0SeCfwS+DHFDVk7RbA8ERusHxUmXk6cDrAnDlzRrq/Oq7NKkmSKlY2mXs58JHMHLHfXJvcC8yIiBhWOzej6fzk0tTM6tqskiSpChOZNPjSKgMpYQEwDXj8sPLBvnJXtTecEnqapyaxZk6SJLVe2WTup8BzqgykhAuAR4FXDyt/DcUkxpNrJCu4AoQkSapc2WbWLwLfjogBivnc1mrSzMwby35pRLy88fEpjf2LI2IpsDQz5zWu6QPOzMw3NZ5/V0R8FjghIlZQLCN2NHAIcGTZ724r55mTJEkVK5vMDTaxngR8ZJRreifwvcMnGf5yYz8POKjpecOf+SHgAeC9wHbANcBRmfnTCXx3+5jMSZKkipVN5t7IyCNJ10lmjjkCdbRrGpMXn9rYJr9epyaRJEnVKrsCxLcqjqM7DZmaxGROkiS13oRWgIiInojYJyKeGxGbVhVU13A5L0mSVLHSyVxEvBO4E7gCuBDYo1H+k4h4TzXhdTiX85IkSRUru5zXW4DPAz8BjmLoqgu/A17W+tC6gDVzkiSpYmVr5o4HPp2ZxwL/M+zc1TRq6TSMo1klSVLFyiZzuwC/GuXcg8BWrQmnyzQ1s04NV4CQJEmtVzaZuxuYPcq5PYDbWhJNt2lqZnVtVkmSVIWJLOd1YkTs2lSWEbE1cBxFXzoN59QkkiSpYmWTuQ8DK4ErgbkUEwh/AVgI9AMnVxJdpxuyNqvNrJIkqfVKJXOZeQ8wB/g4MBW4gWLC4S8Bz8jM+yuLsJM5AEKSJFWs7HJeZOYK4JTGpjJ6nZpEkiRVq3QyFxE7AttTNLHekZkOehiPNXOSJKli4zazRsRxEXETcBNwGfBH4OaIWBQR76o6wI7WNJp1apjMSZKk1huzZi4izgReC/wFOAu4mWL1h8cBhwOfj4gnZ+abqg60I7mclyRJqtioyVxEvJAikTsuMz8/wiUfjojjgE9FxPcyc25VQXaspmbWXpM5SZJUgbGaWY8BfjlKIgdAZn4WuAB4fYvj6g7Nzawmc5IkqQJjJXNPBc4t8Yxzgae1Jpwu09u8AkQ/ZNYYjCRJ6kZjJXPbAYtKPONGilGuGi6CfnrXHA84cbAkSWqtsZK5zYCHSjzjEWCT1oTTffqaX7HJnCRJarHx5pnriYjxpi/pHef8Bq2PKUxjVXHQvwqmTq83IEmS1FXGS+YuaUsUXazPZlZJklShsZK5/2hbFF2sL3uLmfmgqJmTJElqoVGTucw0mWuBoTVzJnOSJKm1xl3OS+tnlc2skiSpQiZzFRtSM9dvMidJklrLZK5iNrNKkqQqmcxVbGjNnMmcJElqLZO5ijk1iSRJqlKpZC4itmzVF0bE4yLi3Ii4PyKWR8SPI2KnkvfuFBFnRsTNEfFQRFwbEadGxKatiq/V+tJkTpIkVWe8SYMH3R4R5wD/nZn/t65fFhGbABcCK4FjgAROBS6KiH0z88Ex7t0UmAtMBf4duBl4KsV8eE8Ajl7XuKpkM6skSapS2WTuk8AbgddHxBXAV4DvZuYDE/y+twC7Antk5vUAjeddB7wV+MwY9z6TImk7NDN/3Si7KCJmAu+LiE0ys8xasm21ygEQkiSpQqWaWTPzJGA28E/A7cCXKWrrvhIR+0/g+44ALhtM5BrPXkSxbNiR49y7UWO/fFj5fRQ/RzAJ9dtnTpIkVaj0AIjMHMjM8zPzcODxwOcpkrPLI+KPEfH6iJg2zmP2Bq4coXwBsNc4986lqMH7RETsFRGbRcQhwHspmn9HbaKtk/PMSZKkKq3raNblwL3AAxQ1YlsCXweuj4hnjXHfTGDZCOX3AjPG+sLMfAR4FkXMC4AVwG+AnwHvGu2+iDg2IuZHxPylS5eO9RWVWNXckm0zqyRJarEJJXMR8cyI+DZwG8XAgwuB/TLzicCewI3AV8d5TI706BLfvTHwfWAb4LXAc4H3Uwx8+K9Rvyzz9Myck5lzZs2aNd7XtNyQ0awOgJAkSS1WagBERLybYoDCnsBCiiTq25m5YvCazLw2Ij5CUVs2mmUUtXPDzWDkGrtmbwIOAnbLzBsaZb+NiPuB0yPivzPzb2V+nnbqa86XB/rrC0SSJHWlsjVzn6Jo2jwkM/fJzP9qTuSaXAecPMZzFlD0mxtuL+CqcWJ4ErCsKZEb9KfGfs9x7q9Fn82skiSpQmWTuZ0y8+jMnDfWRZl5W2b+xxiXnA8cEBG7DhZExGyKaUfOHyeGO4EZEbHbsPKnN/a3jXN/LZxnTpIkValsMndpROw30omI2Ccibiz5nDOAxcB5EXFkRBwBnAfcQlNfu4jYOSL6IuLEpnu/RTHo4RcRcUxEHBwR76eoNbycYnqTScd55iRJUpXKJnOzgdGmHdkY2LnMQxrThxwCXAucBZwNLKJovm2egDiA3ub4MnMxcADwV4pVI35BMQnx6cALMnOg5M/SVkPnmbPPnCRJaq2yK0DAyKNQAeZQTNxb7iGZNwMvG+eaxYwwwjUzrwKOKvtdk8Eqm1klSVKFRk3mIuI44LjGYQI/jYhHh102nWJ06jnVhNf5hkxNYjOrJElqsbFq5m5kzTQjxwDzgeGz7q6kGIX6tdaH1h1cAUKSJFVp1GQuM8+jGJxARACc3FhHVRPQ59qskiSpQqX6zGXmG6oOpFv1OZpVkiRVaKw+cycCX8vM24dNETKSzMxTWhtadxiyNqsDICRJUouNVTN3EnABcHvj81gSMJkbQZ9Tk0iSpAqN1WeuZ6TPmpiha7NaMydJklrLJK1ifWkzqyRJqo7JXMUcACFJkqo01gCIAUZf9WG4zMyJrCaxwVhlnzlJklShsRKwkymfzGkU/S7nJUmSKjTWAIiT2hhH11plM6skSaqQfeYq5tQkkiSpSk4aXLG1lvPKhGJ5NEmSpPXmpMGVC/rppZdGrdxAH/ROrTckSZLUNZw0uA366FmTzPWvMpmTJEktY5LWBn3NObODICRJUgtNaG64iDgYeAawA3AbcGlmXlRFYN1kSL+5/r76ApEkSV2nVDIXETOBHwIHUfSPWwbMKE7FxcArMvPeimLseKuyFwbHPAyYzEmSpNYp28z6BeCpwGuB6Zk5C5gOvA6YA3y+mvC6Q79zzUmSpIqUbWb9R+CEzPzuYEFmrgLObtTanVpFcN1ilatASJKkipStmesHrhvl3DWN8xrFWnPNSZIktUjZZO484OhRzr0S+ElrwulOQ0ezmsxJkqTWGWsFiEOaDn8KfC4ifk4xEGIJsC1wFLA38N4qg+x0fc05s82skiSphcbqMzeXYuRqNO13BF48wrU/gua2RDXrcwCEJEmqyFjJ3MFti6LLrcopa6YmcZ45SZLUQmMt5zWvnYF0MwdASJKkqricVxsM6TNnM6skSWqh0st5RcQ+wJuAPYCNh53OzHxeKwPrJkNGs9rMKkmSWqhUzVxEPB2YTzH44VCKpbx2pVjeazfW9Agr86zHRcS5EXF/RCyPiB9HxE4TuH/PiPhhRNwdEQ9HxDURMalH0zoAQpIkVaVsM+vHgB9TTEMSwJsyczbwfIpRrKVWgIiITYALgScCx1AsD/YE4KKI2LTE/XOAPwLTgDcDhwGfZpKPpF1lnzlJklSRss2s+1IkX9k47gXIzAsj4lTg48DTSzznLRQ1entk5vUAEXEFxeoSbwU+M9qNEdEDnAn8JjP/qenURSV/htr0p8t5SZKkapStmZsKPJiZA8C9wPZN564B9in5nCOAywYTOYDMXARcAhw5zr0HAXsxRsI3WVkzJ0mSqlI2mbsB2KHx+QrgjRHR06gtewNwZ8nn7A1cOUL5AopEbSzPauw3jojLImJVRNwVEV+IiOklv78WTk0iSZKqUjaZ+ylFzRgU/edeDCwHlgGvonxt2czGPcPdSzGoYiyPbey/D/waeAHwnxR957472k0RcWxEzI+I+UuXLi0ZZmsNSeZsZpUkSS1Uqs9cZp7U9HluRDwDeBkwHbggM389ge/MEcrKjIYdTDy/k5knNj5fHBG9wGkRsVdmXjVC7KcDpwPMmTNnpO+unKNZJUlSVUrPM9csM/8M/Hkdbl1GUTs33AxGrrFrdk9j/7/Dyn8NnAbsD6yVzE0GQ2vmbGaVJEmtM6FkLiJ2A55G0X/uNuBPzYMZSlhA0W9uuL0YPxFb0NgPr10brNUbmEAcbbWq+TXbZ06SJLVQ2UmDN46IbwALge8An2jsF0bE1yJiWsnvOx84ICJ2bXr2bOCZjXNj+SWwEnjRsPJDG/v5JWNou760mVWSJFWj7ACITwGvBj5CseLD5o39SRQT/36y5HPOABYD50XEkRFxBHAecAvw1cGLImLniOiLiMG+cWTmPRTz2b0tIj4WEc+PiA8AJwJnTrCGsK36m1+zzaySJKmFyjazvhL4j8z8WFPZjcBHIwLgOOA94z0kMx+MiEOAzwJnUTSR/gb4l8x8oOnSoJiYeHiyeTKwAngH8D7gDopE8pSSP0ctbGaVJElVKZvMTQP+NMq5PwIblf3CzLyZYiTsWNcsZoQRrpmZFNOgdNTEwY5mlSRJVSnbzDoXeOEo515Isd6qRrHKeeYkSVJFRq2Zax6kQFETdlZEbAr8EFgCbAscRbHY/WuqDLLT9Q+pmeuvLxBJktR1xmpmvZ6h04AE8HbgbcPKAOZBc8aiZqtsZpUkSRUZK5l7Q9ui6HJDpiaxmVWSJLXQqMlcZp7ZzkC6Wd+Q0awmc5IkqXUmugJEUKzWMJNiea2FjRGmGkNf8zgT+8xJkqQWKjualYh4M8W8blcAFwN/B26PiDdVE1r36HM0qyRJqkipmrmIeDVwOsUEv98B7gS2o1gV4vSIeCgzv1dZlB1ulc2skiSpImWbWf8fcHZmvnZY+ZkRcRbwb4DJ3CiG1sy5AoQkSWqdss2se1DUyI3kO43zGsWQtVmzH+xmKEmSWqRsMrcC2HGUczs2zmtUMXTiYPvNSZKkFimbzP0S+FhEPLu5MCKeAZzaOK8xOHGwJEmqwkT6zB0AXBwRt1GMat2Oolbu+sZ5jaGPXuYuXALA8Sf+nOVsCsDi0w6vMyxJktThStXMZeadwP7Ae4FLgeXAZcC7gSdn5pLKIuwSD+T01Z+3jAdqjESSJHWTcWvmImIqcBhwRWZ+CfhS5VF1obtyBtvFvQBsyzJuYduaI5IkSd1g3GQuM1dFxA+AFwGLqg+pu6xuRr38brimqJH7nyvvAwe0SpKkFig7AOJGYJsqA+l6m2+/+uO2sazGQCRJUjcpm8z9J/ChiJhVZTBdbfPtVn/cxmROkiS1SNnRrIcAM4FFEXEZxWjW5obCzMxjWh1cV7FmTpIkVaBsMvcsYBWwFHh8Y2tmD7DxbLo19EyBgT425yGm8wgPs3HdUUmSpA5XKpnLzF2qDqTrRcBm28Ly24Cidm5xbj/OTZIkSWMr1WcuIraOCKuR1ldTU+s23FdjIJIkqVuMmsxFRG9EnBQR9wFLgOUR8aOI2Kp94XWZpkEQ9puTJEmtMFYz69uAE4GLgf8DdgX+iWL1hzdUHlk3aq6ZM5mTJEktMFYy9xbgjMx862BBRLwV+FJEvDUzH608um4zpGbOZlZJkrT+xuoztyvww2Fl3wd6gZ0ri6ibOT2JJElqsbH7GuM6AAAYuklEQVSSuc0omlSbrWjsN68mnC63yUzonQrApjzMpjxcc0CSJKnTjTc1yQ4RsWvTcW9T+ZB2wsy8saWRdaOIRu3crYC1c5Ikaf2NNzXJucB1TdvVjfKfDCu/ruwXRsTjIuLciLg/IpZHxI8jYqeJBh4RJ0RERsTvJ3pvrRzRKkmSWmismrmWj1iNiE2AC4GVwDEUK0ecClwUEftm5oMln7Mr8CHgrlbHWLkhc82ZzEmSpPUzajKXmWdW8H1voRhYsUdmXg8QEVdQ1Oy9FfhMyed8BTgb2IPyS5JNDtbMSZKkFiq1AkQLHQFcNpjIAWTmIuAS4MgyD4iIVwH/AJxQSYRVGzLXnNOTSJKk9dPuZG5v4MoRyhcAe413c0TMAD4L/L/MvLfFsbXH8Jq5zBqDkSRJna7dydxMGLGj2L3AjBL3fxK4FvhW2S+MiGMjYn5EzF+6dGnZ26qz8VaspJieZDorYeXw2V8kSZLKa3cyB8Wgh+FivJsi4tnA64C3Z5avzsrM0zNzTmbOmTVr1gTCrEgEd2VT3rrizvpikSRJHa/dydwyitq54WYwco1ds68CXwdujYitImIrisEPvY3jaa0NtTpLhiRzd9QXiCRJ6njtHgm6gKLf3HB7AVeNc++eje1tI5xbBhwHfG69omuTJdbMSZKkFml3Mnc+8KmI2HVwxYiImA08E/jAOPcePELZ5yhWpXg3cP0I5yelJVgzJ0mSWqPdydwZwLuA8yLiwxT9504BbqFoRgUgInYGbgBOzsyTATLz4uEPaywpNmWkc5OZNXOSJKlV2tpnrrHCwyEUI1LPopj4dxFwSGY+0HRpUNS41TFAo3J3De8z5/QkkiRpHbV99YTMvBl42TjXLKbECNfMPKg1UbXXCqbzMNOKqUn6VsIj98H0MjOzSJIkDdWVNV+TX9jUKkmSWsJkriZ35VZrDhwEIUmS1pHJXE2smZMkSa1gMleTu5yeRJIktYDJXE2smZMkSa1gMleTtZI5pyeRJEnrwGSuJg8ynQeZXhz0PwoPLq03IEmS1JFM5mq0OLdbc3Dn3+sLRJIkday2TxqsNa4a2Jm5Cy8GYP6CH/Df/Y8AsPi0w2uMSpIkdRJr5mq0IGev/rxnz80EA/UFI0mSOpLJXI1uza25n00B2JSH2TmW1ByRJEnqNDaz1mBIM+ofFsPi3zF34RL2jptYnNvXFpckSeo81szVbft9V3/cq2dxfXFIkqSOZDJXt233Wf1xt7idaTxaYzCSJKnTmMzVbZOZsNVOAPTSz+5xa80BSZKkTmIyNxls96TVH/fquanGQCRJUqcxmZsMtlvTb26fWFRjIJIkqdOYzE0G2+xJP70AbB/3wEP31hyQJEnqFCZzk8GUaVybO645vvOK+mKRJEkdxWRukrhqYOc1B3eYzEmSpHJM5iaJK5uW9uLOv0NmbbFIkqTOYTI3SdyS27CCTYqDlcth2eJa45EkSZ3BZG7SCBYO7LTm0H5zkiSpBJO5SWTB8KZWSZKkcZjMTSJDBkHctRBWPVJfMJIkqSOYzE0iy9iC23Pr4mCgD276fb0BSZKkSc9kbpL53cCapb249leOapUkSWOaUncAGur3A/vwi4W/ZyNWAUv4xO9O57rckcWnHV53aJIkaRKyZm6SeZiNuXRgr9XHz+v5c43RSJKkya7tyVxEPC4izo2I+yNieUT8OCJ2KnHfnIg4PSKujoiHIuLmiDg7InZpR9ztdNHAk1d/fkrPdWzFihqjkSRJk1lbm1kjYhPgQmAlcAyQwKnARRGxb2Y+OMbtrwT2Br4ALAB2AP4dmB8R+2fmLZUGX7G1mlHn3sTceRcRDHBQz98ofnxJkqSh2t1n7i3ArsAemXk9QERcAVwHvBX4zBj3fiIzlzYXRMQlwKLGc0+sJOK67P4imHcRAM/t/Rv0r4LeqTUHJUmSJpt2N7MeAVw2mMgBZOYi4BLgyLFuHJ7INcpuApZS1NJ1lx3nsCw3B2BzHoKbL605IEmSNBm1O5nbG7hyhPIFwF4jlI8pIvYEtgEWrmdck09PLxcP7L/m+Npf1ReLJEmatNqdzM0Elo1Qfi8wYyIPiogpwH9T1Mx9fYzrjo2I+RExf+nStSr3JrXfDuxLP73FwT3Xwz031BuQJEmadOqYmmSkWXBjHZ7zJeBA4DWZOVKCWHxZ5umZOScz58yaNWsdvqY+K9iEPw08cU3BtRfUF4wkSZqU2p3MLaOonRtuBiPX2I0oIj4OHAu8MTN/3aLYJqXfNE1Twk1/gAc6q3ZRkiRVq93J3AKKfnPD7QVcVeYBEfEh4APAezPzrBbGNiktzu25IR9bHAz0wZ+/VWs8kiRpcml3Mnc+cEBE7DpYEBGzgWc2zo0pIt5DMS/dhzLzixXFOOn8oP+gNQe3zofbLq8tFkmSNLm0O5k7A1gMnBcRR0bEEcB5wC3AVwcvioidI6IvIk5sKnsl8DngAuDCiDigaZvwSNhOckPuwEkLtmHuwiXMXbiEc75yMk/4wHl1hyVJkiaBtiZzjRUeDgGuBc4CzqaY9PeQzHyg6dIAeofF96JG+YuAS4dtX648+Jqd2/8cHmQ6AFvH/RzWc1nNEUmSpMmg3StAkJk3Ay8b55rFDBvhmpmvB15fVVyT3QNswo/7n81re4vxHof1/gmW3wFbbF9zZJIkqU5tT+ZU3lrrteZhnPHvf2eXuINe+uHyb8JBJ0Csy8wukiSpG9Qxz5zWVQRn9b+AHKy0vONvcMsf641JkiTVymSuw9yc2w5d5uvyM+GR5fUFJEmSamUy14F+3P8sVrBJcfDwvfD7z0B/X71BSZKkWpjMdaCH2Zhv9R3K6jEidy0s+s/lSCulSZKkbmYy16H+lrvBfkevKbh+Llz7q/oCkiRJtXA0awebfdZU3tI7k6f3LAQgF/4nL3jHY2H7fWuOTJIktYs1cx0t+Fb/i1iU2zeOBuD3n4Xlt9cclyRJaheTuQ63iil8qe+l3MfmjYKHYN4n4MF76g1MkiS1hc2sHWatiYSB2R/4OV/seykfmPK9omDFnfC/J8IhH4ItHtvmCCVJUjtZM9clbsrtOKPvcIjeouChu4uE7p4b6g1MkiRVypq5LvLn3J3Dr5jKO6ecx0asApaw8q9v4/B3fNpBEZIkdSlr5rrMgtyFT/UdxYNMB2Aaq4o+dDddWnNkkiSpCiZzXejGfCynrfpnlmVjUMRAH1zyOZj/Teh7tN7gJElSS9nM2gVGGxTx8b5X8a9Tfrim8NoLYMmVcOC7Ycbs9gUoSZIqYzLXxe5lCz7W9yruWHAB+/dc3yhdQv9lb+LQVx8PexwGEbXGKEmS1o/NrF3uQabzpf6Xclb/C1nVyN176Yc/fxsuPAWW3VRzhJIkaX2YzG0QgnkD+/Efq17HzbntmuIlC+CX/wZ//Co8vKy+8CRJ0jqzmbVLjdaP7qN9r+alPZeQC/9EkMWJhd9j5c/O5fCj3wZPfAlMmdbmaCVJ0rqyZm4D008vPxp4DietOoYFucvq8mmsgit+AOe/G678EaxcUWOUkiSpLJO5DdRtzOKzfS/nc30v4/bces2JR+4vkrqfvB3+dAYsv72+ICVJ0rhsZt2AjNb0elXfbJ7d83fuX/gHtuSBNSevPJvnX/8b2H4/2OU5sOMcm2AlSZpkTObEAD3MG9iP3w/sw9N6ruaFPfN5XNwFwNyFd8LCO4FfsZKpXD6wBye+61jYdh/osWJXkqS6mcxptX56uXRgby4d2Isnxi28sGc++/bcsPr8NFZxYM+VcNFHYdoW8Nj94bH/UKz7utGmNUYuSdKGy2RuAzda0+vVuRNX9+/ErP77eHrPQp7RcxXbxr0AzF24BFgCf70O+CFJDy947nOK5thZe8JjHg+9U9v7g0iStIEymdNaRk7wfsbsuJMDehby1J6r2ZIHV58LBpg772LgYgD6mMKi3I63v+IlsPUTYMYusMnM9gQvSdIGxmROJQWLc3sW92/POf0HMzvuZN9YxL49NzA77hxy5RT6eELcCgv+Z03h9BlFUjdzF9hqZ9hyB9hsO+j1V1CSpPXhf0lVymjNsecPHMgWPMjePYvZI25h97iVbaJYTaJojh20BLia5+/ZtAJF9MLm2xWJ3eaPhc22gc22LbZNHuMAC0mSSmh7MhcRjwM+C7wACGAu8C+ZeXOJezcGTgFeA2wF/BX4t8z8bXURazSjJXhb8AC7x608oec2do4l7BR3sRGrgOEJHsDtwJ/Xes7z996haJrd5DFN29ZF2cZbwsZbFfspG1Xwk0mS1DnamsxFxCbAhcBK4BgggVOBiyJi38x8cKz7ga8DhwPvB24E3gn8KiKekZl/rS5yTcRyNmN+PpH5/U8Eij5127GMnXuWsFMsYYe4h+25h5mxfNRnzF1wG3DbuN/1/H13gY23gGmbFyNsp20OG23W2G9abFM3Kco22gSmTi+OezeCiFb9yJIk1abdNXNvAXYF9sjM6wEi4grgOuCtwGdGuzEi9gNeBbwxM7/ZKJsHLABOBo6oNnSVMVpt3R08hjsGHsNl7LW6fBqPsn3cw/ZxL9uwjFlxP7PiPraJ+9ich0p939wrFq1TnEkPD7MRj+RGrGQqK5nKI2zEypzKvx62L/ROK2r9ejcqPvdOLSZM7plafO7dqNj3TGnspxb9/3oaZT1ToKd3zTXR2yiz6ViS1FrtTuaOAC4bTOQAMnNRRFwCHMkYyVzj3lXA95vu7YuIc4APRMS0zFxZUdxaDyMleCOZ/YGfr/48jUeZyQpmxgpmxIrG5+VswUNsGQ+yZTzIFjxIDwPrFFMwwCY8wibxyPATzL3ghpFvaoEkGKCH/sY20LzPHvoJkh4GCPrp4fXP3LVIBCMgeooEMXqKQKNn2Mawc9F0HGvKYc15aDo3bD943VrXMMbnkY4Z+szVxwwtW+tc0/kRa1FHet5I1uG6sYwXSyu0pdbYmmlpnWz3JNh82/Gva6N2J3N7A+eNUL4AeEWJexdl5vAqmwXARsBujc/qUBNP+pLNeLjY4mE2X71/iE3jETZhZbHFI2zKI2zMSqbHo2zMo0ylr7ofZAxB0ks/vfSPdHItc/+wtPqgJEmlfbnvSJ59yOEc94Ld6w5ltXYnczOBZSOU3wvMWI97B8+vJSKOBY5tHD4QEdeUiHN9bA3cHZ+o+Fs2TFsDd9cdRJfy3VbHd1sd3221fL8jmsf/nHY8x6/fQ8q+253LPKyOqUlyhLIy9f2xLvdm5unA6SWe3xIRMT8z57Tr+zYkvtvq+G6r47utju+2Wr7f6rT63ba7N/YyRq5Bm8HItW7N7h3j3sHzkiRJG5R2J3MLKPq+DbcXcFWJe3dpTG8y/N5HgevXvkWSJKm7tTuZOx84ICJ2HSyIiNnAMxvnxrt3Kk0DJSJiCnA08OtJNJK1bU26GyDfbXV8t9Xx3VbHd1st3291WvpuI3OkbmjViIhNgb8BDwMfpugDdwqwObBvZj7QuG5n4Abg5Mw8uen+c4BDKSYNXgS8HXgJcGBmrr2MgCRJUpdra81cY4WHQ4BrgbOAsymSskMGE7mGAHpHiO8NwDcpVo34OfA44EUmcpIkaUPV1po5SZIktZZrC7VARDwuIs6NiPsjYnlE/Dgidqo7rk4XEQdFRI6w3Vd3bJ0mInaMiC9GxKUR8VDjPc4e4bqNI+KTEXFHRDzcuP457Y+4c0zg3Y70u5wRsX/7o578IuLlEfGjiLip8bt4TUR8PCI2H3bdjIj4WkTcHREPRsTciHhSXXF3ijLvNyJmj/F7u1Wd8U9mEXFoRFwYEXdGxMqIuDUifhARew27rmW5Qx3zzHWVxujaC4GVwDEU/QBPBS6KiH0bTctaP+8B/q/puJ7lGzrbbsBRwOXA74AXjnLd14HDKfql3gi8E/hVRDwjM//ajkA7UNl3C/At4KvDyq6tJqyO9z7gZuCDwK3Ak4GTgIMj4sDMHIiIoBgctwvwbooprk6g+Pu7f2beWkvknWHc99t07cdZe5DiinYE2aFmUvw9+DKwFNgJ+ABwWUQ8KTNvannukJlu67EB7wX6gd2aynahSDiOrzu+Tt6Agxq/4M+vO5ZO34Ceps9vbrzX2cOu2a9R/oamsinANcD5df8Mk3Ur824b5xI4te54O2UDZo1Q9rrGezykcXxk4/jgpmu2pJh39At1/wyTeSv5fmc3jt9cd7ydvgF7NN7lvzaOW5o72My6/o4ALsvM1fPcZeYi4BKKPzRS7XLov7JHcwSwCvh+0319wDnAoRExraLwOlrJd6sJysyRFiYerKHfobE/Arg9My9quu9+4Kf493dMJd+vWueexn5VY9/S3MFkbv3tDVw5QvkCigmNtf7Ojoj+iLgnIr5rf8TK7A0sysyHhpUvADaiaE7U+nl7ow/NQ40+Nc+uO6AO89zGfmFjP9bf350iYrO2RNU9hr/fQR+PiL5G367z7ZNYTkT0RsRGEfEEiu4Vd1L84xhanDvYZ279zWTkpcjuZc1SY1o39wOfBuYByyn6dHwQuDQinpyZd9UZXBca63d58LzW3XeAnwG3Uyye/X7gwoh4QWZeXGdgnSAidgBOBuZm5vxG8Uxg8QiXD/7OzgAeGOG8hhnl/a6kSEJ+TdH364kUf4P/EBFPy8zhSZ+G+iPwlMbn6ymarwf/u9XS3MFkrjVGmt8l2h5Fl8nMvwB/aSqaFxG/Bf5EMSjiw7UE1r0Cf5crk5mvbTr8XUScR/Ev81OBZ9UTVWdo1LCdR9Gf6A3Np/B3dr2N9n4z8w7gbU2X/i4iLqCoPfoQ8Jp2xtmBXgtsAexKMeDkfyPiWZm5uHG+Zb+7NrOuv2WMXGMxg5Gzbq2HLCaIvhZ4at2xdKF7Gf13efC8WiQzV1BMfu7v8hgiYmOKkZS7Aofm0BGq4/3O+jd4HOO837Vk5i3A7/H3dlyZuTAz/5iZ3wOeB2xGMaoVWpw7mMytvwUUbd/D7QVc1eZYNhSj/Wtc62cBsEtjyHyzvYBHKZoJ1Fr+Lo8hIqYCPwKeBhyWmX8fdslYf39vzqErC2mYEu931Fvx93ZCMvM+ir+hg32PW5o7mMytv/OBAyJi18GCxoShz2TteXm0niJiDrA7RV8Etdb5wFTgFYMFETEFOBr4dWaurCuwbhQRW1DM6efv8ggioodiycfnAUdm5mUjXHY+sENEPLfpvi2Af8S/v2Mq+X5Hum8niv+++Xs7ARGxLUWfwxsaRS3NHVzOaz1FxKbA34CHKfpwJXAKsDmwr/8yXHcRMbh275+B+ygGQJwAPAT8Q2beXWN4HSciXt74+DyKfjDvoOjUvDQz5zWuOQc4lKJz/iLg7cBLgAPTNZBHNd67jYj3UcwzdRFrBkAMlj0vM3/X/qgnt4j4CsW7/CjFwJFmt2bmrY2E5PcU63S/nzWTBu8L7NdoEtQISr7fT1NU+lxK8fu8B8X73RJ4emZe08aQO0ZE/A/Ff7euoBi8tztwHLAd8LTMvLbluUPdE+l1w0Yxu/OPGv+jrQB+wgiThrpN+L2e0Pg/w/0Uc/PcApwObF93bJ24Nf5YjLRd3HTNdOAzFEPoH6H41/dBdcc+2bfx3i1FTdElwN2N3+V7KP71/bS6Y5+sG8Uo1dHe60lN180EvkHRf+4h4DcUiVztP8Nk3sq8X+CNFHPPLaMYHHEn8F1gj7rjn8wb8G8UK0Dc1/idvIZiVPDsYde1LHewZk6SJKmD2WdOkiSpg5nMSZIkdTCTOUmSpA5mMidJktTBTOYkSZI6mMmcJElSBzOZkyRJ6mAmc5IkSR3MZE6SWiAiNo6In0TEwoj4a0T8qnndRUmqismcJLXOVzJzz8zcH/gp8LW6A5LU/UzmJKkFMvORzPxVU9FlgDVzkipnMidJ1Xg3cF7dQUjqflPqDkCSuk1EnADsDjyv7lgkdT9r5iRpHBHx/oh4OCIujIhZTeV7RMQDEfHFprL3AS8DXpyZD9URr6QNS2Rm3TFI0qQWEbOBQ4H/Aj6Ymf8ZEdOBPwKrgAMzc2VEHA+8Gnh+Zi6rK15JGxaTOUkqKSL+ANySmUdHxBnAUcBTMvP6iNgRuAW4EVjRuKUvM+fUFK6kDYR95iSpvMuBQyPiVcCbgVdm5vUAmXkrEHUGJ2nDZJ85SSrvz8BuwFeB/87M79ccjySZzEnSBPyFovbtBuC4mmORJMBkTpIm4m2N/Tcz85FaI5GkBpM5SSohIo4G3koxuGH/msORpNUczSpJ44iIJ1AMfjiHopn1aZm5X71RSVLBmjlJGkNEbAz8AFgMvIei39xejXnmJKl2JnOSNLbPUYxgfUWjn9z/UUzrdFpEPLnWyCQJ55mTpFFFxCsp+sm9JjOvaRTPB04HXg88HnhJPdFJUsE+c5IkSR3MZlZJkqQOZjInSZLUwUzmJEmSOpjJnCRJUgczmZMkSepgJnOSJEkdzGROkiSpg5nMSZIkdbD/H6q5DpJqxf24AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fbb2d1b4ba8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "distribution_comparison_plot(\n",
    "    chi2_per_dimension.ravel(), \n",
    "    distribution=scipy.stats.chi2(df=1), \n",
    "    hist_kwargs={\"bins\":101,} \n",
    ")\n",
    "plt.title(\"$\\chi^2$ D.o.F = 1\")\n",
    "plt.ylabel(\"Probability Density\")\n",
    "plt.xlabel(\"$\\chi^2$\");\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Although it is clear that the theoretical $\\chi^2$ and the observed distributions are very close the long tail of the distribution makes it difficult to compare the data over the full range of values. To squeeze the x axis down a little bit and make the plot easier to read we instead will compare the square root of the $\\chi^2$ value to the theoretical $\\chi$ distribution. This quantity is sometimes a little more intuitive since it corresponds to the absolute value of distance from the distribution mean divided by the standard deviation along that dimension wich can sometimes be easier to think about than squared distance divided by variance."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5,0,'$\\\\chi$')"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fbb2d1b4400>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "distribution_comparison_plot(\n",
    "    np.sqrt(chi2_per_dimension).ravel(), \n",
    "    distribution=scipy.stats.chi(df=1), \n",
    "    hist_kwargs={\"bins\":101} \n",
    ")\n",
    "plt.title(\"$\\chi$ D.o.F = 1\")\n",
    "plt.ylabel(\"Probability Density\")\n",
    "plt.xlabel(\"$\\chi$\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can see that the distribution of PCA coefficients for this data set really is fairly well normally distributed. However the observed distribution of residuals tends to be a little bit closer to 0 than we might naively expected. \n",
    "\n",
    "Unfortunately even after converting from $\\chi^2$ to $\\chi$ it is still not clear from this plot how well the behavior in the high $\\chi$ tails matches to the expected theoretical behavior. We can get a much better view of the low probability tails by moving from probability density to log probability density. This will greatly expand the scale of the plot as we move close to 0 emphasizing relative changes at the expense of making absolute changes in probability difficult to gauge.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.0001, 1.0)"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fbb2d039b38>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "distribution_comparison_plot(\n",
    "    np.sqrt(chi2_per_dimension).ravel(), \n",
    "    distribution=scipy.stats.chi(df=1), \n",
    "    hist_kwargs={\"bins\":101, \"log\":True} \n",
    ")\n",
    "plt.title(\"$\\chi$ D.o.F = 1\")\n",
    "plt.ylabel(\"Probability Density\")\n",
    "plt.xlabel(\"$\\chi$\")\n",
    "\n",
    "plt.ylim(1e-4, 1.0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In the log scale the density variations close to the core of the distribution are squeezed to insignificance (since although they are significant in terms of counts they represent a fairly small fractional difference). At the same time it is clear that the tails of the observed PCA coefficients are heavier than one would expect for truly normally distributed variables. Do those heavy tails represent the presence of outlier images?\n",
    "\n",
    "How unlikely exactly is a $\\chi$ value of above 5? Supposing that the fitted probability distributions are exact a naive calculation gives a lottery winning level of rarity."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5.7330314373604807e-07"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "1-scipy.stats.chi(df=1).cdf(5.0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Which might be enough to merit a look at the images showing these high $\\chi$ coefficients. Individually rare events still happen in large volumes of data. How many such 5+ events should we expect given that we are looking at such a large number of coefficients?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.08026244012304673"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(1-scipy.stats.chi(df=1).cdf(5.0))*max_components*len(faces)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The fact that we expect on average much less than one such coefficient over the whole data set and that we get several is enough to make a strong claim that the images aren't drawn from exactly the normal distribution that we are using to analyze them but it isn't really cause to think that we have found any anomalies.\n",
    "\n",
    "Intuitively we know that images of faces aren't really perfectly normally distrirubed and we shouldn't forget that our estimates of the amount of variance in each dimension is based on just 400 observed images and is itself quite uncertain. \n",
    "Unless we have reason to think that the form of our probability distribution is exact and its parameters well estimated we ought not take our distribution too seriously. However that is not to say that we can't still use an approximately correct distributional form to detect outliers. After all if one of the $\\chi$ coefficients was 50 instead of just 5 that point would be an outlier. \n",
    "\n",
    "If all of the coefficients corresponding to $\\chi$ values above 4 or 5 come from the same few images we certainly should take notice. Lets find the image with the most anomalous coefficient and take a look at it. We can compare the full distribution of all the coefficients for that image and investigate what the image would look like if we decreased the magnitudes of the outlying coefficient(s) into the more normal range of 2 or 3 sigma."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(264, 118)"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "anom_tup = np.unravel_index(np.argmax(chi2_per_dimension), dims=chi2_per_dimension.shape)\n",
    "anomalous_image_i, anomalous_coeff_j = anom_tup\n",
    "anom_tup"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5,0,'$\\\\chi$')"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fbb2d09cbe0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots()\n",
    "distribution_comparison_plot(\n",
    "    np.sqrt(chi2_per_dimension).ravel(), \n",
    "    distribution=scipy.stats.chi(df=1), \n",
    "    hist_kwargs={\"bins\":101, \"label\":\"All Images\"},\n",
    "    ax=ax\n",
    ")\n",
    "hres = ax.hist(\n",
    "    np.sqrt(chi2_per_dimension[anomalous_image_i]), \n",
    "    bins=51, \n",
    "    normed=True, \n",
    "    histtype=\"step\", \n",
    "    lw=3,\n",
    "    label=\"'anomalous' image\"\n",
    ")\n",
    "plt.legend()\n",
    "plt.title(\"$\\chi$ D.o.F = 1\")\n",
    "plt.ylabel(\"Probability Density\")\n",
    "plt.xlabel(\"$\\chi$\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Comparing the distribution of other coefficients for the same image to the typical distribution of coefficients we can already see that there is probably nothing remarkable about this image since the distribution of other coefficients is quite typical. \n",
    "\n",
    "What does this most anomalous image look like and how different does the reconstructed image look if we set the offending coefficient to zero?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fbb2e831dd8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axes = plt.subplots(2, 2)\n",
    "axes = axes.ravel()\n",
    "\n",
    "anom_im = faces[anomalous_image_i]\n",
    "vmin, vmax = np.min(anom_im), np.max(anom_im)\n",
    "\n",
    "ax = axes[0]\n",
    "view_as_image(anom_im, ax=ax, vmin=vmin, vmax=vmax)\n",
    "ax.set_title(\"Original Image\")\n",
    "\n",
    "ax = axes[1]\n",
    "#use the corresponding PCA expansion to reconstruct the face image\n",
    "cur_coeffs = projected_coeffs[[anomalous_image_i]].copy()\n",
    "cpca = pca_expansions[fold_indexes[anomalous_image_i]]\n",
    "full_reconstruction = cpca.inverse_transform(cur_coeffs).squeeze()\n",
    "view_as_image(full_reconstruction, ax=ax, vmin=vmin, vmax=vmax)\n",
    "ax.set_title(\"PCA reconstruction\")\n",
    "\n",
    "ax = axes[2]\n",
    "\n",
    "#zero out the offending coefficient\n",
    "cur_coeffs[0, anomalous_coeff_j] = 0.0\n",
    "zeroed_reconstruction = cpca.inverse_transform(cur_coeffs).squeeze()\n",
    "view_as_image(zeroed_reconstruction, ax=ax, vmin=vmin, vmax=vmax)\n",
    "ax.set_title(\"Zeroed Anomaly\")\n",
    "\n",
    "ax = axes[3]\n",
    "enhanced_chi = 30\n",
    "cur_coeffs[0, anomalous_coeff_j] = enhanced_chi*np.sqrt(cpca.explained_variance_[anomalous_coeff_j])\n",
    "enhanced_anomaly_reconstruction = cpca.inverse_transform(cur_coeffs).squeeze()\n",
    "view_as_image(enhanced_anomaly_reconstruction, ax=ax, vmin=vmin, vmax=vmax)\n",
    "ax.set_title(\"Enhanced Anomaly $\\chi$={}\".format(enhanced_chi));"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The image its reconstruction, and its reconstruction after zeroing out the potentially anomalous coefficient all look more or less the same. If instead we enhance the anomalous coefficient so that the corresponding $\\chi$ score is much larger say $\\chi=30$ then the picture looks clearly anomalous.\n",
    "\n",
    "In this case leaning on our understanding of faces and images we can fairly confidently say that there is nothing really particularly unusual about this image. The type of variation is of a typical sort in the sense that the variation looks one of our principal components it is slightly a-typical in magnitude but probably not enough that we need be concerned. On the other hand if the signal were stronger (say $\\sqrt{\\chi^2} = \\sqrt{400} = \\chi = 30$) then even though the character of the variation is of a typical sort the sheer magnitude of that variation would be enough to arouse suspicion."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# $\\chi$ distribution for multiple degrees of freedom.\n",
    "\n",
    "Analyzing the variation in the images one PCA coefficient at a time is a perfectly legitimate strategy to pursue for anomaly detection but it suffers on several accounts. Because we have a potentially large number of coefficients which we are monitoring for anomalies we increase the chances that we will detect an \"anomaly\" which is really just normal random fluctuation. In addition each coefficient by itself is less strong of a signal than we can get by combining the variations in coefficients together.\n",
    "\n",
    "Lets take only the first k PCA components and analyze the $\\chi^2$ distribution arising from analyzing all those dimensions together. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fbb2d442b00>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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Y4fqOKyLpUWEyZ2a3AgWEdeQcmBgrl35tBG4Bnk95pCKSPdxh3pvwxk2wfumu6k+KD4BT/wz79IowuCSq3xgG/hgG/iTsAwth8eEP/x+8/SfYviHa+ESkTqism3VC7N0ICdtjwJdlztkBzAFeTXpkIpKdtm+AKQ+HrbhiCsjjuaIhTCjuzc9r424K+x8ddqGYeD+s/TzULf8IRv8qJHrtekYbn4jUahUmc+7+NvA2gJk58Ki7V7y3jojI2oUw4U+wfX28rnlHfl9wKstpXfF1tUHTdjDsd/DJszA39v122zoYdwf0OAsOPSdMpBARSbJKx8yVcPfblciJSKVWzoWxv9s9ket2Kpz4h9qfyJXIzQtjAYfcCA2axSo97CAx5lbYvCrS8ESkdqqwZc7MHgd+7+6LYp8r4+5+SXJDE5Gs8dUn8M7d8UWA6zeGQddA+8OjjSsq7Q+HU/4Ekx8MW4MBrJ4Pr98Ix/1as11FJKkqGzN3HHBf7PNQKl9+RNO2ROqqL6aGddaKC0O54V5htmqLTtHGFbX8luG/w5yRMOM58OKwjMnY2+HoX9SeSSAiErnKxsztX+pz57REIyLZZdE7MPmhkKgA5LeGob+FZvtEG1emMAvj5fY+BN7+c0jmCneEma4DfwKdBkYdoYjUAgmNmRMR+YZ5b8KkB+KJXNN9wgQAJXLf1KYbDLsd8luFcnFhaM2c/1a0cYlIrZBQMmdmg8zs9FLlVmb2rJnNNLN7Si0sLCJ1weyXYNpj8XLzTnDCbdC4VVQRZb699oNhv4dm7WMVDh88CjNf0ALDIrJHEm2ZuwvoW6p8N3AqMA+4Cvh1kuMSkUzkDh8/G5bfKNGqKxx/CzRqHl1c2aJxKzjhdmhZagLEzOdh+hNK6ESkxhJN5g4BpgGYWT3gu8D17n428BvggtSEJyIZwx2mPQ5zXorXte0BQ2+GBk2iiyvbNGwGx98M7Q6N1817Hd7/OxQVRheXiGStRJO5JoStuwCOABoT3/XhQ6BjkuMSkUxSXByW2Zj/Zrxu375w7I1Qr2F0cWWreo3g2F9BxwHxuiUTw/IuBduji0tEslJlS5OUtgw4DHgXOAWY5e4rY8daAFtTEJuIZAJ3mP6vMHO1RKdBMODqsEhuxDrfOCqh8xbfdVqKI6mm3How6Fqo3wQWjAl1X30M4+8IiV6DptHGJyJZI9GWuWeBO83sBeBnwL9LHesDzE/0gWbWwcxeMLMNZrbRzF40s4Ra9szMK3j1TvT5IlJNc1/dvUXugONh4DUZkchlvZwc6H8p9Dw7Xrd6fthJY8em6OISkayS6E/j24DtwADCZIi/ljp2GPB8Ijcxs3xgHLADGE5YbPgOYLyZ9XL3LQnc5gng4TJ18xJ5vohUT1/7DD6aEq/oNAiOuCysnybJYQa9zg0tcdOfCHXrl8KEu8J4RHVji0gVEkrm3L0I+EMFx86qxvMuA7oA3dx9AYCZzSC07F3B7kliRZa5++RqPFNEauAAW8alea8BseVG2nSDI6/KiEQu0S7TRLtgM0K3U6BefhibCLBmAbx7T+hyza0XbWwiktHSvWjwGcDkkkQOwN0XAROBM9Mci4hUoA3ruCbvf9QjNruy6T5wzA2QVz/awGq7LsdCv4vj5a9nwvv3hwkoIiIVSHTR4PpmdquZzTWzrWZWVOaV6Hz6HsCscupnA90TvMdVZrYjFsc4Mzs6wetEJBHbN3J93gs0YVsoN2gGQ27UgPx0Oeik0O1a4oupMHWE1qETkQolOmbubuBqYDTwImHMW020BNaVU7+WMCu2Kv8mLImyHOgE3ACMM7Nh7j6hvAvM7HLgcoCOHbWCikilCnfCO3ezt60HoIA8OPaX0LRdxIHVMT2+Azs2w2evhfLC8VC/MRz+g4zo5haRzJJoMvdd4FZ3L3fcXDWV9/UyoZ9O7n5hqeK7ZjaS0NJ3B3BUBdeMAEYA9OvXT19tRSriDpMfgNVhPpFjPFJ4Gqe0PjDiwOogM+hzEezcAoveDnVzXw2toz2qM0xZROqC6iwaPCkJz1tHaJ0rqwXlt9hVyt03AaOA/nsYl4h8/DQsjc8t+k/RED70gyIMqI4zgyOvgP36xes+eRbmj4kuJhHJSIkmc68AxyThebMJ4+bK6g7MqeE9jfJb+0QkUfPehE9f2VUcW9yHt4r7VnKBpEVOblhYuG2pH5sfPApL3o8uJhHJOIkmc38HzjezW8ysn5l1KftK8D4vAwNKn29mnYHBsWPVYmbNgNOAKVWdKyIVWDY97LlaYt9+/F/RcSQ4+kFSLa9+mEncqmuswuH9f8DyjyINS0QyR6LJ3CTgQMLiwVMI68KVfSXiEWAxMNLMzjSzM4CRwBeUWgjYzDqZWaGZ3VKq7hdm9oiZXWBmQ8xsOGFJk3bAbxN8voiUtm4JTLyPXY3bLQ+AQdfgaV+1SCpVr1GYUdxs31D2Inj3L7BybrRxiUhGSHQCxMUkoSvT3beY2VDgXuApwlf/scB17r651KkG5LJ7svkZ8O3Yay9gIyGZu8Tdp+5pbCJ1TsE2eO9eKIxNTm/cOsxc1Y4DmalBUxj6W3jrZtiyGooK4O0/wUl3QrN9oo5ORCKU6A4QTyTrge6+FDi7inMWU6aPx91fIYzdE5E95Q5TH4FNX4Vybn049kZo1DzauKRy+S3DFl9v3QLbN0DB1lhC94ewdImI1EnV2inbzHIIkxVaAdMS3EtVRDLNgrGwZGK8fMRl0LxDdPFELKu2/WraLmzxNebW0Dq36avQwjrkpqQ+pib/TSrbZi3Z9xORuIQHxpjZ1cDXwAxgHNAtVv+Smf00NeGJSNKtXQTT/xUvHzAU9k/GZHVJm1YHwICr4+WvZ8KHT0YXj4hEKtHtvC4D7gNeAs5l9y7Qd6mi21REMsTOLaEVpzi2A1/zjtD3R9HGJDXTaSAcek68PO8NhuR8HF08IhKZRLtZfwb8xd1/ZWa5ZY7NJWyrJSKZzB2mPAybV4RyXgM46vqw9IXsklVdez3Phg1f7Frs+fu5Y/naWzLXk7t1YTq7T7Oqy1skQyTazbo/8EYFx7YAGjUtkunmvQFflFqS8cgroVn76OKRPWcGA34clpQBjGJ+nDeSvau/oY6IZLFEk7nVQOcKjnUDliUlGhFJjTWfw0dPxcsHDoNOg6KLR5InrwEc8wto1AKAfLZzbd6LoUtdROqE6mzndUuZnR7czFoD1xPG0olIJtqxGd77a3ycXIv9oc/waGOS5MpvCcfcQEFs5ExbWxsbG1kUcWAikg6JJnO/BXYAs4AxhAWE7wc+BYqA36UkOhHZM+4w+aGwyCyEnQSOug5y60UblyRfqwN4rPCUeFkzXEXqjISSOXdfA/QD/gjUAz4nTJ74BzDQ3TekLEIRqbm5o2DZtHj5yKvCOmVSK03zg3m5qFT3+bw3YP5b0QUkImmR8KLB7r4J+H3sJSKZbtU8+PiZeLnbKdDxyOjikbR4uXgQ7W0NJ7A+VEx7HJruA+16RhuYiKRMdRYN3s/M+ptZPzPbN5VBicge2rEJJv4tbMgO0Kor9P5BtDFJmhiPF50CLWNDnL04jJ/bvCrasEQkZapM5szsejNbAiwBJgNTgKVmtsjMfpLqAEWkBqY9DlvXhM/1G8Pg6yC3Wrv3SRbbST045oZdM1zZuTkkdEUF0QYmIilRaTJnZk8CfyEsTfJH4Crgx7HP64H7zOyxVAcpItWwZBIseT9ePvIqaNImungkGvktw6LQJeu8r/1cEyJEaqkKv6qb2YnAhcD17n5fOaf81syuB+4xs2fdfUyqghSRBG1dCx88Gi/vfyx06B9dPBKtNt3g8B/Ek7j5b0Hrg7QXr0gtU1nL3HBgdAWJHADufi/wOvDDJMclItXlDlMfCV1qAPmtoa/Wk6vzup0CHQfEy1NHwLol0cUjIklXWTLXH3ghgXu8AByRnHBEpMYWjoflH8bLA64K4+WkbjPbfeu2ooKwiLR2iBCpNSpL5toBixK4x0Jgn+SEIyI1snkVTH8iXj7oZC1FIXH1GsHRPw9bfwFs+josJu0ebVwikhSVJXNNgK0J3GM7kJ+ccESk2txh8gNQuCOUm+4DvS+INibJPHvtB0dcES9/+QHMfTW6eEQkaapamiTHzCp9AbnpCFREKvDZa7Dy01jBYODV8RYYkdI6Dw6ttiU+fgZWzIkuHhFJiqqSuYlAQRWvd1MZoIhUYsOXu+/y0OMsaH1gdPFI5jv8wvjfES+GifeFWdAikrUqW0X09rRFISLVV1QIkx6E4sJQbtEZen430pAkC+TmweDr4fVfhZ1Ctq8PCd3Qm7WwtEiWqvBfrrsrmRPJZHNeCgvBAuTkwYAf65exJKZxKxh8LYz7A+Cwai588iz0uTDqyESkBhLem1VEMsiaz2HWi/Fyr3OhRafo4pHs0+7Q8PemxNxXYemU6OIRkRpTMieSbQp3wqQHwItCufVBcPC3oo1JslOPb0P7PvHylIdg04ro4hGRGlEyJ5JtZjwHG5eFz7n1w+zVHP1Tlhqw2OznxrG9ewu2hfFzRYXRxiUi1aLfACLZZNVnMHdUvHz4hdC0XXTxSPZr0AQGXwcWW2Vq7edh/JyIZA0lcyLZoqgApjwMxFbtb9cLDhwWaUhSS7TuCr3Pj5fnvkov+zy6eESkWhJK5sxsr1QHIiJVmDMy3r2a1wCOvCJ0k4kkw8GnQ/vDdxUvyRtNczZFGJCIJCrRdQyWm9n/Af909w/25IFm1gG4FxgGGDAGuM7dl1bzPjcBdwIT3f2oPYlJJONt+BJm/y9ePux8aNy62rfpfOOoqk+SWq2yvwNNOIDb673HXmymMXB53ijuLjy3wvNFJDMk2s16NyH5mmxmH5nZ5WbWpLoPM7N8YBxwMDAcuBA4EBhvZo2rcZ8uwG+AldWNQSTrFBfDlH/GFwdu1RUOPCnamKRW2kw+DxeejhNafA+yL/hWzqSIoxKRqiSUzLn7bUBn4NvAcuBBQmvdQ2bWuxrPuwzoApzl7i+5+0jgDKATcEWlV+7uIeBp4NOqThTJevPfhNXzw+ecPDjySs1elZSZ5x14pWjQrvK3cifBitkRRiQiVUl4uXh3LwZeBl42s07ApcDFwOVmNo2QYD3r7jsquc0ZwGR3X1DqvovMbCJwJvDXquIwswuAPsD5wItVnC6S3bashk9K7b3a/Uxo3iEpt15812lJuY9krwr/DhSfAuN+DyvnhPL7f4dT/gQNNXxaJBPV9Ov9RmAtsJkw7m0v4DFggZlVNn6tBzCrnPrZQPeqHmpmLQjj7X7p7toZWmo3d/jgUSiMfT9q1j4s8iqSajk5MOgaaNA0lLetg8kPhb+TIpJxqpXMmdlgM/t/wDLgdsL4t8Pc/WDgEGAh8HAlt2gJrCunfi3QIoEQ7gbmAU9UI+bLzWyamU1btWpVopeJRG/J+7D8o1jBQvdqbr1IQ5I6JL9lWFC4xPKPwpZfIpJxEl2a5BozmwW8Q+jivAHY192vcveZAO4+D7iVMLmhMuV9tatyfQUzOxq4CLjKPfGvh+4+wt37uXu/Nm3aJHqZSLR2bILpT8TLBw6DNt0iC0fqqPaHhyVLSnz8LKxeUPH5IhKJRFvm7iF0hQ51957u/oC7l7cA0Xzgd5XcZx2hda6sFpTfYlfaw4Su3C/NrLmZNSeM+cuNlRtU+acQyRYfPgU7NobP+a3CUiQiUTjs/DCDGsJ+wBP/Bju3RBuTiOwm0WSuo7t/z93fruwkd1/m7rdXcspswri5sroDc6qI4RDgSkLSV/IaDAyIfb6qiutFssNXM2BRqX9q/S+B+vnRxSN1W24eDL4W6sX+Dm5ZBVNHaPycSAZJNJmbZGaHlXfAzHqa2cIE7/MyMCC2TlzJ9Z0JSdnLVVx7XDmvTwgTKo4DXkgwBpHMVbA9/KIs0XEg7Ns3unhEAJrsHXYcKbF0MiwcH108IrKbRJO5zkBF3ZgNCevEJeIRYDEw0szONLMzgJHAF5SaOGFmncys0MxuKalz9wllX8B6YEOs/GWCMYhkrpnPh5YPgPqNoe8PIw1HZJeOA6DrCfHytH/BhmXRxSMiu1RnNmtFber9CElV1Tdw3wIMJcxIfYqw8O8iwli8zaVONSC3mvGJZLe1GMgKAAAgAElEQVQ1n8PcUlst9bkIGjWPLh6RsvpcBM32DZ+LdsL795NHYbQxiUjFiwab2fXA9bGiA6+Y2c4ypzUiTGj4v0QfGNuD9ewqzllMAjNc3X1Ios8VyWhFhTDlYXZ9Z2rbE/Y/NtKQRL4hr0EYP/fGr8P2cusWc3ZuEc8VHRd1ZCJ1WmU7QCwExsY+DwemAWUXattBmLjwaPJDE6lD5o2G9UvC59x6cMRlYFV+nxFJvxad4PAf7Fo6Z1jONGYXd2KWd6n8OhFJmQqTudi+qSMBLPxS+Z27L0pTXCJ1x+ZVMOM/8fKh50DTdtHFk2KdbxxV9Um16LlRSemf96CTw6zr5R8CcEneaG4t+GHqnicilUpoTJq7/0iJnEiKTH8ijD8CaN4RumnPVMlwZjDgSmgYxnQ2ZSsX543WciUiEalszNwtwKPuvrz0rNIKuLv/PrmhidQBX06DZdPi5f6XhnW9RDJdw73Cdl8f/RSAnrYIPnsNDtaXEZF0q+y3xm3A68Dy2OfKOKBkTqQ6CrbDtMfj5QOOr7Vbdi2+K5pf8FE9Nypp//Pu04s3ivtzUs4HofzxM7B3d2i5f3rjEKnjKuxmdfccd59a6nNlr9z0hSxSS8x8HrauCZ8bNIPe2rJLss+LRUez2GNjPIsLYeJ94YuKiKSN1nETicK6xaFLqkSfC6FB08jCEampInIZUXg6O6gXKjZ9tWumq4ikh5I5kXRzh6mPgBeH8t7dofPR0cYksgdW0oKni0rtDrFwPCyZFF1AInVMhcmcmRWbWVGCLy0BLpKoBWNhzYLwOScvTHrQmnKS5d4v7gGdBsUrpo4Iy+6ISMpVNgHid1S8hZeI1MS29fDx0/Fy9zNhr32ji0ckaSx8MVk9D7ashoKt8P79cMJtkKNh1SKpVNmiwbelMQ6RuuGjp8IvOYAmbaH7WdHGI5JM9RvDoGthzK1hGMHqeTD7f3Dod6OOTKRW05g5kXT5eiYsfi9e7n8J5NWPLh6RVGhz0O7J28wXYOXc6OIRqQO0aLBIOhTuhA9KbWHcaRDsc1h08YikUvdvhy8vKz8FHN7/O40YyjYaRh2ZSK2kRYNF0uHTl2HT1+FzvUZw+IXRxiOSSjk5MPAaGH0D7NwCW1czPPdN/ln0LUCTfUSSTYsGi6Taxq/CuKESh50P+S2ji0ckHRq3giOu2FXsl/MZg3NmRRiQSO2lMXMiqeQO0x4LK+MDtDwAug6LNiaRdOl4ZNimLuaC3LG0ZW2EAYnUTtXa0dvMjgMGAvsCy4BJ7j4+FYFJ3dP5xlHVvmZP96JM+TOXvB/GDgFgcMSlkJNTo+cmqq7tRyoZrs9FsOpTYAUNKOCKvFeh6DzIrRd1ZCK1RkItc2bW0szGAmMI68+dG3sfY2ZjzUx9RiJl7dwCH/6/ePmgk6Bll+jiEYlCvYYw6KcUEUbjdLQV8Mn/RRyUSO2SaDfr/UB/4EKgkbu3ARoBFwH9gPtSE55IFpvxH9i+Pnxu1AJ6fS/aeESi0nJ/Xig6Jl6e+yp89Ul08YjUMol2s34LuMndnympcPcC4OlYq9wdqQhO6q7KugpT1UWZ1GeuXQjz3oiX+1wE9fOr/dxEpbLbViQZ3iruS4+cxfS0RaFi0gNw6t3QcK9oAxOpBRJtmSsC5ldw7LPYcREBKC6GqY+yaze8dodCx4GRhiQSPePxwlPYSONQ3L4BJv8zTBISkT2SaDI3Eqioj+g84KXkhCNSCywYA2s/D59z8qDfJWBaW0tkI415vPDkeMXyD2He69EFJFJLVLYDxNBSxVeAv5nZKOB5YAXQljARogdwbSqDFMka29bDJ8/Gy93Pgmb7RBePSIaZ5V2gWzP47LVQ8dG/Ye9DoEXnSOMSyWaVjZkbQ+gnslLv+wGnlHPufwEtHCzy0b+hYGv43KQtdD8z2nhEMlHvC2DlHFi3OKzBOPF+OOnOMPNVRKqtsmTuuLRFIVIbrJgNi9+Nl/tdDHn1o4tHJFPl1oPB18LoX0HRTti4DKY/AQOujDoykaxUYTLn7m+nMxCRrFZUCB88Fi93HADte0cXj0ima9Y+fOGZ8s9QXjg+TBYSkWrTdl4iyTD31dC6AJDXAPoMjzYekWzQZQh0GhwvTx1BG9ZHFY1I1kp4Oy8z6wlcAnQDyg5scHc//ptXidQBm1fBrBfi5V7fg3xtiiJSJTPofymsWQCbV0Dhdq7Ie4U/Fl6wa8cIEalaott5HQlMI0x+OAloAXQBhgBdCZMjEmJmHczsBTPbYGYbzexFM+uYwHWdzGykmS0xs21mttrMJphZeRMyRNJn+r+gqCB8bt4JDjq58vNFJK5+fhg/lxPaFjrb13wn990qLhKR0hLtZr0TeJGwDIkBl7h7Z+AEwizWhHaAMLN8YBxwMDCcsD3YgcB4M2tcxeVNgNXAb4FTCa2Em4HXzOw7Cf45RJLry2mwbHq83P9SyFGLgki1tDoADjt/V/GknA/oaQsjDEgkuyTazdqLkHyVLNWdC+Du48zsDuCPwJEJ3OcyQoteN3dfAGBmMwi7S1wB/LWiC919NiGB2yW27t0i4EeEZFMkfQq2w7R/xcsHHA9tDoouHpGI7dG2cgefBl/PhE/DNniX5I2Grd+vcMhCTZ6VjK3zRDJRoi1z9YAt7l4MrAVKr4L6GdAzwfucAUwuSeQA3H0RMBGo9oJc7l4IbAAKqnutyB6b/SJsXR0+N2gKvc+v/HwRqZgZDPwxG2gCQFO2wqR/hO3xRKRSiSZznwP7xj7PAC42sxwzyyG0in2d4H16ALPKqZ8NdE/kBrHn5plZOzO7GTgIeCDB54skx/ov4NNX4+Xe3w8JnYjUXMO9eKTwNLxkGPaK2TBHu0WKVCXRbtZXCJMdniGMnxsFbASKCGPZfprgfVoC68qpX0uYVJGIPwM/j33eDJzn7mMTvFZkz7nD1BHgRaHcpltYYkGkDkp21+Vc78ioogGcnjspVMx8Htr2CP/OahDDHnX9imSJhFrm3P02d7889nkMMBC4D3gMOMXdq9My5uXUVWcX8r8B/YFvAaOBZ8zs9IpONrPLzWyamU1btWpVNR4jUoHPx8HqeeGz5UL/y0IXkYgkxcvFg1jgsc4gLw7bfe3YHG1QIhmsRosGu/uH7v4bd/+Zu79ZjUvXEVrnympB+S125T37S3ef5u6vuvu5wGTgnkrOH+Hu/dy9X5s2baoRqsg3NWUrfPx0vOKQb0HzDtEFJFILFZPDiMLToV5+qNi6GqY+HFrFReQbqpXMmVlXM7vAzG6IvXet5vNmE8bNldUdmFPNe5WYRljrTiTlzs0dDzu3hELjNtBTq+KIpMJamsGAq+IVX0yF+W9FF5BIBkt00eCGZvY48Cnwb+BPsfdPzexRM2uQ4PNeBgaYWZdS9+4MDI4dq5bYBIyjCBM0RFLqYFvKwJxS3zn6XxK27hKR1OhwBBx4Yrz84ZOwRj/uRcpKtGXuHuD7wK2EVrCmsffbCAv/3p3gfR4BFgMjzexMMzsDGAl8ATxcclJst4dCM7ulVN1tZna/mX3PzI41s+8BrwNHxOISSZk8Crkwt1SrQMcB0P7w6AISqSsOvxBadA6fiwvhvXvjreMiAiSezJ0H3O7ud7r7QnffEnv/A/A74IJEbuLuW4ChwDzgKeBpwqK/Q9299OhWIyxMXDq+Dwnr2f0deJMwq3U7cLS7/1+Cfw6RGjk1ZyptbW0o1GsEfYZHG5BIXZFXH466HvJiW4JvWQWTH6T8uXQidVOiS5M0AKZWcGwKUD/RB7r7UuDsKs5ZTJkZru7+MjXoihXZYxuXc1ru5Hj5sPMrXJVeRFKgabswfu69e0P5y2kMy9nKW8X9oo1LJEMk2jI3BjixgmMnEvZbFal93OGDR8klrCm32NtB12ERByVSB3UcAAedvKt4Tu7bHGDLIgxIJHNUmMyZWZeSF2HP1HPN7AEzG2Jmh8TeHwTOpZKlQUSy2uJ3wyr0gGM8WXQi5NRoRR8R2VOHXwitwuIFORRzZe4rNGFrxEGJRK+ybtYF7D4owYCrgCvL1AG8TRjjJlJ77NgEHz61qzimuC9feNsIAxKp43LzYPB18PqvAGhhm7g07zXw72rhbqnTKkvmfpS2KEQy0cfPwo6NAKzzprxUNDjigBKj7Yuktqjo73Iv681P8xYC0NMWwez/ac1HqdMqTObc/cl0BiKSUVZ9Bp/Ht/x9puh4diQ+z0dEUmiGH8DooiM5JXdKrOI/Ye/WtuWtSS9S+1V3Bwgzsx5mdrSZdTdTu7bUQkWFMPWReHnffnzkB0YXj4h8w/+Kj2K+7xcrOUy8D7YltCukSK2T6NIkmNmlwB1A6Q1OV5rZb939saRHJhKVz0bBhi/C57wG0O9HMHpKtDFVYfFdp0UdgkhSVOvv8tbBMPpXYTjE9g0w8X4YerMmKUmdk+h2Xt8HRgAzgYuBU2PvM4ERZnZ+yiIUSadNK2Dm8/HyoedA49bRxSMiFctvCYOuYddcvJVzdv/3K1JHJPr15ZfA0+4+zN2fdPc3Yu8nAs8Av0pdiCJp4g5TH4aiglBu3gm6nRptTCJSuX16Qc9S69DPfhGWfxRdPCIRSDSZ6wb8u4Jj/44dF8luC8fvWlMODI68AnK04o5Ixut5NrTtGS9PvB82fR1dPCJplmgytwnYr4Jj+8WOi2Stvdi825pyHHwatDoguoBEJHE5OaG7tVFsm72CrfDuX6Bge7RxiaRJosncaOBOMzu6dKWZDSRMihid7MBE0un7uWPDLwCAJm2h17nRBiQi1dOoORz9M8iJzetbvzQMm9ht7XuR2qk6Y+Y2ABPMbKmZTTGzJcB7wMbYcZGs1Mfm0SdnXrziiMvDLFYRyS6tD4R+F8fLS97npJxp0cUjkiYJJXPu/jXQG7gWmERI4CYD1wCHu/uKlEUokkKN2M738+KLA9PlOGjXs+ILRCSzdT0eup6wq/jd3Lc5xJZEGJBI6lW5zpyZ1SMsRTLD3f8B/CPlUYmkyTm5b4fxcgANm8PhP4g2IBHZc31/COuXwOr5GM6Vea/wu4ILo45KJGWqbJlz9wLgP0DnlEcjkk4rZnNMzox4ud/F0KBJdPGISHLk1oOjfha+oAGN2cZP8l6Cwp0RByaSGomOmVsI7J3KQETSqnAnTHl4V/HD4oOg45ERBiQiSZXfEo7+GUWE5YU62EqYOiKsJylSyyS6ndefgd+Y2Th3X5XKgETSYubzsDkM9dxGA54uOj4ps3g63zgqCXcRkaRo041ni47jB7ljABgz+gWefXUtY4v7JuX22kZPMkWiydxQoCWwyMwmA1+x+3xvd/fhyQ5OJCXWLoS5r+4qPld0HBtQ96pIbTShuDedbQVH5cwE4LzcCXzhezPPO0QcmUjyJNrNehRQAKwCDoiVjy7zEsl8RYWhe9WLAZjrHXmvWLNXRWov4+miE1js7WKlYq7Ke5kWbIw4LpHkSahlzt33T3UgImkx91VYtzh8zq3Hk4UnsmuT7iRTF4xI9Hb9O9xyFLx+I+wISdy3W82C42+FvPrVup+GUkgmSqhlzsxam1nDVAcjklIbl4exciV6fY9VtIguHhFJn8at4KjrwWK/9tYs0IQIqTUqTObMLNfMbjOz9cAKYKOZ/dfMmqcvPJEkcQ8/uIsLQ7llF+h2arQxiUh6te0OfS6Klxe/C7P/F108IklSWTfrlcAtwATgA6AL8G3C7g8/SnlkIsn02Wuw8tPw2XLhyCsgJzfamEQk/Q46Oezb+vm4UJ7xHDTdBzoNjDYukT1QWTfrZcAj7j7U3X/l7ucAVwM/MLPqDTIQidKGL+HjZ+LlHmdBi86RhSMiETKDfpdA2x7xuskPwOr50cUksocqS+a6AM+XqXsOyAU6pSwikWQqKoRJD8a7V1t0hh7fiTQkEYlYbl7YIaLpPqFcVADv3A2btYyqZKfKkrkm8I2525ti701TE45Iks15CdZ+Hj7n5MHAq8MPchGp2xo0gSE3Qv3YGpPbN8A7f4adW6ONS6QGqprNuq+ZdSl5EVrrvlEfOyaSWdZ8DrNejJd7fQ+ad4wuHhHJLE3bwdE/D1/0IIyle/9+KC6KNi6RaqoqmXsBmF/qNTdW/1KZeg02kMxSuBMmPQAe+6HcphscfHq0MYlI5mnbHY64LF5e/hF8+P+ii0ekBirrb0rJjFUz6wDcCwwjrNY6BrjO3ZdWcV0/4HLgGKAjsBp4F/ituy9KRaySxWY8BxuXhc95DWDAjyEn0Q1PRKRO6TIENn4VhmUAzHsdmu0LB50YZVQiCaswmXP3J5P9MDPLB8YBO4DhhP1d7wDGm1kvd99SyeXnAT2A+4HZwL7AzcA0M+vt7l8kO17JUivmwNxSq7QffmHoThERqchh58Gmr+CLKaE8/V/QZG9o3zvauEQSkO6R4JcRxt11c/cFAGY2g9BNewXw10qu/ZO77zbVyMwmAoti970lJRFLRiu7tU4DdnJ73hO0tg0AzPb9uXfGDhbflbpnikgtYBYmSG1ZHSZNeTFM/BsM+z0071DuJYn+LNDWfpJq6e53OgOYXJLIAcS6SCcCZ1Z2YdlELla3BFhFaKUT4dzcCbsSuW004F+FJ5GqvVdFpJbJawDH/ALyW4VywTZ4+y7Ytj7auESqkO5krgcwq5z62UD36t7MzA4B9gY+3cO4pBboaQs5NueTXeWni05gvVbREZHqyG8Jx/4yJHYQWuom3KUlSySjpbubtSWwrpz6tVC9Hc/NLA/4J6Fl7rFKzrucMHGCjh21LEVtUG6XxY5N8NorsK1tKHc4gktHdUvtM0WkdmrRGQZfC2/fDTisWwTv3gNDbkr4Z4GGY0g6RTG9z8upq0k/2D+AQcAP3L28BDE8zH2Eu/dz935t2rSpwWMkK0x7HLbF/ho0aAb9L0XdqyJSY/v23X3JkhWz4f2/Q3FxdDGJVCDdydw6QutcWS0ov8WuXGb2R0Jr28Xu/maSYpNstWQSLHk/Xj7yCmi4V3TxiEjt0PX4MMu1xBdTYNpj4OW1SYhEJ93J3GzCuLmyugNzErmBmf0GuBG41t2fSmJsko02r4KpI+Ll/Y+F/fpFF4+I1C7dz4Jup8bLC8bAzLLblotEK93J3MvAgNLbf5lZZ2Bw7FilzOynhHXpfuPuf09RjJItigrh/fugIDYwOb819B0ebUwiUruYQZ+LoPNR8bpZ/4XPXo8uJpEy0p3MPQIsBkaa2ZlmdgYwEvgCeLjkJDPrZGaFZnZLqbrzgL8BrwPjzGxAqVe1Z8JKLTDzP7A6tpOc5cDgn0L9xtHGJCK1jxkceRXsU2oB4elPwOKJkYUkUlpak7nYDg9DgXnAU8DThEV/h7r75lKnGpBbJr6TY/UnA5PKvB5MefCSWZZ/DHNGxsu9vhf2XxURSYXcPDjqemjVNVbhMPlB+OqTSi8TSYe0z2Z196Xufra7N3P3pu5+lrsvLnPOYnc3d7+tVN0PY3XlvYak+Y8hUdq6FiY9EC+36wXdK11zWkRkz9VrCENuDPu2AhQXwrt/gdULKr9OJMW087hkl+LisDzAjo2h3LA5DPpJ6AYREUm1Bk3huN/Ed4ko3AET/ggblkUbl9RpSuYku8x+EVaWTHw2GHSNliERkfRq3CokdPWbhPLOzTD+D2G3CJEIKJmT7LFiNsx8IV7ueTa06xldPCJSd+21Lwy5Kb7t19Y1MPZ2JXQSCSVzkh22bwjdqyUbiOx9SEjmRESi0rorHP1zyIntjLl5ZSyhWxNtXFLnKJmTzOcOkx4stV1XUxj0U8jRX18Ridg+h8HRPyuT0N1GCzZGG5fUKfptKJnv05fhq4/j5YFXQ355u8KJiERg377fSOh+mfecEjpJGyVzktlWzYNPnouXDzkD2h8eXTwiIuXZty8cFU/o2th6blBCJ2miZE4y147NMPE+8KJQbtU1LA4sIpKJ9ts9ods7ltBpDJ2kmpI5yUweW119a2xmWL18GHxdWIVdRCRT7dcXjrqeInKBkNBpUoSkmpI5yUwznoNl0+PlAVdBkzbRxSMikqj9+vFQ4Rm7Ejo2r1BCJymlZE4yzhH2Kcz+X7zi4NOhwxHRBSQiUk0fe1cldJI2SuYko3Syr/lR3uvxin16Q+/vRxeQiEgNlSR08VmusYRu86poA5NaR8mcZIxmbOaavJeoR2GoaLoPDNZ6ciKSvT72rnDU9WClWujeugXWL402MKlV9FtSMkPhTn6SN5LmbArlevlw7C+hfuNo4xIR2VP79dt9Hbpta+GtW2Hl3GjjklpDyZxEzx0+eJQutjwUMRh8LTRrH3FgIiJJsl8/GHIj5DUM5YKtMP4O+HJ65deJJEDJnERv7ihY9Pau4n+KhkD73tHFIyKSCu0OhRNuhQbNQrmoAN69Bz4fF21ckvWUzEm0ln8EH/17V3FicU/eKu4bYUAiIinUsguc+HtosncoezFMeTjM4HePNjbJWlqBVWqs842jqn3N4rtOixc2LAs7PBB+gH3u7XmqaBhgyQmwlJrEKiKSDOX9/GnGUVyf91862MpQ8el9nHDmeuj7Q7Dk/wyU2k0tcxKNHZvhnbuhYFso57figcIzKdT3CxGpAzbShD8Vnsdc7xivnPc6vH8/FBVGF5hkJSVzkn7FRaFFbtNXoZxbD475BRtpEm1cIiJptJ0G/K3wbKYXd4tXLnkf3r4r/kVXJAFqBpGk2K37tIzduhjc4cMn4esZ8boBV4dxJHyatphERFIp0Z8/nW8cxT+LTucC8jmBMKOfr2fC2N/BMTdAfssURim1hVrmJL1m/RfmvREv9/gOdBoYXTwiIhFzcni66HjodW68cu1CeOPXsHp+dIFJ1lAyJ2lzfM50mPl8vKLjgN1/eImI1FkGPc+GIy4Di/1q3rYOxtwGCydEGZhkASVzkhYDc2Zzfm6ptZTa9YKBP9GsLRGR0rqeAMf9GurHxhAXF8Lkh2D6E2G8sUg5lMxJyvW2BVyc+3q8ovWBcPTPw8QHERHZXbtD4aQ7Ya8O8brPRsP4O2HHpujikoylZE5Sa8Vsrsx7BaM4lJt3hGNvhHoNo41LRCSTNW0LJ94BHY6I162YBa/fBOuWRBeXZCQlc5I6az6Ht/9MHmHNpJXeHIbcBA20BImISJXqNYSjfgaHnhOv27IK3roZlk6JLi7JOErmJDU2fBm6BAq3hyJN+GvhuZpmLyJSHWZw6HfDMiV5DUJd4Q54768w4z/aAkyACJI5M+tgZi+Y2QYz22hmL5pZx6qvBDO708zeNLM1ZuZm9sMUhys1sXlVSOR2bgZgC434S8E5rGaviAMTEclS+/WDE/8ATdrG62b9F965J+yoI3VaWpM5M8sHxgEHA8OBC4EDgfFm1jiBW1wDNAJeTVmQsme2rYfxd8DWNaGc14D7Cr/DclpHG5eISLZr3gFO+kOYIFFi2TQY/UtYMSe6uCRy6W6ZuwzoApzl7i+5+0jgDKATcEUC1+/l7kcDv09hjFJTO7fAhD/Cpq9DOScPjrmBhd4+2rhERGqLBk3D2OODT4/XbV0Tdoz45Dnt61pHpXs7rzOAye6+oKTC3ReZ2UTgTOCvlV3s7sUpjk8os/1WorZvhAl3wbrFsQqDwdfGvkEuTWJ0IiJ1XE4u9LkQ9j4krEG3czPgMPtFRjw/kkcKT2MVzRO+XcLbMSbhfpIa6W6Z6wHMKqd+NtA9zbFIkrRgI4y5FdZ+Hq888ordp9SLiEhy7dcPTr0b2vbYVdXFlnNrvScZkKNu17ok3clcS2BdOfVrgRapeKCZXW5m08xs2qpVq1LxiDqtLWu5Ke9Z2BjbIBqD/pfBAcdFGpeISJ2Q3xKG3gy9LwDLBaAhO7k0dxSX5I6iITsiDlDSId3drADlzaNO2Z5O7j4CGAHQr18/zeGupkqby9cuhPF/hB2NQjknDwZeDZ0GpSc4EREJy5d0PxPa9mTl7J+zt60H4OYea7i58bgw5KX1gbtdkuzu0xoNz5GkSXfL3DpC61xZLSi/xU4y1Yo5YcDtjo2hnFs/rIOkRE5EJBqtDuD2wuFMLO4Zr9uyCt66BWa+oMkRtVi6k7nZhHFzZXUH1MGfLZZNhwl3QsG2UK6XD0N/C+17RxuXiEgdt4P6/KvoFEYUnh5+NgP4/2/vzsOkqs48jn/f7gYaWYRGFhWh2bERAVFQ0QGEiCYKJpqYRcfEmGjik8VJfFyyjFvGxIlJnnEyGbeYBU2MQxJITIQgLkQWQTZBZJNVFtllbeiuM3+cW3RVU91dvVTdutW/z/Pcp6lz76k+93D71lvnniUGb78A0++BXWvCLaBkRLaDuWnAhWbWO55gZqXAqGCf5Lr1s/0klZXH/eviDjD+Pug8IMxSiYhIgjfd2XDlI3Ba/6rEfZtgxvdgwVO05mh4hZMml+1g7klgAzDVzCaZ2URgKrAZeDx+kJn1NLMKM/t+YmYzG21m1wFXBEnnm9l1QZpk2qqXYO5/+295AG06w0fuh449wy2XiIicrG1n/2V72I2+KwwADtb8g4daPMN5tprU3dglarI6AMI5d8jMLgN+CvwWP/DhZeCbzrnE9UgMKOTkYPN+YHTC69uDLZ5HMsE5v2zM2y9UpZ3aHcZ+R2utiojksoJCOPsqOGskLHwati4G4FQO8tWiqSyN9YFDF0GbTiEXVBoj66NZnXObgGvrOGYDKYIz59yYzJRKalRxDBb+Et57pSqtU18Yc7efiVxERHJf284w+i7YNA/eegbYAcCQgnXw4h1w7qeh/xVQkPUl26UJ6H9NatSJ/TDzvuRArttgP6eRAjkRkWgxg54XwVU/5bXYkKr0inJY9GuY8V0/5ZREThjzzEkElNkGbi36K+xpX5VYegmMvA0KW4RXMBERaZyWbfht5eXMjZVxU+GMqvQ96+Cle6HXpXDu9dDmtPDKKPWiYE6SOceVBfP5ROFsDAe097OKn3ejb4I3dZqTTw8AABK6SURBVE0UEckHa1137qu4iRvPPQ7L/wixCsDB+tdh4xwY8FFaU8wRisMuqtRBwZxUOXYY5v2cawtfr0or7gCX3AFdBoZXLhERyYhKCuGcidDjIlj0W9i6yO+IVcDKafywxYe8WDmSWbFh4RZUaqVgTrx9m2H2o3Bg24mkta474694WCNWRUTyXfszYMxdsGMFLH7WP3IF2nCETxW+yriCxbChE/QcpSc0OUjBXA7L5Fp3SWvsbZwL83/hO8EGZsaG80LlaG5TICcikhXp3vNrXTO7SX7vxZxvnbi2cDadg7itk+2HOY/Byr/CsBug2zknvU+uaup1aHORgrnmrLIClj4H7yZc6IUtebLiKua7s8Mrl4iIhMhY6AayuKIfYwqWMLFwLm0Ilm/cux5mPehnNii7BroOUktdDlAw11ztXgfzH4d9G6vS2naFS7/F/MXLwyuXiIjkhEoKeTk2nDmxQVxZ8CbjC9+vWspx+9t+69TXB3U4NHd/eBTMRURTNPmW3v0iLahgUuEbMGNy1bJcAGcOh4tuh5ZtAAVzIiLZkO69vam73dT/M+VaOLTbrwT03qucWAZs91qY/WMeKjrO32IjmR/L7ac6tZ13Jrs2ZZqCuWZkgG3ipsLpdLF94Lr6xMIWfj6hgVepqVxERGrWphNceBsMugZW/sUHdbEKALrZHm4u/DsfL/gnvFsIfcZBC01pki0K5pqDY4dgyXPcWfR8cnqXMhh5K7TrFk65REQketp1gxFfgnOuhdUvwerpJ3Z1tAOw6Dd+3rr+V0D/y6H41BAL2zwomMt3WxbCgqfgyN4TSUdo5f8Q+4xTa5yIiDTMKSUw9LNQNokpS37E5YULacdhv+/YQVj+f/DOn+GsEdB3vG9A0GdORiiYy1dH9vnFlDfNS0peHOvH5MrxXN13fEgFExGRvNKyDX+PjWRmbDijCpYzvs02OLTT74tV+NUkNs6BdqdD33HQazQUt6/9PaVeFMzlm4pjsGYGrPiT/2YU16o9v6gYyVuuPxpxJCIiTe04RbwaGwpX3+0bElb9zQ+QiDuwDRZPhqW/9611fcZpapMmomAuX1RWwHuvwPIpSY9UAf8t6LwbeWvB66nzioiINJWCQigd5bc962Hdy7Dhn3A8mKsuqbWum38EW3oJtO4YbrkjTMFc1MVisGG2Hy4eb9aOa9PZ9407fUg4ZRMRkeatpBeU3AJDb4BNc2HtzGqtddt9a93iZ6FrmV8j9qwRGjRRTwrmoso52Dwflv0BPnw/eV9xBzjnE9DnMj/1iIiISJhaFEOfsX7buwHWvuwbIuKtdTi/LuyOFbDgaf/49URgp/51dVEwFzXOwdbFsOx5/weRqGVbKJsE/SdAUatQiiciIlKrjqVwwRdh6Od8a9361+CDdzkxETEOdiz328IgsOt5MXS/AFq1C7HguUvBXFRUVsCWBb5D6a7VyfuKiv2kvwM/GqzgICIikuMSW+sO74HNb/rgbucqTgR2Lla1dNibT0HnAb7r0BlDoUNPDZ4IKJhrQg1ZCqSuJVU6sZ/RBUvhz3+G8g+Tdxa28JMylk2q97eVsJYtifJyKSIikiGnlMCAK/x2eI/vRrRxTnLjhauED97x29Lf+QET3c71gV23wU3aapfuZ1VTLLXZFBTM5aJYDLYt5huFUzinYD2Gg/KuVfsLinx/uEEf938AIiIi+eKUEhhwpd8O7YbN83yL3a41yccd2esf0a5/DTDo1AfOGOZb7kp6+1G1zYSCuVxyeI+fXmTty3B4N4MLdiTvb13iJ1zsc5mCOBERyX9tOsHAj/nt8B7Yvgy2LYVty5LnUsX5UbK71/rZHYpaQad+0HkgZfYB69wZlNMytNPINAVzGVJb02tS8235QT+gYfN8eH+Rb0auZoXrxfhLvwpnnteobxphNQfnSjO0iIhE2Ckl0HuM32Ix2LPOB3ZbF8PudVQNoAAqyk8Movi3oh04jM2uCyz8ADoP9H3vqjWKpPtZlYvdhRTMhaCEDxlWsIahBevgj8+mDOBo1Y6/V5byemwwO+nIN866IPsFFRERyUUFBXBaP78Nvg7KD/hBEluX+CDu8O6kww1HD9sBq1/yG0Cb06Ckjx9dW9LL/4zoxMUK5rLBOdi3yY9G3bKQR1okrJfquiYf2+Vs6PsROGsEUxbMyG45RUREoqhVOz99Sc+L/etDu/yo2J0r2fzODLrbTt//PNGhXX7bPL8qrbiDD+riW0kvaNs150fNKpjLpJ2r/Pp0W970F0xNOvWF7udD9xFw6pnZK5+IiEg+anOa30pHcf+U02nNUfrYVsYP6gI734Xda6Dy+Mn5ju6DbUv8FldU7AO7sffm7ByuCuYyafV02PjGScmVFLLS9WBJrC/jr/mKBjOIiIhk0BGKWe56w5CgX1xlBezf5Cff37Pe/9y30fe1q67iKBzckbOBHCiYy6zuF1QFcy1a+yHT3UfwjWXbOEpwUSiQExERya7CIj99SUlv6BOkxWJwcHtVcLc3+Fl+wLfM5bCsB3NmdhbwU+AjgAEzgW865zalkbcYeBC4AegALAHucs69nrkSN8IZQ6Hf5T6o61LmLx7gKLk3EkZERKRZKyiA9mf4rXSUT3POz2dXcTTcstUhq8GcmZ0CzALKgZvw44gfAl4xs3Odc4fqeIungY8BdwLvAbcD083sIufcklpzhqFFa7/+nIiIiESPWSSeoGW7Ze5LQG9ggHNuLYCZLQPWALcCP6kpo5kNAT4L3OyceyZIew1YATwATMxs0UVERERyT0GWf99EYF48kANwzq0H3gAmpZH3OPB8Qt4K4PfABDPL3Z6JIiIiIhmS7WBuELA8RfoKoCyNvOudc4dT5G0J9G188URERESiJduPWUuAvSnS9wB1TbtcW974/sjJxWVBREQkd+X650auly8fhTE1iUuRls7UytaQvGb2ZeDLwcuDZrYqjd/VaPajjL3faUAtMxA3O6qPKqqLZKqPZKqPZHlfH/X8HMr7+oB61Ula9dHUn/Up9EznoGwHc3tJ3YLWkdStbon2AD1qyBvffxLn3BPAE+kWMNeZ2ULn3PlhlyNXqD6qqC6SqT6SqT6SqT6SqT6SRa0+st1nbgW+71t1ZcA7aeTtFUxvUj3vMWDtyVlERERE8lu2g7lpwIVm1jueYGalwKhgX115WwCfTMhbBFwPzHDOpViDQ0RERCS/ZTuYexLYAEw1s0lmNhGYCmwGHo8fZGY9zazCzL4fTwsmBX4e+JmZ3WJm4/DTkvQC/j2L5xC2vHlk3ERUH1VUF8lUH8lUH8lUH8lUH8kiVR/mXKoxBRn8hWY9SF7O62X8cl4bEo4pBdYD9zvn7ktIbw38AD95cAdgKX45r1ezUngRERGRHJP1YE5EREREmk62H7NKCmbW3cweM7O5ZnbYzFzQOplO3g3B8dW3azJb6swws+vMbIqZbTSzI2a2ysweNrN2aeQtNrP/NLNtQd65ZvYv2Sh3pjSyPlJdF87Mhmaj7JlgZhPMbJaZbTezcjPbYmZ/MLO6Jh3HzDqa2VNmtsvMDpnZTDMbnI1yZ0pD68PMSmu5Pjpkq/yZZmYvBef0UBrH5t39o7p61kc+3j/G1HBO+9LIm9PXRxjzzMnJ+gKfAt4CZgOX1zP/dOC+amlZmU8vA74NbALuBbYAw/DnNtbMLnbOxWrJ+zTwMeBO4D3gdmC6mV0U9LmMosbUB8CvSOiPGljdxGXMphL838n/ADvx0xXdDcwzs8HOuY2pMpmZ4QdR9QK+hp8K6R7gFTMb6pzbko3CZ0CD6iPBw5w8+OxAk5cyBGb2GWBIPbLk4/3jhAbUB+Tf/SPu68CChNcVaeTJ7evDOact5A0oSPj3LfjJkUvTzLsBmBz2OTRhXXROkfavQZ1cVku+IcExX0hIK8IHtdPCPq9s10dwnAMeCvscslBHA4Jz/VYtx0wKjhmbkHYqfn7K/wr7HEKoj9LgmFvCLm+G6qADsB34TDp/B/l6/2hofQR58u7+AYwJzmt8PfPl/PWhx6w5wNXdutJsOOd2pkiOf4M6s5asE4Hj+BHP8feqwI94nmBmrZqskFnUiPpoTnYHP4/XcsxEYKtz7pV4gnNuP/AXfKCXT9Kpj3z3CLDCOfe7NI/Py/tHgvrWhyTL+etDwVx+uDroa1duZvOi2l+uFqODnytrOWYQsN45d7ha+gqgJf5Rdr5Ipz7ivhJcF4eDvlWXZrJg2WJmhWbW0sz64R8DbcffWGsyCFieIn0F0MPM2magmFnTgPqIe9j8NFD7zWxa1PsQApjZJfjW66/WI1ve3j8aWB9xeXn/AJ41s0oz221mz5mfZaM2OX99KJiLvr/g+wBNAD4HHAX+ZGY3hFqqJmJmZwIPADOdcwtrObSE1EvC7UnYH3n1qA+Ayfgb+Hj8+sSdgFlmNiajhcyO+UA5vv/OufhHzh/Ucnxd10fHFPuipL71UY4P+m4FxuL7Zg4G5pjZ2Rkua8aYWQv8ef3YOVeffsN5ef9oRH1Aft4/9gOP4rszXQY8iD+/uWbWpZZ8OX99aABExDnnvpb42sz+BMzDd2yeHEqhmkjQWjIV3zn1C3Udju/TkCo9L9SzPnDO3ZjwcraZTcW3Tj0EXJKRQmbPjUB7oDc+EPmHmV3iEuarrCbfr4961YdzbhtwW0LSbDN7Cd/S8B0gql8G7wLi85HWR75eHw2tj7y8fzjnFgOLE5JeM7PXgTfxgyK+W0PWnL8+1DKXZ5xzlcALQHczOz3s8jSUmRXjR9n1Bia4ukcb7iH1t6OOCfsjqwH1cRLn3AHgReCCJi5e1jnnVjrn5gd9gMYBbfGjOGtS1/WR6lt3ZDSgPlK9x2bgn0T0+ggelX0H+B7Qysw6JEyzEn9dWEP2vLt/NLI+TpJP949EzrlF+Bbt2s4r568PBXP5Kf5tIZIzQgePBqYAI4CPOufeTiPbCqCXmZ1SLb0MOAasbdpSZk8D66PGtyOi10VNnHP78P+/tfVbWYHv91JdGbDJOXcwE2ULQ5r1UZMoXx+9gWL8E4m9CRv41sq9+EfJqeTj/aMx9VGTKF8ftanrvHL++lAwl2fMrAj4JP4DanvY5akvMysAnsW3Lkxyzs1LM+s0oAX+3OPvVQRcD8xwzpU3dVmzoRH1keq92uPnSZrfRMXLCWbWFRgIrKvlsGnAmWYWHzwSr4+rOXmetUhLsz5S5esBjCK618cSfP+/6hv4gGYsNX/o5uP9ozH1cZI8vn+cD/Sn9vPK+etDfeZyhJldF/xzePDzSjPbCex0zr0WHFMB/No598Xg9Wfw0yr8DdgMdMVPZDgcP59QFP0c/wfzA+CQmV2YsG+Lc26LmfXEf1A94Jx7AMA5t8TMngd+FrRkrQe+gp8k9nNZPYOm1aD6MLNv4+cbewXYCvTEfxvvRoTrI+gTughYBnyIvwnfge9H+GhwzGj8ms83O+d+E2SdBswFJpvZnVRNGmz4aRsiqaH1YWaP4r/Mz8VPNjwAXx8x4D+yexZNI2iRfLV6up8vmo0uWMO7udw/GlMfeXz/eBb/f7sI2IefhP0e4H3gseCYaF4fYU90p81v+CbeVNur1Y75VcLrC4FZwA78HDj7gZn4PlWhn1MD62FDLXVxX3BMaeLrhLytgZ/gp2U4iv+mNSbscwqjPvAtTm8Au4JrYzc+oBkR9jk1sj7uwq94sA84jJ+083ESJtmmamLQz1fLWwL8Et+/5TA+wBkS9jmFUR/Azfj5CvfiA7/twHPAgLDPKQN1lDT5bXO6fzS0PvL4/nEP/ovP/uC8NgNPAKdH/fqwoJAiIiIiEkHqMyciIiISYQrmRERERCJMwZyIiIhIhCmYExEREYkwBXMiIiIiEaZgTkRERCTCFMyJiIiIRJiCOREREZEIUzAnIlIPZnanmR0xs1lm1jkhfYCZHTSzx8Isn4g0P1oBQkSkHsysFJiAXzf3XufcI2bWGr+8z3HgYpcDC2+LSPOhYE5EpAHMbA6w2Tl3vZk9CXwKGO6cWxty0USkmdFjVhGRhnkLGGZmnwVuAb6sQE5EwqBgTkSkYRYBfYHHgf91zj0fcnlEpJlSMCci0jCLAQPWAXeEXBYRacYUzImINMxtwc9nnHNHQy2JiDRrCuZEROrJzK4HbgUOAENDLo6INHMazSoiUg9m1g8/+OH3+MesI5xzQ8ItlYg0Z2qZExFJk5kVA38ANgBfx/ebKwvmmRMRCYWCORGR9P0MP4L1k0E/uQVAEfBDMxsWaslEpNkqCrsAIiJRYGafxveTu8E5typIXgg8AXwe6ANcFU7pRKQ5U585ERERkQjTY1YRERGRCFMwJyIiIhJhCuZEREREIkzBnIiIiEiEKZgTERERiTAFcyIiIiIRpmBOREREJMIUzImIiIhE2P8DDust10gB9bUAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fbb2cedba58>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fbb2e77e588>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fbb2cebb828>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fbb2cf8c400>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fbb2ce7b0f0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fbb2e7c5fd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "for degrees_of_freedom in [1, 10, 25, 50, 100, 150, 300]:\n",
    "    fig, ax = plt.subplots()\n",
    "    \n",
    "    distribution_comparison_plot(\n",
    "        np.sqrt(np.sum(chi2_per_dimension[:, :degrees_of_freedom], axis=1)).ravel(), \n",
    "        distribution=scipy.stats.chi(df=degrees_of_freedom), \n",
    "        hist_kwargs={\"bins\":51},\n",
    "        ax=ax\n",
    "    )\n",
    "    plt.title(\"K = {}\".format(degrees_of_freedom))\n",
    "    plt.ylabel(\"Probability Density\")\n",
    "    plt.xlabel(\"$\\chi$\")\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Unlike the situation when we were analyzing the distributions of the individual coefficiets we can now clearly see that as we include more and more dimensions to the analysis that the distribution of $\\chi$ values becomes less and less like a theoretical $\\chi^2$ distribution.\n",
    "\n",
    "Since there is no one \"true\" probability distribution over face images in a meaningful sense there is no \"right\" answer about why this is happening. But intuitively this sort of behavior makes sense if we suppose that the first few principal components are fiting to real structure within the image data and then eventually turning over to mostly picking up random fluctuations. This is really just a much more sophisticated version of the discussion about empirical noise models way back in part 1 of this blog post series. This is especially clear as the dimension of the PCA expansion starts to butt up against the number of sampled images. Just as you can't really robustly estimate the variance of a 1D variable from just a single sample you can't estimate the covariance of a D dimensional vector value from just D samples. In the multivariate case though we can fairly accurately estimate variance along certain special directions but we start to run out of statistical power as we start to deal with variations in directions which aren't well represented by our dataset.\n",
    "\n",
    "Acting under that assumption then it seems that the sensible thing to do would be to use only the first 25 or so principal components and their associated variances to gauge how unusual the variations of a given image are. But this means we are using just a 25 dimensional subspace of a 4096 dimensional feature space! What do we do with the other 4071  data dimensions?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## A Subspace Isn't Enough\n",
    "\n",
    "If we stop short of having a full rank covariance matrix we lose all ability to reason about the variations outside of our chosen k dimensional subspace. To see that this is potentially a foolish idea lets have some fun and design some adversarially modified faces to illustrate how easy it to fool our k dimensional $\\chi^2$ statistics."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "def random_orthogonal_vector(\n",
    "    basis, \n",
    "    seed_noise = None,\n",
    "):\n",
    "    \"\"\"\n",
    "    Generates a random vector which is orthogonal to the given basis\n",
    "    \n",
    "    The input basis is assumed to be orthonormal.\n",
    "    \"\"\"\n",
    "    if seed_noise is None:\n",
    "        #generate seed noise\n",
    "        seed_noise = np.random.normal(size=basis.shape[1])\n",
    "    \n",
    "    coeffs = np.dot(basis, seed_noise)\n",
    "    \n",
    "    #coeffs_lsq = np.linalg.lstsq(basis.transpose(), seed_noise)[0]\n",
    "    #assert np.testing.assert_allclose(coeffs, coeffs_lsq)\n",
    "    \n",
    "    #project noise onto the given basis\n",
    "    basis_projection = np.dot(basis.transpose(), coeffs)\n",
    "        \n",
    "    #subtract off the component of the noise that lies in the spanned subspace\n",
    "    resid = seed_noise-basis_projection\n",
    "    \n",
    "    #normalize the resulting vector\n",
    "    resid /= np.sqrt(np.sum(resid**2))\n",
    "    \n",
    "    return resid\n",
    "\n",
    "#make a perturbation vector which is orthogonal to the PCA basis\n",
    "perturbation = 30*random_orthogonal_vector(\n",
    "    pca.components_,\n",
    "    seed_noise = scipy.ndimage.filters.gaussian_filter(\n",
    "        np.random.normal(size=(64,64),),\n",
    "        8,\n",
    "    ).reshape((-1,))\n",
    ")\n",
    "\n",
    "#add the orthogona perturbation in to the faces dataset\n",
    "perturbed_faces = faces+perturbation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.1207800033138807e-14"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#double check that the data coefficients in PCA space don't change\n",
    "np.mean(np.abs(pca.transform(faces) - pca.transform(perturbed_faces)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4.7758220040336825e-15"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# and that the reconstruction of both the perturbed and unperturbed faces are identical\n",
    "pca_reconstructions = pca.inverse_transform(pca.transform(faces))\n",
    "perturbed_reconstructions = pca.inverse_transform(pca.transform(perturbed_faces))\n",
    "\n",
    "np.mean(np.abs(pca_reconstructions-perturbed_reconstructions))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fbb2ccfaa20>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axes = plt.subplots(1, 2)\n",
    "\n",
    "ax = axes[0]\n",
    "view_as_image(faces[0], ax=ax)\n",
    "ax.set_title(\"Example Image\")\n",
    "\n",
    "ax = axes[1]\n",
    "view_as_image(perturbed_faces[0], ax=ax)\n",
    "ax.set_title(\"Perturbed Image\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "I don't think anyone would think that the two images above should be considered nearly identical. But from the perspective of their PCA coefficients they are exactly the same. Clearly simply ignoring the subspace not spanned by the typical variations of our data is not a good strategy for detecting anomalies. How can we alter the $chi^2$ statistic in order to deal with the other 4,000+ dimensions we are leaving out in our PCA expansion?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Putting it all together\n",
    "\n",
    "If you squint hard enough you may recognize this as being the problem of the covariance matrix $\\Sigma_k$ having determinant 0 coming back to haunt us. The easiest way to regularize a covariance matrix to be positive definite is to simply add an identity matrix to it with some small magnitude. Thus instead of using the covariance matrix $\\Sigma_k$ we use the slightly modified covariance matrix $\\Sigma_k + \\epsilon I$.\n",
    "\n",
    "If we subtract off the PCA model for a data point keeping K components the results will contain all of the variation in the M-K orthogonal subspace. If we simply sum up the square of these residuals multiplied by some characteristic noise level $\\epsilon$ the $\\chi^2$ value over the first k dimensions captures the learned structured variation from the $\\Sigma_k$ term (call this $\\chi_k^2$) and the sum of the residuals left over captures the $\\epsilon I$ term (call this $\\chi_\\epsilon^2$. Thus we can calculate a nice consistent $\\chi^2$ value over the fully dimensional space via.\n",
    "\n",
    "$$\n",
    "\\chi_{full}^2 = \\chi_k^2 + \\chi_\\epsilon^2\n",
    "$$\n",
    "\n",
    "The parts of any anomalous variation which lie in the PCA subspace will alter the PCA coefficient magnitudes and the orthogonal part will leave residuals which will be collected in the squared residual sum. Following the logic of the post about empirical noise modeling (see the link at the top of this post). We pick the factor of $\\epsilon$ to use to scale the residuals as the inverse of the variance of the last principal component whose value we incorporate into the $\\chi_k^2$ value. Lets look at this total $\\chi$ distribution and see how it looks. I've picked the 100'th component as the cutoff point for the PCA expansion because the rise in the captured variance curve starts looking very close to linear at around that point (again see the empirical noise model post for details)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 98,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fbb29d31cf8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "k_cut = 100\n",
    "pca_partial = sklearn.decomposition.PCA(n_components=k_cut).fit(faces)\n",
    "\n",
    "projected_coeffs = pca_partial.transform(faces)\n",
    "chi2_vals = projected_coeffs**2/pca_partial.explained_variance_\n",
    "\n",
    "chi2_k = np.sum(chi2_vals, axis=1)\n",
    "\n",
    "pca_reconstructions = pca_partial.inverse_transform(pca_partial.transform(faces))\n",
    "residuals = faces - pca_reconstructions\n",
    "\n",
    "eps_scale = pca_partial.explained_variance_[-1]\n",
    "chi2_eps = np.sum(residuals**2, axis=1)/eps_scale\n",
    "\n",
    "fig, ax = plt.subplots()\n",
    "chi2_full = np.sqrt(chi2_k + chi2_eps)\n",
    "distribution_comparison_plot(\n",
    "    chi2_full,\n",
    "    distribution=scipy.stats.chi(df=200),\n",
    "    hist_kwargs={\"bins\":51},\n",
    "    ax=ax\n",
    ")\n",
    "\n",
    "plt.ylabel(\"Probability Density\")\n",
    "plt.xlabel(\"$\\chi_{full}$\", fontsize=20);\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "I chose a total number of degrees of freedom for the whole distribution at 200 because if you plot up the curve for 4096 degrees of freedom like you might expect from the number of pixels in our images or 400 degrees of freedom like you might expect from the total number of samples you just get a flat line close to 0. It is clear from looking at the cumulative variance curves that the effective number of dimensions peters out around dimension 200 and so it isn't much of a surprise that the effective numbers of degrees of freedom is around 200 as well.\n",
    "\n",
    "From the plot above we can clearly see that the resulting distribution for $\\chi_{full}$ isn't consistent with a $\\chi$ distribution. The reasons for this are pretty clear when you take a look at the residuals for one of the images at the chosen level of approximation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 101,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fbb29cfbdd8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axes  = plt.subplots(2, 2)\n",
    "axes = axes.ravel()\n",
    "\n",
    "for i in range(len(axes)):\n",
    "    view_as_image(residuals[i], ax=axes[i])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We are treating these images as though they were structureless white noise but they clearly retain a huge amount of structure that we can't accurately capture with just a simple linear model. The fact that the first few dozen dimensions look so convincingly normally distributed is really more of a testament to the central limit theorem than to anything else. The fact that the distribution is clearly not a normal distribution as we push out into hundreds of different dimensions isn't telling us that our statistical framework isn't useful. But simply that we shouldn't take the assumption of our distribution of faces being normal distributed too seriously.\n",
    "\n",
    "This $\\chi_{full}$ distribution can't be fooled by shenanigans occuring outside of our k-dimensional PCA subspace but still takes into consideration the typical sorts of variations that we see in our data. \n",
    "\n",
    "I hope you enjoyed the tour of PCA as a probabilistic framework. Have fun applying the ideas to your own data!"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.3"
  },
  "nikola": {
   "author": "Tim Anderton",
   "category": "",
   "date": "2018-04-10",
   "description": "",
   "link": "",
   "slug": "pca-and-probabilities",
   "tags": "PCA, probability, generative models, anomaly detection",
   "title": "PCA and probabilities",
   "type": "text"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
