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Last active October 18, 2022 14:54
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Understanding Cross Validation: Leave-One-Out
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{
"cells": [
{
"cell_type": "markdown",
"id": "ac58a442-1485-474c-949e-491dd230e044",
"metadata": {
"tags": []
},
"source": [
"# Pareto smoothed importance sampling leave-one-out cross validation\n",
"\n",
"##### Brett Morris\n",
"\n",
"In this tutorial, we will construct a linear model with numpyro and carry out Pareto-Smoothed importance sampling Leave-One-Out Cross Validation on the results. \n",
"\n",
"To begin, let's import the necessary packages. In the example I'll assume there is only one CPU core available – you can increase this number to fit your machine."
]
},
{
"cell_type": "code",
"execution_count": 1,
"id": "7ac4a0b0-8e77-4d0f-9805-4c03d49e4448",
"metadata": {},
"outputs": [],
"source": [
"number_cpu_cores = 1\n",
"\n",
"%matplotlib inline\n",
"import warnings\n",
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"from scipy.special import logsumexp\n",
"\n",
"import numpyro\n",
"numpyro.set_host_device_count(number_cpu_cores)\n",
"\n",
"from numpyro.infer import MCMC, NUTS, Predictive\n",
"from numpyro import distributions as dist\n",
"\n",
"import jax\n",
"from jax import random, numpy as jnp\n",
"\n",
"import arviz\n",
"from arviz.stats.stats import psislw, _gpdfit"
]
},
{
"cell_type": "markdown",
"id": "6cdd7639-cd99-4cba-91c8-8d22686ffd8a",
"metadata": {},
"source": [
"Now let's generate some simulated observations $y(x)$ where \n",
"$$y \\sim {\\cal N}(a x^2 + b x + c, \\sigma)$$\n",
"where $\\sigma$ is the uncertainty on each observation, and the mean is a quadratic function.\n",
"\n",
"We'll begin by including no significant outliers, but you can adjust the number of outliers with the ``n_outliers`` parameter."
]
},
{
"cell_type": "code",
"execution_count": 2,
"id": "67926f21-6bd2-4532-8c8b-2dbadb37a8bf",
"metadata": {},
"outputs": [
{
"data": {
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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"np.random.seed(42) \n",
"n = 25\n",
"true_slope = 2\n",
"true_int = 0.5\n",
"err_scale = 0.5\n",
"\n",
"x = np.linspace(-1, 1, n)\n",
"y = 2 * true_slope * x ** 2 + true_slope * x + true_int\n",
"y += np.random.normal(0, err_scale, n)\n",
"\n",
"# Set the number of outliers in this dataset:\n",
"n_outliers = 0\n",
"\n",
"if n_outliers > 0:\n",
" outliers = np.random.randint(0, n, size=n_outliers)\n",
" y[outliers] += np.random.normal(0, 5 * err_scale, len(outliers))\n",
"\n",
"yerr = 1 * err_scale\n",
"plt.errorbar(x, y, yerr, fmt='o', color='k', ecolor='silver')\n",
"plt.gca().set(xlabel='x', ylabel='y');"
]
},
{
"cell_type": "markdown",
"id": "ab2852b1-274e-43f5-bec6-65a248280042",
"metadata": {},
"source": [
"Let's construct a simple linear model with ``numpyro``. The model computes the linear regression coefficients $\\beta$ which give $y = {\\bf X}\\beta$, where ${\\bf X} = [{\\bf x}^2~~{\\bf x}~~ {\\bf 1}]$ is the Vandermonde matrix."
]
},
{
"cell_type": "code",
"execution_count": 3,
"id": "65c2562a-7051-4189-bc5d-c5e3ae1a9353",
"metadata": {},
"outputs": [],
"source": [
"X = np.vander(x, 3)\n",
"\n",
"def model():\n",
" # linear regression coefficients beta\n",
" beta = numpyro.sample(\n",
" 'beta', dist.Uniform(\n",
" low=np.array([0, 0, 0]), high=np.array([5, 5, 5])\n",
" )\n",
" )\n",
" # uncertainty on y\n",
" sigma = numpyro.sample(\n",
" 'sigma', dist.HalfNormal(0.1)\n",
" )\n",
" # define the linear mean model\n",
" mean_model = numpyro.deterministic(\n",
" 'mean_model', jnp.dot(X, beta)\n",
" )\n",
" # define the Gaussian likelihood of observations y\n",
" numpyro.sample(\n",
" 'obs', dist.Normal(mean_model, sigma), obs=y\n",
" )"
]
},
{
"cell_type": "markdown",
"id": "fee942a8-e86b-4063-b74f-3438ae8aa67a",
"metadata": {},
"source": [
"With our model defined, we are ready to sample from the posterior distributions for $\\beta$ and $\\sigma$. We'll sample with the No U-Turn Sampler (NUTS) for 5000 steps, after 100 warmup steps. By default the number of chains will be equal to the number of CPU cores you set in the uppermost cell of this notebook. \n",
"\n",
"We'll then run the sampler."
]
},
{
"cell_type": "code",
"execution_count": 4,
"id": "cf421342-26d8-4674-92ee-974a38ef1881",
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"sample: 100%|██████████| 5100/5100 [00:02<00:00, 2184.59it/s, 15 steps of size 4.77e-01. acc. prob=0.95]\n"
]
}
],
"source": [
"rng_key = random.PRNGKey(0)\n",
"\n",
"mcmc = MCMC(\n",
" sampler=NUTS(\n",
" model,\n",
" ),\n",
" num_warmup=100,\n",
" num_samples=5000,\n",
" chain_method='parallel',\n",
" num_chains=len(jax.devices()),\n",
")\n",
"mcmc.run(\n",
" rng_key,\n",
")"
]
},
{
"cell_type": "markdown",
"id": "16908ccb-d6dc-4b43-b3e4-146476301e8c",
"metadata": {},
"source": [
"For convenience we'll extract the log likelihood from the ``mcmc`` object using ``arviz``. We'll also define a variable ``b`` that represents the number of draws in the posteriors:"
]
},
{
"cell_type": "code",
"execution_count": 5,
"id": "d7ff774f-879a-40f1-9e73-128767cf0d02",
"metadata": {},
"outputs": [],
"source": [
"idata = arviz.from_numpyro(mcmc)\n",
"b = 1 / (mcmc.num_samples * mcmc.num_chains)\n",
"\n",
"# Stack the chain and draw dimensions of the log likelihood\n",
"log_likelihood = idata.log_likelihood['obs'].stack(\n",
" __sample__=['chain', 'draw']\n",
")"
]
},
{
"cell_type": "markdown",
"id": "cf65e833-e4d1-41c4-9916-1faa922f7c88",
"metadata": {},
"source": [
"The log pointwise predictive density or ${\\rm lppd}_{\\rm LOO}$ is given by\n",
"$$ \\log \\prod_{i=1}^{n} \\int p(y_i | \\theta) p(\\theta^{s}) d\\theta \n",
"\\approx \\sum_{i=1}^n \\log \\frac{\\sum_s p(\\theta^{s})}{S} \\\\\n",
"= \\sum_{i=1}^n \\left(\\log \\sum_s p(\\theta^{s}) - \\log(S)\\right)\n",
"$$\n",
"for posterior probability $p(\\theta^{s} | y)$ and samples $s = 1, 2, \\dots, S$. \n",
"\n",
"We can succinctly implement this log of the sum of the exponentials of the log-likelihoods with the ``logsumexp`` function:"
]
},
{
"cell_type": "code",
"execution_count": 6,
"id": "24b07369-75bd-4531-ac6f-f1b51c1f78a5",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"-14.095360571471577"
]
},
"execution_count": 6,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# evaluates the lppd for every point\n",
"lppd_loo_i = logsumexp(log_likelihood, axis=1, b=b)\n",
"\n",
"# the sum of the lppd's is the lppd_loo:\n",
"lppd_loo = lppd_loo_i.sum()\n",
"\n",
"lppd_loo"
]
},
{
"cell_type": "markdown",
"id": "9f37e1ff-eeab-40b3-97d2-b69bc668e44a",
"metadata": {},
"source": [
"The expected log predictive density ${\\rm elpd}_{\\rm LOO}$ is given by\n",
"\\begin{equation}\n",
"{\\rm elpd}_{\\rm LOO} = \\sum_n \\log p(y_i | y_{-i}),\n",
"\\end{equation}\n",
"where the leave one out predictive density without data point $i$ is \n",
"\\begin{equation}\n",
"p(y_i | y_{-i}) = \\int p(y_i|\\theta) p(\\theta|y_{-i}) ~ d\\theta. \n",
"\\end{equation}\n",
"\n",
"The importance sampling uses importance ratios: \n",
"\\begin{equation}\n",
"r_i^s \\propto \\frac{\\prod_j p(y_j | \\theta^s) p(\\theta^s)}{\\prod_i p(y_i | \\theta^s) p(\\theta^s)} = \\frac{1}{\\sum_i \\log p(y_i|\\theta^s)} \\Rightarrow -{\\rm loglike}\n",
"\\end{equation}\n",
"where $j = \\{1, \\dots, j-1, j+1, \\dots, N\\}$\n",
"<!-- Posterior predictive density is the empirical average over posterior draws\n",
"\\begin{equation}\n",
"p(\\tilde{y}_i | \\theta) \\approx \\frac{1}{S} \\sum_S p(\\tilde{y}_i|\\theta^s). \n",
"\\end{equation}\n",
" -->"
]
},
{
"cell_type": "code",
"execution_count": 7,
"id": "eaece49c-dafe-465e-94d5-1b2985c3fbbd",
"metadata": {},
"outputs": [],
"source": [
"log_weights = (\n",
" - log_likelihood - logsumexp(-log_likelihood, axis=1, b=b)[:, None]\n",
")"
]
},
{
"cell_type": "markdown",
"id": "181896db-8ae6-4df5-a562-c94f107e5aab",
"metadata": {},
"source": [
"Let's plot the pointwise weights for every posterior sample, and compare them to the expectation if all samples had equal weight, remembering that the Generalized Pareto distribution is given by: \n",
"$$p(y | u, \\sigma, k) = \n",
"\\begin{cases}\n",
"\\frac{1}{\\sigma} \\left(1 + k \\left(\\frac{y-u}{\\sigma}\\right)\\right)^{-\\frac{1}{k} - 1 } & k \\neq 0\\\\\n",
"\\frac{1}{\\sigma} \\exp{\\left(\\frac{y-u}{\\sigma}\\right)} & k = 0\\\\\n",
"\\end{cases}$$"
]
},
{
"cell_type": "code",
"execution_count": 8,
"id": "1352cbbd-c293-4e27-b4b6-94cbacc484d0",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"reff = 0.8030332158992549\n"
]
},
{
"data": {
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\n",
"text/plain": [
"<Figure size 720x864 with 25 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"# effective sample size\n",
"ess = arviz.ess(idata, method='mean')\n",
"# relative mcmc efficiency\n",
"reff = np.mean([ess[v].mean() for v in ['beta', 'sigma']]) * b\n",
"print(f'reff = {reff}')\n",
"# choose the length of the tail to consider based on n_samples, reff:\n",
"tail_len = int(3 * ((1/b) / reff)**0.5)\n",
"sorted_probs = np.sort(np.exp(log_weights.values), axis=1) * b\n",
"\n",
"def khat(k, M):\n",
" # Regularization for khat\n",
" return (M * k + 10 * 0.5)/(M + 10)\n",
"\n",
"gpd_k, gpd_sigma = np.array([\n",
" _gpdfit(p[-tail_len:] - p[-tail_len]) for p in sorted_probs\n",
"]).T \n",
"u = np.finfo(float).tiny\n",
"elws = np.array([p[-tail_len:] - p[-tail_len] for p in sorted_probs])\n",
"\n",
"panels_per_side = int(gpd_k.shape[0] ** 0.5)\n",
"fig, ax = plt.subplots(\n",
" panels_per_side, panels_per_side, figsize=(10, 12)\n",
")\n",
"counter = -1\n",
"\n",
"for i, (k, s, elw) in enumerate(\n",
" zip(gpd_k, gpd_sigma, elws)\n",
"):\n",
" weight_grid = np.linspace(0, elw.max())\n",
" ax = fig.axes[i]\n",
" ax.axvline(b, color='k')\n",
" counter += 1\n",
" ax.hist(\n",
" elw, log=True, density=True, \n",
" bins=10, alpha=0.5, color=f'C{i}'\n",
" )\n",
"\n",
" warn = 'r' if k > 0.7 else 'k'\n",
"\n",
" ax.set_title(f'$\\\\hat{{k}} = {k:.2f}$', color=warn)\n",
" ax.set_xlabel('$w_i$')\n",
" \n",
" gpd = 1 / s * (\n",
" 1 + k * (weight_grid - u)/s\n",
" ) ** (-1/k - 1)\n",
" ax.plot(weight_grid, gpd, color=f'C{i}')\n",
" plt.setp(ax.get_xticklabels(), rotation=25, ha='right', color=warn)\n",
" \n",
"while counter < panels_per_side**2 - 1: \n",
" counter += 1\n",
" fig.axes[counter].axis('off')\n",
"fig.suptitle('$\\\\leftarrow$low lnlike \\t\\t\\t high lnlike$\\\\rightarrow$')\n",
"fig.tight_layout();"
]
},
{
"cell_type": "markdown",
"id": "1e6ae487-ce66-48aa-94a4-54d9f4af4c93",
"metadata": {},
"source": [
"Let's plot the posterior draws in the data space for all samples (left) and where the opacity of the line is weighted by the likelihood weighting (right): "
]
},
{
"cell_type": "code",
"execution_count": 9,
"id": "b5fcf704-5c68-4c42-879c-64c80b009215",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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o8NPti32cTYW5VopmCpHSeoJW/GELNgX1XWbRZ5fXlPjMtECmVbMkp5/lJfFrgyRoISbJdXd4WP/NpWz4QiYNt5bTu85zyP296zw03FrO7uttLFxQjsfjifFIQohkWuPx8OHLL+Uj5x3DhSeV88c/emj2wkAAlBU613tY+83j+PFVLpYvjV8syyIxISbBb+7zcPd3KtB+LwChjlo6HqwAIGelm951HjoerEAHzP21tbVUVJj73W53chothDiCx+Oh4rMV9PebWN3fUMtf/qeCcjc4T3LjfcNDjaeCkD/+sSw9aCEmwVe/UXkgOQ/SAS9dj1UC0PVY5YHkPMjr9VJZWZmwNgohRnbTTZUHkvOgkN9L3V8qsSjY+7fKA8l5ULxiWRK0EBPU1AudTXVR7wt11B3y/+Hq6qLfLoRIjvr66DEZ6Kgjywa+tsTFsiRoISbop2vBlu+Kep81crs1xv0uV/TbhRCJ5wvC7LnRY9Ke78Jug9zixMWyJGghJmB7Gzz4Lpz+qSqU/dBKBcruJG91FQCnfKIKp/PQ+51OJ1VVVQlrqxBieM1e+K/KKrKyjozl+R+oosAJ19yQuFiWBC3EYYYWyR/JD18Bpw0sJ7jJv7o60lNWWPPLyL+6mpyVZtHIUz90U11dTWlpKUopysrKqK6ulgViQsTRWGK5P2BKeH74ajffvKOanKK5gMKeX8a8/1fNvHPcLC6Ab34hcbEsq7iFGKe1DfDsHli9xGyOkbPSfSAhD+U+DmZkmhWey5YtA2DFihUJbq0QYjhNfWDF1NNecq6bc25fRUNvBmGLE6cdCjLhooVQkpO4WJYetBDjoDX84GUoyYa3mmIfZwG+e36iWiWEGI8eH/QFzLaRTT2wsRHa/RYChLFYwZEBy4rhtHmTvyHGcCRBCzEOj++EDfvhvDKzw00s3z4PbLIhhhApS2vTe7ZbIByGLa2wvR28fhugsFugJAsuXgwz41TSMxYZ4hZiDDZu3EggrLjjrRNYUgAvDXNlRYYVrlmRsKYJIcZo48aN9ASsFJQvJy8DajphU5NJ2KHITu7ZDjixFE6ek/j2SQ9aiDF6urGQmi44az409sY+7jeXJ65NQoixC2vo8NvJtJpa+pubYHsrDPhBo7ACs3Ph0sUmUSeaJGghxsAbtPBgbQmnzjULw2IpzIJzyhLXLiHE2HUHbAS1IscB9Z1m2qqtH4JhsKDJdWhOnUtcN8QYjiRoIYbweDysWrWKk046ifLyI4vg/7l+Fl0BOyfNhhZvjAcB/vSR6LevWLFCVnALkQAjxXIwbLaTdFpC9PhhQxPs7IB+PyggOyuHo2fnctlicESZDE5ELMsctBARHo+HiooKvN7oRfBrOuEv9bM4p7idh94tiPk4y4pgYX4iWiyEiGakWAZTolcDmbYQO9th0z7o8IIOm4Wd+ZlwtguWFiXrp5AetBAHVFZWHgjoQUOL4H/3RbBZNPOcA7QPxH6ch2P0noUQiTFSLPcHoNMHubYgXX4bb+2H3Z0Q8AMWyHTA0cVw2RKwJjFLSoIWIiJWsfu6ujqe2wPP7YEPz2/ir3tnxXyMz5+UnMUkQoiDhotlMIs77RZwWDT1vXbebIQePwQ12BQUZ8NFi6F0RiJbfSRJ0EJExCp2P2++i1tfgOwtHn712VPZep2DhlvL6V136JyWXcGN5ySipUKI4cSKZZfLRUc/9Afh+b95+PD7L+W6VUfx6LXltLzqwWaDnAyzKOzc+QludBSSoIWIqKqKXgT/PZ+u4t3nPOy+r4LulgZAE+qopePBikOS9JoPJrjBQoioYsXy975fRXMfPPOoh+u/WEFL0z7QGn97LQ0PVNC9zsO8PHjfEsjNTFLjh4h7glZKWZVSG5RS/4j3cwkxEW73kUXwf/iLatYWuvE/VYlv4NA5LR3w0vWYmdMqzYHTU+CMO54klkW6iBbL1dXVXHiFm6CGn1RV0t9/ZDw3/r2S0+fBSUkoShJNIlZxfwXYAiR5NF+IkR1eBP+Lj0N4N/S1Rp/TCnWY25/4WMKamEwSyyJtHB7LA0HY1WE2vdhbHz2efe11rFoC9hQpzxvXHrRSah6wGrgnns8jRDy8Ug//2AFfPAWyCqPPaVnzXVyyEPITXKM30SSWRbpr7DELwPIyYdac6PFcNNvF4sIEN2wY8R7i/hnwdSAc5+cRYlIFw/CdF2DeDDhpNmReWoWyH7mJ+8zVVdz1viQ1MrF+hsSySFNdA+ANwqxsaO6DCz5ThcVxaDzbMswcdSqJW4JWSr0PaNZarx/huAql1Dql1LqWlpZ4NUeIMXl8XzHb2+Dmc6DyX2av5/yrq7HmlwEKa34Z+VdX8+Mb3FgSuP1cMkgsi3QWjuxWlWUDhxU2N0NomZu5H6vGlj8fUGQVlXHDbdVc+59H7ueeTPGcgz4LeL9SahWQCcxQSq3RWn986EFa62qgGmDlypU6ju0RYlQ6/Tb+WDOb88rMtZG1Xeb2nJVuclYeDOAsG3xqRXLamGASyyJtdfhtZIRhXq7ZGvaVWqjpgJwVbhau+AC5tjBXHpfLV85IdkuPFLcetNb6m1rreVrrcuCjwD8PD2ghUtF9u0vxhxXfPBtueT72cQ98KGFNSiqJZZGuAmFFd8DGzAzwhWBdA7y5H7wBU2/bAczNCnDZEnCmYIEhqcUtxBBv7IN/NhVy7cnwt23QF4h+3KKZsKI0oU0TQozRrIUnkBs0lcE2Nprec1MfhIJgs0GuJcQJRb0sK4ldWz+ZEpKgtdbPA88n4rmEGK+BIHzjWZibCx9fDufeF+tIzZoPTvGJ5xgklkW66ByA3oCpUdDeD6/UwTut4IvsVpVlhwVZA5xe2JMyl1UdTiqJCRHxy9fNdZI/uABuecEsLonm4tmtzJErgYVIWYEQ7O8Fpw1yHbCpCf7dYJJ2WIPdAXPz4LSibkqcMYbJUoAkaCGAzS1w13r48DEwO9tsjBGNXYX57JJ9iW2cEGJM9veZRDwnF/Z2w8t7YE8rBAJmd6oZWXDGXFhR5MWawoNhMgctpr1gGL7+LMzMgJvPhSseiH3sr1dbOHXRCYlrnBBiTLp95mOW0yTptfXw+j7whiL7P9vh6AK49Cg4btbxyW7usNKqBx0ImTdTISbTPRvg7Wb47nvMPFVNV/TjTpgFFy1KbNumMi0XYolJFgqboe1MGxQ5YVsLPL/H3BYKmeRcmgsXLITFqbku7BBpk6C7fHD5A3DvxmS3REwlezrgJ/+GSxbBBeXwladiH/urVQlr1pTX5TPXpMaa5xdiPPb3mk7c3FxoH4CX6uHtFhgIgFWZS6lWzIZzy00ST3Vpk6Bz7WCzwI9fNXMKQkxUWMONz0GGFb53Plz3JARijNB86RRw5SW0eVOaVZk30Pb+ZLdETBW9fuj0QaHT1NxeWw8v7IEOr1m1nemAhTNh9VFQ7Bzp0VJD2iToHj/UdII/DDf/S4bHxMT98R14rQEqz4FWLzy9O/pxeRlw3amJbdtU5wuCPwhNvebyNiEmIqxhX48p5VnshB3t8M89sLsdQhpsVpO4L1gAx84yC8XSQZo00+xA8u1zzS/inzXw5K5kt0iks8Ye+MHLcOY8uOpYuOpPsY/96SXpMRyWTgqyzBtp1wC09MkJt5iY5j4z+jU3F3p9pue8rsFskKGAbAcsnwXnL4QZGclu7eilTYIG+MixZmm8RZledI8v2S0S6UhrswFGIAy3XwDfe8kUNIjmHJc56xaTSymYnQPZGaayU7fEshgnbwDa+s0+z1k2eG0vPFcDrX2ANkPb82bAZYvNArF0kjYJuj8AH7q/i4X2BqwKWrzwo38nu1UiHf19u7nO+atngNMee+GhRcFt701o06aN19Zv4oV17zI7B/whaOyVKzTE2OnI0LbdYraS3N0Bz+6C3W3m78lhgfwMOHM+HF+afiNhaZOgu32woWMGD9SW8vmTzW33bYJN+5PbLpFemvpMlbAVJfCfK+CyP8Q+9iunysKweOny29jnzSAcNkPdrV7zIcRYNHvNJhilOeYy3H/tMutK+oJgxYzQHFUElyyBwqxkt3bs0iZBZ9rAojQhbeFfNbC0wAyTff1ZOfMWoxPW8NWnzZDYjy6G324wIzHRlGTDtSsT277pxGkNEQgrajrNfHSW3Vwi0+dPdstEuujzm5O6/EzIzYDX6uGp3dDaC+EwZGaYIe3VR5kT7XRZGDZU2jRZa7MaD8x1bRcsMLdtbYPfbkxq00SauHcDvFgHN59j9ob93suxj/3BBek3HJZOAmFFIKxo85pFYrOzzc5hjb1ybbQYWSgMDZFV27NzoL4TntoJOyOrtjOtMDMTznTBiXPSa2HYUCMmaKXUl5RS+YlozHDqu8CsxzOqN8BHl5nP/0eujRYjeLcFfvgqXLwQ3MvhEk/sY69YOnUXhqVKPHcFrXQGrAyETMESpUxPqLlPro0WI9sXWbMwL9ck62d2wyt7Ta96cGh7WbEpQFSSnezWjt9oetCzgTeUUg8ppS5VSiWltPjhL3IwbHYomZ1tFpl8S66NFjH0B+DLT5oz6h9eCI9uhdoY5TzzM+HW8xLbvgRLiXh26CCNXhvdPujzmRoHRVmmGFFDj1wbLWLrHIjU2s42UyNv7IPHt0FLr7nf6YD5M2D1Epg/0/Sy09WICVpr/S1gCfAb4D+AHUqp25RSCa1K/I/tB1p04LbNrXDxInPLv2rk2mgR3fdfMkNfP7kIsu3wX0/HPvaHF0J+Gi4mGa1Uied3u3Ko682kvhN6AqbX3DFg3nS7fdDcKyfc4ki+oKlhkG03tbb398Dft8LODghqyLJCvhPOK4djS0yRoXQ2qjlorbUG9kc+gkA+8Cel1B1xbNshtj3voeHWcuqut9Jwazm968wYpedtuDAyHFn5T7meUhzqmd2w5m347ElwThmcf1/sY69YaobEprpkx7PH4+H2T5/DPz5dzB1XlfPUox76/GZUw67Mm+r+XollcSitzeiKUqYgyUAAntwJL9SZ9Qt2ICcLlpfA+QugJMccm85GMwf9ZaXUeuAO4BVgudb688DJwJVxbh9gAvpn36og1FEHaEIdtXQ8WEHvOg8hDXVd5oyqrR9ufSERLRLpoKnPrPI/thi+dgbc9pKZu4pmGgxtA8mPZ4/HQ0VFBR3N+wCNt7WWB26v4JlHPHQPQF03FGeZ3tDeHjN9JQSYS6r6g2Zlts0CL9fBX7dAe59JZFkOcM2A9x0Fc2ek99D2oNH0oIuAD2mtL9FaP6y1DgBorcPA++LauojKykr8A4deD6MDXroeqwRge/vBXvSftsATOxPRKpHKwhpuiFxS9ctLza5V//dm7ONvv2BqD20PkdR4rqysxOs9NJZDPi8P3VmJ129WdHf5zV6+Hf1mCFOGusXQS6ryMmBbKzy6Bba19OHT/WTYzPX0711grntO96HtQaOZg/621ro2xn1bJr9JR6qrq4t6u+lRG//YAWfPN+u8v/6sWQ0qpq/fbICX6kz9dlcerBqmIMn7j4JLFyeubcmU7HiOFcs9LXXUd5th7bpOc4lbboa57KpjIN6tEqns8Euq2r3wl83wRgMMYMVOmBmZcEIpnFNuEnW6D20PSovroF0uV9TbrfkHbw9pM281M9PU6L7haTnznqo2btzIxo0bY97/bgvcEbmk6mPHwRV/hFgjpQVZcOv5cWikiCpWLGfku9jSAp39pue8tzty5YYyl2HJqu6pa6R4PvySqmd3wZM7zEYrNsJkKliYD6uWmL+ZjClUvyAtEnRVVRWZWYdu4KnsTvJWVx1y284OOL/MrOp+sc4sIBPTS9cAfP6xg5dU3b0eNrfFPv6295okLRKjqqoKp/PQWLY4nMy+oormXnNy1eszPeeuAfOG2+0z9ZalgMn00+Y9eElVps30mv/4DjT1m16ynTBFjiDvXQCLCk3cTyVpkaDdbjf33F2NLd8FKKz5ZeRfXU3OSvcRxz66DS5daD6/9UVTPF1MD6Gwud55Xw/87yozFFb1SqyjNZcfZXa4EYnjdruprq6mZHYpKEVucRknf6aaotPctA+YgkQ7O6B7wFwbbcWcQDX2Sq3u6abPbxZ65jrMJVW1nfCHt2BXu4n1TBvk20IsK+zljPlTa2h7UNoMBqy+0s2Stqvo0zaGVhSL5qV6WDDTBPiXnoC/fdSs+hNT20/XwvO1cO2SetjfzupXT4hxpGaGPch3z7cntH3CcLvdLFi6nLq+DJodS9neBjvazQKx9n7zBpyfaYYqazthYYFZ7Le3G3IcZgcyMbUFQub3bbdCy+6N1AcVLw2cwGt7zXRHptXs8bwgw8+Zxb3MmmJD24PSKm2FLaNrbl8AMixgVWbI7Fevj/w9I82DiNT25E745etw9TK4tLSNmzcsZCDmJTqKLx61V4a2k8gXthDUFo4vgdkzoGymecP1BqGpF7a0QpcPmrxmweesLBPXe7tN72k4EsvpLazNuoOwNhXBANY25/DUdrO+yKZMMl5QAGeVdFGYGZxyQ9uD0iZBz8yED7uaGKn3PGhrO5w+z3z+87Xw0IvbJWinqB3t8N9Pmy0kv3s+PN5QyJbe6Duz967z0P79+Xzh4kWUl5fj8QxTlFvETa4tSI4tRIYDjp9lrn0un2n27+3ywfZ9nbyypYlOnxn29oVNKdCmXjPsKUl46mrsMdc7z50BGVbY0ZXJE/sKaOwz7/4ZNpiTA84tHr79yXO59MzlLFgwNWM5bRI0wJXzmzlvVvuoj3+5HpYVQRi4Y3M5A6G0+nHFKHT7oOLvkGWDu1bD5hao3jUv6rF96zx0PVRBb+tetNbU1tZSUVExJQM71dksUJrlI9dh5g6PLjaVn2Znm6svOoMZNHgz2N1qFgrVdJi6y04H7O2CvqDE8lTU3g+dPvM3MSPDTFP+tb6QfV4HYQ0Ou9nXOXO7h/urKmhpapzSsZxWf+VKwZeW1nNCCVhGuRhgdyfk2KHF5+A3u+bEtX0i/jweD6tWreKkk06irKyc99/koa4b/ne1GRL70EMQa5Sl6/FKQv5DVxp5vV4qKyvj33BxhAyrZn4eZNqhPB8WzjTXrBc5QaPp8FvZ1m4qijX3muHtggwIaNjf75B94KeAofHsKivnnvs85DrMqu3mPvjDJtjS7qQfKw6LeS8/bja8dG8lA/1TP5bTKkEDOCyauy83QTyaJN0fPFgh6unGIv66Lb7tE/EzWCaysdGcNdfV1fLiLyu4sNfDsmK4+P6hW6kcaWhhm6FiFc8Q8ZeXYYYyM+1wTDGUFZhknWUNMxC20dQDm5vNKu69XdDtNz2o7oCN5gGH1DpIY4fHc31dLbf8dwUv/N1DzwD86R1TFbIXC1bCZNpgcSGsPgr275sesZxWCXrFihWsWLGCkmy493KwW0Y3I13fDa4sc7b11Wdga2t82yniI1qZSB3w8uRdlVzxAPQOU8zik8fHLpIR63YRP4OxDKa3NDvH1FI+ttj0omdnDOBQIXoCJn63tJj5592RGa5sW5CWAYdUDExj0eJ5oN/LtyoreWI7PLLF7K9gATIIMyfXlHReVADz50+PWI5bglZKzVdK/UsptUUp9a5S6iuT+fjLS+CnlwzfYxqqrt/J7Mx+/CG45q9mIYpIL7HOjuvq69gZud69d93grmcWGm4tp2+d6V1XnhO9SIbT6aSqqirKo4pB8Y5lMLsTFTnNYtBjimFOTpDZGT4s2hQu2dMBO1tNVamaDnBaw9gtYWo7JZbTVax4rq+v4/53zGKx7jc87Ll1Ke9eP4OXvlpO81oPs7LhttumRyzHswcdBG7QWh8DnA58USl17GQ+weolcP1poz1a0zbgINdhgvy6xw9WJho6DyIre1NXzJKvM83tves8dDxYQaijlsFdz9ofrODiPg+ZtoNFMkpLS1FKUVZWRnV1NW73kQVvxCHiHssWBWV5pihJSQ7Md/qYnROgNA+0MvW4t3dAbbvZ8ardbyfPESSoTfIeLAUqsZw+YsVzVqGLunboesND4wMVBDvqAU1nUy3f/u8K/vqwZ/rEstY6IR/AX4GLhjvm5JNP1mMVCmt9wQ1rtDXfpUFpa36ZLvj4Gu36mT7wUfDxNdqaX6ZBaXtBmS76hLn/p69pvWbNGu10OjWmM64B7XQ69Zo1a8bcFhFfd/92jbY4Dv1dKbvzwO/b/I454qOsrOyQx9mwYYPesGFDUn6GyQCs0wmK22gf8YplrbX2+rW+7c41umDWHI1SOre4TB9TsUYv/5XWJ96p9fvu1/oDN67RM4vnaqWUnjOvTFf+bI3e2qL17++XWE4n/3fvGp2Zdejvy5bh1PM/tUYf83Ot7aOI53SPZa2Hj+dEBXQ5UAfMGO648QT1mjVrdJYz9pt2wcfXaGU/9H6L4+D9JXNH96Yukqs/oPWVD2k965NrdOGsOVqpI0/GQEX9XSqlDnmsdA/qZCboeMay1tHj2Zbh1Es+vUYv/6XW5des0dbDTtIys5y68mdr9Nx5EsvpomtA63eatf753Wt0aWmpVkrpGbPK9MJr1uijf6H18b8cXTyneyxrPXw8K3N//CilcoAXgCqt9SNR7q8AKgBcLtfJtbVRd8KLqby8nGjfY80vY+4tNTTcWh4Z8jyUo6CM2d+uoe56C9FmspVShMNyHUcqCIXh84/D07vgV5dBTuc7XPPvYwkfNkMT63ddVlZGTU3Nga8HC1wMLlJKN0qp9VrrlUl43rjGMsSO5+yiMo75Xg2bbionEOV3PHtuGU376oj2fiaxnFq8AXN9c6bNFKd56Y23eGRPIW/2zKWjH1DgtME7N5fT3zp8PKd7LMPw8RzXVdxKKTvwZ8ATLaABtNbVWuuVWuuVxcXFY36OkfaKjnVpjb+9jsKsQ7esHGqqrQZMV1rDzf+Cp3bBLefB2S743NpjjkjOAHmrq1D2qb9wJBkSEcsQO5772upYMBMCMeK5aV8ds+ZILKe6gSDUdZka2648s2PZ0/vyWdeWQ0e/WW+QYYVZOfDhLx25i+F0i+d4ruJWwG+ALVrrn8TreUbaKzpWArbmu2jrh1nvlzf1VPbzteB5B764Ej50NJz5GxgIW6Mem7vSTcnHqikqmTO1F44kWKJiGWLHc9FsF8tnmwVE0RSXurihsoqMaf6Gnsr8IZOcBxcE9vrg4XfhtaYZtAdsaKtJzjMzTZnmr1/r5se/mgYLwYYRzx70WcAngPcqpTZGPlZN9pNEu3QmM8tJ0eUmKKP1qobuJW0/0U3B1dVY88tgmv4RpKo/vG12qPrIMXDtyXDGvdA3zLXOGrj3W26eefIx3nzzTWpqaqL+HodegytGJSGxDNHjOSvLyedvrGJhAVz02SosjkPvt2U4ueizVZyxys0tP6qmYJY5QXO5JJZTRShsknNYm56z1w8PbYbHt8H+ASsaK3ZghgNOngOXHWUKTH3+GjePP/54zHie6rEctw26tNYvM9qdLSZg8Bf2ta99jf379+NyuaiqqsJ1tpv/+BsH9ozueuwmQh31WPNd5K2uOmQv6dyVbrJXugHNr1erSd8jeCrMkyTaU7ug8l/wnnK46Ww44zfDJ2eAG88y+zvLHgqTK1GxDLHj+axVbmq64ANXufGH4J/3fBN/x17s+S6WfKSK3JPcrGuEC69wU37sKfSHrbznxEWUz5zc9kksj11Ym+TsD5me80AA/rwZntxuqsNprFgJkWODo2fB5UdDcaR4zVTb33mspsQOmm63m2XLlgGHBs6dl5nFRTkr3eSs/Fjk1iN/42HARoggVr74ODxwJZw6N/7tFtE9txuuewJOKIHb3wtn/c5sQzicq441vWyR/qLFc1ibOA2G4UNXuZm57EJ29zkZ0LkoZa6RBlNdsJgQDmWSgs0C82bIG32yhLXZjcwbNL8HXxD+sg2e3AF7O8EP2AhiAxYUwQeWmuNKssGaVnUu42NKvwSXLoYfXTT41fARGsRCliVESMMn/gLbpBxoUjy+Az73GCwthJ9eDO+536z6jMWi4Ix5UPVeeROeygbnLctmwvyZsHiGjwVOL7kZZmqjow92dJi63e905uC0BnFYzWrhJikHmhShMNR2Qm/AVIoLBuHvW01y3tMBAxrsCnKduSwsyWX1YlhcZArVZEyJruPETekEDXDlMWaPYGO4d3BFf1iRZTMrDT/yJ2jojn/7xEF/2QpfegKOL4GfXwqX/WH45GxTUJ5ntpl0RF83JqYQqwUWzDQfJdlBluT5ObrQ7HAUBNp6YVsb7OrK4O2ubPIzzfftbDdbVorECYWhtstsVjRvBgRD8I8d8NROqGkDvzbxm2mD0ly4ZBGcNNcMbTvtyW596pjyCRrgUyfAJxfsG8WRFvqDZiVhlw+ufBg6B+LePAE8+C5c/xScMhduPQ8uuT9E/zDD2nYL5GTAb68wqz7F9GCzwMJ8mJvlY7YzwImlZrQly26GwNt7obbPwY7uLF6ph5kZJllsbZNYTpRgGGq6TEdn3gxYt+Ed7v7nHp7aYU6WBgaTs9Xs+3zRIji73JR5zctIdutTy7QZSLjS1UyWNcT/7Zw/4rH+kPkDauyFDz8Mf/+oeQMQ8fH7TXDz83BeGXzkWHj/AxAmdpd4cBez6vcRdRGQLOCZ2uxWmJ/tw6LAWmASs9bwThv4/NAZtFPfAxsbIRA0UyCtPtjSCsuLzYmdiI9AyPScAyEzrN3mhX+35PJ6cw7NQfCFwaog02J6y5csgXPKzIrtImf0x5zO8TxtEjTAqrltLF8yny8/eXCjjGg0ENRmeGFHO3zyL/DHK83Zu5gcg6th3wiv4PsvmW3klhSYIe7hDP4O/u99cJos5Ju2bBaYl+0jr8h8HQybpLC1AwZ0Nn1h2N5qkrdfw5lzoMMPm1vNFErmtHrni7+NGzcSDENe+QqCISjNgX3d8HwdrGvJobHXTsBu1hJkWqA4B967AM4rN8m5JDvZP0FqmjIpZ6Tr4Qbvv/wouO8K0wsbSRjTU3t9n1lVPJ6qqLK7TmwP1Zbw/ZfM/NNAEH69fvjjrcr8Pu5abYJbTF2jieeTT1zBwnw4rhgWF8IJc2BxPjjs4A9Dax9sb4a398OLe8FpNbtivdtsVhOPlcRybIGwYl9/BsGQ6Rnv7DCleV+ugYYeK33YUMosCivMgXPL4MLFMDNLLqcazrQ8jzy3DB7+CHz0zwe3qYtlMCc/vhP++2n48cXmLHA0PB4PFRUVBzYlr62tpaKiAmBaF08IheF3u0p5dG8JFy+Ed5qgoXf477EoE8R3roILFyamnSL1WZRZ2W2NTHuENYQwq4QDQejoh1Cb6WGHQnDCbGjxmuHuY4pGv1pYYjm2gSA09mcQ1mY9yJZW+HctvLEf9neBHwdWNA4FhblwjgsujRQikeQ8vLhvljEWK1eu1OvWrUvY821vgw89BD3+0RytAcVFC00PbjTD3bEK/x++ecN00uODrzwFz+2Bkwu6eKcrD19o+O+xYIL4V5fBqiUJaWZKS9ZmGWOR6FgG2NcDbzaaued3mswlVgNB8/eTmwGumXDcLMjq24Xdqjht2UKOnTW64W6J5ei6feZql23btpJhCWErWcar9bBhH7T0mfU8fn8fNh1iVsEMznLBFUebBWGluaPv7Exlw8XztOxBDzqqEJ5yw/segPb+0XyH5pndCvcjcP8HR760J1bh/1i3T3U1nfDpv8PudpOc17fPGPF7FCY5/1KSsxjBnFzTk7ZgpkPsCnZ0Qn/AnBjWdJie9CyyKM/x0dADIR1J2iMsApVYPlJLHzR7zWttUyG2dmfR2gtvt5jphZAGLODQQbKzNKfPg8uPkuQ8FlNmDnq85s6AZz8O83JHOlIxeB31aw3wwQdN4A8nVuH/w2/fuHHjgUVTU9XLdWZ19v5ec+nF+va8mMf2rvPQcGs5dddb2HtrOR/0e1gtyVmMQkk2nDbP1HM+vhSOLYRshxn67vVDXQfs6M5kV28G3QOwpxM27jf3DUdi+aCwhvpuUwBGAeEwbOtysqnVycYmk7hDZsCRntc9vPPd43jh2gL+7xPlvPSYR5LzGEz7BA1Q6IR/fhIuGMPCo3daYNUfzJl5LNEK/0+33XW0ht9uhE88aqYFvH6oO1AA5sgo7V3noePBisi+zppQRy133VIhC3LEqBU64SwXnD4fjpsNy4ogJ9Mkjb4g7PdmsL0zky2tJn63tsL6RrP1YSwSy4Y/ZE5qBgu/9Ppg/T5Y3+Zkd28W7b7IFTIaOtZ62Hl/BQPte0FrGhtq+cZXKvjjHySWR0sSdESGDe59P3zjzNF/z+5OuPB+sxAlGrfbTXV1+m6XNtHegC8I33gOvvMCOB3Q1m9Wxpsechl111touLWc3nUHA7brsUp04NCyT16vl8rKynG3Q0w/2Q44Yz68ZwGsmAPHFkFBpjlhHAgr2gbsvNkI7+yHfj+83QT/rp+6sQwTj2dvwExPtXlND3hfN7y+F+7+nYdHvnIKL30+nze/UU7bWg8OGzT8rZKQX2J5Iqb1HHQ0XzgFVpTAx/8SGaY5RGTcZoj9fXDGb0LcuXILF5x+3BGPF2sjj6muqReufQze3G9eMW9kCHGwhzyYhEMdtXQ8aFbD5qx0E+qQuT4xOWwWWDEbZmSY6oBWBVvaoLkbfGFFex9sDJjh7aVF5hrpLh8U971NQUboiHidrrEM5sSltgv6ApBhMRXBNu2HJx7xsL66gnAkEfvba9njqaAkF7xtEssTJT3oKM50wb//E3Idh98TfeKkP2TlM2uX8WJNvFt2pFSb89IaHtkK5/8eNuyP3IbpOUP0HrIOeOl6rBKLgozC0c31CTEaSsGiArNy+OxyWD4L8u1+LBYL/hB0D8C7bbCuEXoGzBz1S0357O07IvjjLtViGUzxl5pOUyq11x8pm9pidpx7sxHe/mPlgeQ8KOz3sv3hSubMlVieKEnQMZTkwIYKU91q6KKlw4dkDU0YxSf+Cu5HRl5wMlW19MHHHoH/esoMh1mjnM/E6iGHOuo4aTb84n9krk9MvuJseP9SsG32sOmW43j7yzm8e3M5LWs9BPywpx3W7jVXc3T4FS+1zOS53dA3TWMZoLMfNjWZa8otmFGw9XsjG160m9dmIEYvuW1/Hd/9vsTyREmCHobdCtdYPHQ/fOiipY4HKw5L0orBkiYv18Pxd0H1uvFVK0pXv38LzvwtvLo3ct0yplzq4az50c+ec2e5+MOHoOKa9J/rE6npb3/yUP2dCvpaGwCNv72Whj9W0LTWQyBs5lZf2wstXhv+QJi1++DPm2FXm1kcNV0Ew2ZXsDf3mxoRmTbY3wP/3GPe35p7YSBketeOgujxPG++i09/SmJ5oiRBj6CyspKgL/qQ7KEOdhdDGqpegTPvhT9viTaXfVC6lw/c1Q7n3wc3/yuyyYglsnlBjOPzVleh7IeeVdsznfz6J1UHqjq53W4ef/xx3nzzTWpqaiSgxaSorKw8UAlsUNjvpfkflYQxJ9Q9PtjSncOOzix8PrOf8T92RBJ339SOZTAbBP27Hmo7TDnkcBDWNcBjO8xe271+CIRNAZiQhkVXVmF1HNlL/sFtppcssTwxskhsBLEWNMQaqh2qtd+UB53vXMrVZU0cGzq0uEk6lw/c3wPfe8kErgYcFlP/OBge/vtyVpqfq+uxmwh11FM8x8VP76hK+Z9XpL9Ysexrr6M0B5r7zL7FoVCYvb5MfA2weKZJ3K/WmfvtfRnkZwQJhMwI26B0jmUwJyY72qHVa+I5ywo72kxFtr3dZl9nf9CUT+3XYNOmuMtRl7g5bR78/c6v097SyPz5Lm67TeJ5skgPegSxFjTEGqqNpt6bxY+2lHPaPfCDl82iC4h+Rp8qlyFE6w2ENTxfA1f9CU671/QsBscN/CMk5qFyVro57fZtPPziFpob5KxaJEasWJ49x8Vli2BxAdjtoFEQCtHZDxubTM+xodusWm7MOIbM0uXUdpkrFfr8ZmFkKscyRI/nYNjMuW/cD683mJ/Hrsxiuad2wXM15rIqf9CcePcHYSAMDiAvE44rhVVL4YbPuXnkH0+yfv2b1NZKPE8m6UGPoKqq6pAzYzBDOFf/dxXPYRaQdT1WSaijDmu+i7zVVQd6iYfr9sH/rYe71sNZ81O3fGC03sA1n6ng5n9BaLn52QZn3ceQlw/49IlwSfY2MqypUwdeTH2xYvmO26s4bampKvi/v/Xw1m+/ib9jL/Z8F64PVBE8zU1bv9lCsddnVn4fO8tUxHM6zBxtqsYyRI/nz362gppOOO0yN4EwZNkgFDQL5XZ2mF2/QmFTdMQXMnPOQW0uV5uVbbbsPGUeLCk0ZTu3Nk6jSfoEkh70CGIVKLj3W24+az2y6tWRC8gOCmqT1CyYs1bLzIldhhCvOa9ovYHAgJe6Rw72BsaTWoud8MCV8O1zkeQsEi5WLH/i426OKoTGtR5e+XUF/o56QBPoqGX3mgra13pMkY4u2NJietQv1sJLdVDfZYaFSyd4SVE856+jxXN/v5df3FaJAgIBs7nFkzvMpZGtXpOs/UHo9pvkDJCXYbbzfO8CuGAxrCg1O4nJ3trxIy/tKMQqUHDPj2Jf0xurFw2m19kXgJmrq2h/qAI95DpCa4aTSz5Xxa4OWDgz9lZskzHnNXjN5YoVK/AFzarNl+qgtnb88+6xXLEUqt5jdhUajelWCEIkxnDFRn70vUp8/UfGc/1fK8k90Y3DblZ69wbMlpV7u80isqWF8J83VPGjmyoYGPL9WVlObrqliv6AqVQYq/70ZM1fD43nYNjsFdAfjN2Lb26s49U6s/itvd8cGw6bhO3X4Aub4Xu7FYqyoCwfTpkLy4phQT44R9hgZJDE8vhJgp6AiSwgA8he6UbDgSHyjEIXcz5QxZNON0/+3gypnT0fTp1rAsKVB7OcJmkPN+c1UlD7Q2ZO7c32XGr7MvlJDaxtMCszrQochS78bUdurTeWefdBGVazE9Uli8b8rUIkVKx4DnTUkZUFAwEz+hUMmV2cuvrNwrG6Dph/jJuPV8KjvzCLpWbPdfHVb1Vx8QfcBzaVyLCZ3qbDaq52sFsmHstghqIDYfAGLQTCir3dBxdrBkJQMsfF/oYj4zmnyMW21shVF2HTa+4LRhJz2LwX5GWZof+ZvnrKLH7OmLfowK5hIv4kQU+Ay+WKukfsWBJZzkp3pLdtyoiGMEltbq7pbT6+PcjDWw7+mjJtJlHXDjPn9ejWg1/vqamlzWcnkD2Hui4zJLevN1LQHpM1y/Lg6EJo6DE9g5zLqg4pxwmg7E7yVo+lwIDm+LxefndVLoXOkY8WItlixXPJHBfXLIfHd5sTW3/IvHEGLOAbMIuq9nth1hI3l//0PSzK9XPy0eU47SaenHaTnAnChrc3A3DMMccCJtENN389tOjRW2+9hQaOWXY8gbBJzMHwYCxDV8AG2tzu9Zvh6e4BuOq6Ku76TgX+gSEjdQ4nx/2/KkLaDGX3h0xxoXDYvBPlZphiTUsKTR3zgRYv850+5sfehE7EgSToCYi16OQj11fxohr+mskjHRz/8oXMRhzmViuFDj+leQ7yMk2w+4KQWeBiIEov1zLTxfVPDb2lDDDzv6U5pie+tMgE9b62Xhq8GdR22antOvgdBy+FGt3it8OV5cF1C7ezZEY/hc4VUY+RYS+RamLF8zdvqWLlfFhUBM/vMdvN9vhMItQatDKruWs6QIVyqe8Nsg8onwlzZpha4DmRxWTegAWH1WRBmxWswJx5Lhrqj4zlOXNdtA7pWHcFzNt1j88kdgXYlHn+wW0fuwNW3mo2+zE3e02idqxwc/518PK9N+Jta8BZ5OK4j1Yx+zQ33T4zcqYjCT/DBsVZsKAQlpfA/Dw4qhAafP0xp9tA4jleJEFPwODw09e+9jX279+Py+WiqspcA7i9zVwD/XbzxJ5Do2jz22lrOfT27Muq8B0+f+1wcqK7Clepme+yKOjp6aHdb6fNl0mL97AHJyfm85qe/ceIVX88GqfdzDN/6BjYuDHGtkBCpKhY8fyxj5lE1tQHlx8DZ5bBa3Wwfj90DpgeqE2bk97+gJWBgJWuRnMNcVEulM2AeXlmN622ngwcNo2jzQx1Z1jhc1+v4ravHzl//Y1bqg5ea63BRgiUwqLAFzBXhXQOQIfPfOxsmkFn0EaOz5zka8ywdUjDvDPdXHD0ZfSHFE5nPgMh6PKbpK4s5vKq/GwznH18CSwoMJedzZ8BFgvsk/2bk0IS9ATFWnRyVCH85Wq4ZwP8+FUzFBXZJnUcjoyOw+evB3u5zYvdNDcOPTJ3XM8Y63ljHfWJ5XDL+WZuTYh0FSue8zJNYY5WL+TYYdYxcF65KW27vtHs9uQPQIAgSikIQVcQuttMVa5MG5RkQ27QSX5mkHAzOGymJzzvLDf/cTM88NOv09naSHGpi09cX0X5OW7eaDg4lF3Xkc1A0MpmTGL2BsxwezBsEm1HXwZKgSUIwcg1y8GwmTvXGroHFAGlCARMj9miTIGhmU6Ykw3lkdG1spmwsEBWZ6cC+RWM0niGcGwWuPZkuHQR/OJ1eGSLWXhhs5gz3Ik6OH+dPMcVw69Xm3lxIdLBeIdjHVYzTZTrgE6fGba+PBvOKzOJ+s19UB+GsNZkZZiT8WDIrKbu8ZseK4FcMlSYd3rNNdTZDvM4WSvcfOBnF2G1aPILSgiH4bldBy/N1GHo7MojFNYUWMzQ+IGT4Uht3WAY+kMW/N2Rqn4hM/wdxiT5AWyEQgp72JxkFDjNEPbiQpiTY+acF8yEmVkTf43F5JAEnQDlM+EnF8N1p8Av3zCJ2q5McHb6ktOmsRRYieb0uXD96eb/4eamhJhKlDILqHIcpi51pw+y7bD6KJOoH329i129WQTspudqU6bnDSZpdofCDIQVLf2gBsyqcJvV9GR1IJNMa5h2bUalLBaThK0W8zi+YBCw0Oc3JTcHAmZYXVuh7kUPWx/6Jr72vWQWulj8oSpmn+kmiOldW61gJYzToVlYBAvzzAKwuTOgKNsUH5mREftSMJEckqATaEG+SdRfOgV++Tr8ZZsJzFnZsK9nfFW5hhMrCfeu8xyySnuwwAowYpJ+3xK4dqXZV3fjxo1saj2yR+LxeKLOywsxVURL1E4bXHPefAJBaOyBt5pheys095vh6AwFOfYgViDTaXq8AQ2h0OBQtAVv2Ep/j3l8S2RbOKWg+d8e9vz5m/jb95JR6GLRlVXMPdONBWh4ycPm31Uc2Jd5oK2WzfdVENIw/2w3mZmmnTb7APOcfs49Ziazc82wfX4WzHDApk0bgeijCxLPyRPXBK2UuhT4OWZE5h6t9e3xfL50sTAffnoJXHfqwUQdjtyeaYXdHaZ6z0R6ucMl4a7HRi6wogCHJYgvbMVuUXz4WPjcSeYkYzjpvmmAiE5iObqhibrHb+aGQ1ZYkgFLiswK6X3d8NZ+eOwRD+t+dyMD7Q1kFrpY8pEq5p7hJmw1PemecAitMcPjg1UHFTS+6mHHfQcTsK+tlq2/qyAUhtlnuNnx58oD9w0K+02BlY993M38GaYs6f66TmbYQywrgZmZpuc/0uiXxHNyxW1Jj1LKCtwJXAYcC/w/pdSx8Xq+dDSYqF+5BirPMXNbm1tNcs7f7qHrodGXET3ccEk4ViGVUEcdpdmRY4ECp43Pnax45Rq4/YKRkzOk/qYBYuwklkemlBkinj8DZueYhG1RZqHV4kKwbjZlRAfa9wKagbZatvy2gsAmD/lZJinbLRqb0tiUGdK2Ri6f2h0jAdc+WsnMLLMbVzR9rXVcfRycWw6LCuGCU5ZywWnHMm+Gad9opqYknpMrnj3oU4GdWuvdAEqpB4ArgM1xfM6kmOg1gHNyoeIk81HXBf/YDjd8v5KQ/8gE2/9kJfPPdtM1MPyQ+HBJ2JrviiT+Q1nzXeRnwVXL4KJFZgHYWOeXU3nTADFu0yaWYWLxrCJzzll20wvuD5oh8Du+W3nIZVQAQZ+XzQ9V8uh/uWnpgze3ddMTsFA0ayZBbS6P0sCzMRLwQHsdn1sJr81x0RSlUticua4DtROc9vHNL0s8J1c8E/RcoH7I13uB0w4/SClVAVTA6AvLT2WuPPjCKfCltugB0N9aR8eAWXW5tAhKIlW6QtqU+wuEzKUXDxS76Gs5MmgdBS5yVh1ZKcyR6eR/7qjiyxMctYpVjUl+t2lNYnkclDqYHPc1RI/n/Q11lOSY1dSnznWZqmAqcjlm2MT13TEKmcyd5+KYYrjx21XcdH0F/UOvo3Y6+eHtVczKntjPIPGcXPG8ajXa+doRlwFrrau11iu11iuLi4vj2Jz0EisAZs1xceNZpmh9Yw/8eSs8sBke3mLmsh/bCc/sgYxLqlD2Q2tsWh1O3vuZKm65zs1//aCaopI5B3b1ufeear78mYnPKVVVVeF0Hvq8TqeTqqqxlAkVKUZieYJixfO8+S5yI8PhAyHT4+4PmBXaAyFz0v3Vb1WRlXVoTGVlObnpO1XkOuA/P+XmzruqmT1kl667q6snZY5Y4jnJtNZx+QDOAJ4a8vU3gW8O9z0nn3yyFsaaNWu00+kcrG2iAe10OvWaNWsOOc4X1LrNq3VTr9aNPVrXd2ld06H1znatf3TXGl1cMkcrpXRZWdkR37thwwa9YcOGcbcx1vevWbNGl5aWxnxeMTHAOh2nuI32IbE8caON51BY62BI60Dkwx80H7/7/Ro9e7aJKZcrekxNJJ6H+16J5/gaLp7jGdQ2YDewAHAAm4Blw32PBPWhJiMwhgu8iQT0SG2baPIXsSUhQUssT4KJxvNIMTXemBtNuySe42e4eI7bHLTWOqiU+hLwFObSjHu11u/G6/mmouH2rk0mufRiepFYnhypGM8Sy6ktrpWTtdaPa62P0lov0lrLpMUUIZdeTD8Sy1OTxHJqk60NxJjJpRdCTA0Sy6lNErQYs1grUuXSCyHSi8RyapMEPY2tWLFiXHNhcumFEKlnPPEssZziYq0eS8aHrPxMH3LpRfKQ4FXc4/mQWE4fEsvJNVw8y25WYlxScUWqEGLsJJZTlwxxCyGEEClIErQQQgiRgiRBCyGEEClIErQQQgiRgmSRmBg3WVAixNQgsZyapActhBBCpCBJ0EIIIUQKkgQthBBCpCBJ0EIIIUQKkgQthBBCpCBJ0EIIIUQKkgQthBBCpCBlNtNIDUqpFqB2hMOKgNYENGeySbsTayq3u0xrXZyIxoyXxHLKSte2T+V2x4znlErQo6GUWqe1XpnsdoyVtDuxpN2pL11/1nRtN6Rv26dru2WIWwghhEhBkqCFEEKIFJSOCbo62Q0YJ2l3Ykm7U1+6/qzp2m5I37ZPy3an3Ry0EEIIMR2kYw9aCCGEmPJSPkErpT6ilHpXKRVWSsVcDaeUulQptU0ptVMpdWMi2xijPQVKqWeUUjsi/+fHOK5GKfW2UmqjUmpdots5pB3Dvn7K+EXk/reUUiclo52HG0W7z1dKdUVe341KqW8no52HtelepVSzUuqdGPen5Gs9URLLiSGxnFhxjWetdUp/AMcAS4HngZUxjrECu4CFgAPYBByb5HbfAdwY+fxG4IcxjqsBipLc1hFfP2AV8ASggNOBtSnwtzGadp8P/CPZbT2sTecCJwHvxLg/5V7rSfq5JZbj31aJ5cS3PW7xnPI9aK31Fq31thEOOxXYqbXerbX2Aw8AV8S/dcO6Argv8vl9wAeS15QRjeb1uwL4vTZeA2YqpUoT3dDDpOLvfURa6xeB9mEOScXXesIklhNCYjnB4hnPKZ+gR2kuUD/k672R25KpRGvdCBD5f1aM4zTwtFJqvVKqImGtO9RoXr9UfI1H26YzlFKblFJPKKWWJaZpE5KKr3WipOLPLrEcf1M1lmECr7ctLs0ZI6XUs8DsKHdVaq3/OpqHiHJb3JenD9fuMTzMWVrrfUqpWcAzSqmtkTOyRBrN65eU13gEo2nTm5hSer1KqVXAX4Al8W7YBKXiaz0qEssSy+M0VWMZJvB6p0SC1lpfOMGH2AvMH/L1PGDfBB9zRMO1WynVpJQq1Vo3RoYzmmM8xr7I/81KqUcxQz2JDurRvH5JeY1HMGKbtNbdQz5/XCn1v0qpIq11Ktf1TcXXelQkliWWx2mqxjJM4PWeKkPcbwBLlFILlFIO4KPA35Lcpr8Bn4p8/ingiN6DUipbKZU7+DlwMRB1JWCcjeb1+xvwyciKxNOBrsFhvyQasd1KqdlKKRX5/FTM33xbwls6Nqn4WieKxPLESCynnvG/3sleATeKFXIfxJyB+IAm4KnI7XOAxw9bKbcdsxKwMgXaXQg8B+yI/F9weLsxKxY3RT7eTWa7o71+wLXAtZHPFXBn5P63ibEKNwXb/aXIa7sJeA04MwXa/EegEQhE/rY/nQ6v9ST83BLLiWmvxHJi2x23eJZKYkIIIUQKmipD3EIIIcSUIglaCCGESEGSoIUQQogUJAlaCCGESEGSoIUQQogUJAlaCCGESEGSoIUQQogUJAlaHEEpdUpk39LMSIWkd5VSxyW7XUKIsZN4Tl9SqEREpZT6PpAJZAF7tdY/SHKThBDjJPGcniRBi6gi9XDfAAYwJfVCSW6SEGKcJJ7Tkwxxi1gKgBwgF3PmLYRIXxLPaUh60CIqpdTfgAeABUCp1vpLSW6SEGKcJJ7TU0rsBy1Si1Lqk0BQa/0HpZQVeFUp9V6t9T+T3TYhxNhIPKcv6UELIYQQKUjmoIUQQogUJAlaCCGESEGSoIUQQogUJAlaCCGESEGSoIUQQogUJAlaCCGESEGSoIUQQogUJAlaCCGESEH/H6viqehKyJJBAAAAAElFTkSuQmCC\n",
"text/plain": [
"<Figure size 576x216 with 2 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"pred = Predictive(model, mcmc.get_samples(), return_sites=['mean_model'])\n",
"\n",
"predictions = pred(rng_key)\n",
"\n",
"skip = 100\n",
"fig, ax = plt.subplots(1, 2, figsize=(8, 3))\n",
"\n",
"ax[0].errorbar(x, y, yerr, fmt='o', color='k', ecolor='silver')\n",
"ax[0].plot(x, predictions['mean_model'][::skip].T, alpha=1, color='DodgerBlue');\n",
"ax[0].set(\n",
" xlabel='x', ylabel='y', title='all samples'\n",
")\n",
"\n",
"ax[1].errorbar(x, y, yerr, fmt='o', color='k', ecolor='silver')\n",
"\n",
"weights = np.exp(logsumexp(log_weights, 0, b=b))\n",
"weights /= weights.sum()\n",
"\n",
"for m, a in zip(predictions['mean_model'][::skip],\n",
" weights[::skip]):\n",
" ax[1].plot(x, m, alpha=600 * a, color='DodgerBlue');\n",
"ax[1].set(\n",
" xlabel='x', ylabel='y', title='lnlike-weighted'\n",
");"
]
},
{
"cell_type": "markdown",
"id": "104068f5-8132-4937-854b-cfea4ec32bc0",
"metadata": {},
"source": [
"The expected log predictive density from LOO-CV is given by: "
]
},
{
"cell_type": "code",
"execution_count": 10,
"id": "3e17ab90-f92d-4289-8a69-131d7c07b0e1",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"-18.73730239689501"
]
},
"execution_count": 10,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"elpd_loo = logsumexp(log_weights + log_likelihood, axis=1, b=b).sum()\n",
"\n",
"elpd_loo"
]
},
{
"cell_type": "markdown",
"id": "247605b9-256b-484f-b515-9a8d20fdb9c0",
"metadata": {},
"source": [
"The effective number of free parameters is simply:"
]
},
{
"cell_type": "code",
"execution_count": 11,
"id": "83e31def-f476-44dc-af47-1d83d4095c7f",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"4.641941825423434"
]
},
"execution_count": 11,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"p_loo = lppd_loo - elpd_loo\n",
"\n",
"p_loo"
]
},
{
"cell_type": "markdown",
"id": "eaeaf098-e256-4de3-af9e-91132b796bef",
"metadata": {},
"source": [
"Now let's us the PSIS log weighting built into ``arviz``. We supply the (negative) log likelihood and it returns the Pareto smoothed log weights, and the shape parameter $\\hat{k}$ for each $i$:"
]
},
{
"cell_type": "code",
"execution_count": 12,
"id": "3e41eb23-fb54-405c-94de-f99113bccb71",
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"corrected_log_weights, pareto_shape = psislw(-log_likelihood, reff)\n",
"\n",
"ax = plt.gca()\n",
"ax.plot(x, pareto_shape, 'ok');\n",
"\n",
"ax.set(xlabel='x', ylabel='$\\\\hat{k}$')\n",
"\n",
"# Label the places where the pareto smoothing is invalid\n",
"for k, ls, label in zip([0.7, 1], [':', '-'], ['ok', 'bad']):\n",
" ax.axhline(k, ls=ls, color='r')\n",
" ax.annotate(label, (0, k), color='r', va='bottom')"
]
},
{
"cell_type": "markdown",
"id": "c8ff21ab-502e-4f83-acbf-958665f7ab75",
"metadata": {},
"source": [
"We can also compute all of the LOO stats with the ``loo`` function:"
]
},
{
"cell_type": "code",
"execution_count": 13,
"id": "18dd0d43-d027-432f-beb7-7684951eb5da",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"Computed from 5000 by 25 log-likelihood matrix\n",
"\n",
" Estimate SE\n",
"elpd_loo -18.74 5.27\n",
"p_loo 4.64 -\n",
"------\n",
"\n",
"Pareto k diagnostic values:\n",
" Count Pct.\n",
"(-Inf, 0.5] (good) 24 96.0%\n",
" (0.5, 0.7] (ok) 1 4.0%\n",
" (0.7, 1] (bad) 0 0.0%\n",
" (1, Inf) (very bad) 0 0.0%"
]
},
"execution_count": 13,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"loo = arviz.loo(idata, pointwise=True)\n",
"loo"
]
},
{
"cell_type": "markdown",
"id": "b1cc4f97-1eaf-41b8-b2d7-c4d39581583e",
"metadata": {},
"source": [
"Now let's compare a poorly-fitting model ``less_complex_model`` with the original ``model`` using LOO: "
]
},
{
"cell_type": "code",
"execution_count": 14,
"id": "9ceebfcb-08f4-4236-af60-201cf4325440",
"metadata": {},
"outputs": [],
"source": [
"X_2 = np.vander(x, 2)\n",
"\n",
"def less_complex_model():\n",
" # linear regression coefficients beta\n",
" beta = numpyro.sample(\n",
" 'beta', dist.Uniform(\n",
" low=np.array([-1, -1]), high=np.array([5, 5])\n",
" )\n",
" )\n",
" # uncertainty on y\n",
" sigma = numpyro.sample(\n",
" 'sigma', dist.HalfNormal(0.1)\n",
" )\n",
" # define the linear mean model\n",
" mean_model = numpyro.deterministic(\n",
" 'mean_model', jnp.dot(X_2, beta)\n",
" )\n",
" # define the Gaussian likelihood of observations y\n",
" numpyro.sample(\n",
" 'obs', dist.Normal(mean_model, sigma), obs=y\n",
" )"
]
},
{
"cell_type": "code",
"execution_count": 15,
"id": "cc3f24f1-680b-47d4-a85b-1f973c04f02f",
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"sample: 100%|██████████| 5100/5100 [00:02<00:00, 2299.17it/s, 3 steps of size 6.59e-01. acc. prob=0.95]\n"
]
}
],
"source": [
"rng_key = random.PRNGKey(0)\n",
"\n",
"less_complex_mcmc = MCMC(\n",
" sampler=NUTS(\n",
" less_complex_model,\n",
" ),\n",
" num_warmup=100,\n",
" num_samples=5000,\n",
" chain_method='parallel',\n",
" num_chains=len(jax.devices()),\n",
")\n",
"less_complex_mcmc.run(\n",
" rng_key,\n",
")"
]
},
{
"cell_type": "code",
"execution_count": 16,
"id": "77e3c797-53f4-4202-a108-35e98f7ce0f1",
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"//anaconda3/envs/pymc/lib/python3.8/site-packages/arviz/stats/stats.py:694: UserWarning: Estimated shape parameter of Pareto distribution is greater than 0.7 for one or more samples. You should consider using a more robust model, this is because importance sampling is less likely to work well if the marginal posterior and LOO posterior are very different. This is more likely to happen with a non-robust model and highly influential observations.\n",
" warnings.warn(\n"
]
},
{
"data": {
"text/html": [
"<div>\n",
"<style scoped>\n",
" .dataframe tbody tr th:only-of-type {\n",
" vertical-align: middle;\n",
" }\n",
"\n",
" .dataframe tbody tr th {\n",
" vertical-align: top;\n",
" }\n",
"\n",
" .dataframe thead th {\n",
" text-align: right;\n",
" }\n",
"</style>\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>rank</th>\n",
" <th>loo</th>\n",
" <th>p_loo</th>\n",
" <th>d_loo</th>\n",
" <th>weight</th>\n",
" <th>se</th>\n",
" <th>dse</th>\n",
" <th>warning</th>\n",
" <th>loo_scale</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>original</th>\n",
" <td>0</td>\n",
" <td>-18.736161</td>\n",
" <td>4.640812</td>\n",
" <td>0.000000</td>\n",
" <td>1.000000e+00</td>\n",
" <td>5.268723</td>\n",
" <td>0.000000</td>\n",
" <td>False</td>\n",
" <td>log</td>\n",
" </tr>\n",
" <tr>\n",
" <th>simpler</th>\n",
" <td>1</td>\n",
" <td>-66.038448</td>\n",
" <td>9.981362</td>\n",
" <td>47.302287</td>\n",
" <td>3.542056e-12</td>\n",
" <td>9.458131</td>\n",
" <td>10.686855</td>\n",
" <td>True</td>\n",
" <td>log</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"text/plain": [
" rank loo p_loo d_loo weight se \\\n",
"original 0 -18.736161 4.640812 0.000000 1.000000e+00 5.268723 \n",
"simpler 1 -66.038448 9.981362 47.302287 3.542056e-12 9.458131 \n",
"\n",
" dse warning loo_scale \n",
"original 0.000000 False log \n",
"simpler 10.686855 True log "
]
},
"execution_count": 16,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"idata_less_complex = arviz.from_numpyro(less_complex_mcmc)\n",
"\n",
"arviz.compare(\n",
" dict(original=idata, simpler=idata_less_complex)\n",
")"
]
},
{
"cell_type": "markdown",
"id": "b3b55eae-68a2-4242-bcf6-28017961a2ab",
"metadata": {},
"source": [
"The warning raised by the comparison indicates that the simpler model isn't a good fit to the data, and its LOO comparison shouldn't be trusted."
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "6090f520-b315-4749-828b-dd0b13a4f4bc",
"metadata": {},
"outputs": [],
"source": []
}
],
"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": "3.8.8"
}
},
"nbformat": 4,
"nbformat_minor": 5
}
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