{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "## Homework 6\n", "\n", "## Markov Chain Simulation and Hierarchical Model\n", "
\n", "This notebook is arranged in cells. Texts are usually written in the markdown cells, and here you can use html tags (make it bold, italic, colored, etc). You can double click on this cell to see the formatting.
\n", "
\n", "The ellipsis (...) are provided where you are expected to write your solution but feel free to change the template (not over much) in case this style is not to your taste.
\n", "
\n", "Hit \"Shift-Enter\" on a code cell to evaluate it. Double click a Markdown cell to edit.
" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "***\n", "### Link Okpy" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "from client.api.notebook import Notebook\n", "ok = Notebook('hw6.ok')\n", "_ = ok.auth(inline = True)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Imports" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": true }, "outputs": [], "source": [ "import numpy as np\n", "from scipy.integrate import quad\n", "#For plotting\n", "import matplotlib.pyplot as plt\n", "%matplotlib inline" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "***" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Problem 1 - Simulated Annealing\n", "\n", "Reference: Newman, Computational Physics (p. 490-497)

\n", "For a physical system in equilibrium at temperature $T$, the probability that at any moment the system is in a state $i$ is given by the Boltzmann probability. Let us assume our system has single unique ground state and let us choose our energy scale so that $E_i = 0$ in the ground state and $E_i > 0$ for all other states. Now suppose we cool down the system to absolute zero. The system will definitely be in the ground state, and consequently one way to find the ground state of the system is to cool it down to $T = 0$.\n", "

\n", "This in turn suggests a computational strategy for finding the ground state: let us simulate the system at temperature $T$, using the Markov chain Monte Carlo method, then lower the temperature to zero and the system should find its way to the ground state. This same approach could be used to find the minimum of any function, not just the energy of a physical system. we can take any mathematical function $f(x, y, z, ...)$ and treat the independent variables $x, y, z$ as defining a \"state\" of the system and $f$ as being the energy of that system, then perform a Monte Carlo simulation. Taking the temperature down to zero will again cause the system to fall into its ground state, i.e. the state with the lowest value of $f$, and hence we find the minimum of the function.\n", "

\n", "However, if the system is cooled rapidly, it can get stuck in a local energy minimum. On the other hand, an annealed system, one that is cooled sufficiently slowly, can find its way to the ground state. Simulated annleaing applies the same idea in a computational setting. It mimics the slow cooling of a material on the computer by using a Monte Carlo simulation with a temperature parameter that is gradually lowered from an initially high value towards zero. The initial temperature should be chosen so that the system equilibrates quickly. To achieve this, we should choose the thermal energy to be significantly greater than the typical energy change accompanying a single Monte Carlo move. \n", "

\n", "As for the rate of cooling, one typically specifies a \"cooling schedule,\" a trajectory for the temperature as a function of time, and the most common choise is the exponential one:\n", "

\n", "$$ T = T_0 e^{-t/\\tau} $$\n", "

\n", "where $T_0$ is the initial temperature, and $\\tau$ is a time constant. Some trial error may be necessary to find a good value for $\\tau$. \n", "

\n", "As an example of the use of simulated annealing, we will look at one of the most famous optimization problems, traveling salesman problem, which involves finding the shortest route that visits a given set of locations on a map. A salesman wishes to visit $N$ given cities, and we assume that he can travel in a straight line between any pair of citiies. Given the coordinates of the cities, the problem is to devise the shortest tour. It should start and end at the same city, and all cities must be visited at least once. Let us denote the position of the city $i$ by the two-dimensional vector $r_i = (x_i, y_i)$.\n", "

\n", "Here is the solution:\n" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAZEAAAGRCAYAAACkIY5XAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nYII=\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Traveling salesman (Newman p. 493)\n", "from math import sqrt,exp\n", "from numpy import empty\n", "from random import random,randrange\n", "from scipy.misc import imread\n", "\n", "N = 25\n", "R = 0.02\n", "Tmax = 10.0\n", "Tmin = 1e-3\n", "tau = 1e4\n", "\n", "# Function to calculate the magnitude of a vector\n", "def mag(x):\n", " return sqrt(x[0]**2+x[1]**2)\n", "\n", "# Function to calculate the total length of the tour\n", "def distance():\n", " s = 0.0\n", " for i in range(N):\n", " s += mag(r[i+1]-r[i])\n", " return s\n", "\n", "# Choose N city locations and calculate the initial distance\n", "r = empty([N+1,2],float)\n", "for i in range(N):\n", " r[i,0] = random()\n", " r[i,1] = random()\n", "r[N] = r[0]\n", "D = distance()\n", "\n", "# Main loop\n", "t = 0\n", "T = Tmax\n", "while T>Tmin:\n", "\n", " # Cooling\n", " t += 1\n", " T = Tmax*exp(-t/tau)\n", "\n", " # Choose two cities to swap and make sure they are distinct\n", " i,j = randrange(1,N),randrange(1,N)\n", " while i==j:\n", " i,j = randrange(1,N),randrange(1,N)\n", "\n", " # Swap them and calculate the change in distance\n", " oldD = D\n", " r[i,0],r[j,0] = r[j,0],r[i,0]\n", " r[i,1],r[j,1] = r[j,1],r[i,1]\n", " D = distance()\n", " deltaD = D - oldD\n", "\n", " # If the move is rejected, swap them back again\n", " if random()>exp(-deltaD/T):\n", " r[i,0],r[j,0] = r[j,0],r[i,0]\n", " r[i,1],r[j,1] = r[j,1],r[i,1]\n", " D = oldD\n", "\n", "plt.figure(figsize = (8, 7))\n", "img = imread(\"map_sacramento.png\")\n", "plt.plot(r[:,0], r[:,1], 'o-', color = 'crimson', zorder=1)\n", "plt.imshow(img,zorder=0, extent=[-0.1, 1.1, -0.1, 1.1])\n", "plt.xticks([])\n", "plt.yticks([])\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now, consider the function $f(x) = x^2 − \\mathrm{cos}(4\\pi x)$, which looks like this:" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAYsAAAEKCAYAAADjDHn2AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "x = np.linspace(-2, 2, 100)\n", "y = x**2 - np.cos(4*np.pi*x)\n", "plt.plot(x, y)\n", "plt.grid(True); plt.xlim(-2, 2); plt.xlabel('$x$'); plt.ylabel('$f(x)$')\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Clearly the global minimum of this function is at $x = 0$.\n", "\n", " 1. Write a program to confirm this fact using simulated annealing starting at, say, $x = 2$, with Monte Carlo moves of the form $x \\rightarrow x + \\delta$ where $\\delta$ is a random number drawn from a Gaussian distribution with mean zero and standard deviation one. Use an exponential cooling schedule and adjust the start and end temperatures, as well as the exponential constant, until you find values that give good answers in reasonable time. Have your program make a plot of the values of $x$ as a function of time during the run and have it print out the final value of x at the end. You will find the plot easier to interpret if you make it using dots rather than lines, with a statement of the form plot(x,\".\") or similar.
" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "..." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ " 2. Now adapt your program to find the minimum of the more complicated function $f(x) = \\mathrm{cos}(x) + \\mathrm{cos}(\\sqrt{2}x) + \\mathrm{cos}(\\sqrt{3}x)$ in the range $0 < x < 50$.

\n", "(Hint: The correct answer is around $x = 16$, but there are also competing minima around $x = 2$ and $x = 42$ that your program might find. In real-world situations, it is often good enough to find any reasonable solution to a problem, not necessarily the absolute best, so the fact that the program sometimes settles on these other solutions is not necessarily a bad thing.)" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "..." ] }, { "cell_type": "markdown", "metadata": { "collapsed": true }, "source": [ "***" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Problem 2 - Hierarchial Normal Model\n", "\n", "Reference: Gelman et al., Bayesian Data Analysis (p. 288-290)

\n", "![alt text](table3.png \"Title\")\n", "Table 1. Coagulation time in seconds for blood drawn from 24 animals randomly allocated to four different diets. Different treatments have different numbers of observations because the randomization was unrestricted.

\n", "Under the hierarchical normal model, data $y_{ij}$, for $i = 1, ..., n_j$ and $j = 1, ... ,J$, are independently normally distributed within each of $J$ groups, with means $\\theta_j$ and common variance $\\sigma^2$. The data is presented in Table 1. (In this case, there are $J = 4$ groups (or 4 sets of experiments - A, B, C, and D), and for each group $j$, we have a data vector $y_j$ with the mean $\\theta_j$; $y_j = [y_{1j}, ... , y_{n_j\\ j}]$ (there have been $n_j$ observations made.) (e.g. j = 1 represents the diet A group. So $y_{i1} = [y_{11}, y_{21}, y_{31}, y_{41}] = [62, 60, 63, 59]$ with $n_1 = 4.$

\n", "The total number of observations is $n = \\sum_{j=1}^J n_j$. The group means ($\\theta_j$) are assumed to follow a normal distribution with unknown mean $\\mu$ and variance $\\tau^2$, and a uniform prior distribution is assumed for $(\\mu, \\mathrm{log}\\sigma, \\tau)$, with $\\sigma > 0$ and $\\tau > 0$; equivalently, $p(\\mu, \\mathrm{log}\\sigma, \\mathrm{log}\\tau) \\propto \\tau$.

\n", "The joint posterior density of all the parameters is

\n", "$$ p(\\theta, \\mu, \\mathrm{log}\\sigma, \\mathrm{log}\\tau\\ \\vert\\ y) \\propto p(\\mu, \\mathrm{log}\\sigma, \\mathrm{log}\\tau) \\prod_{j=1}^J \\mathrm{Normal}(\\theta_j\\ \\vert\\ \\mu, \\tau^2) \\prod_{j=1}^J \\prod_{i=1}^{n_j} \\mathrm{Normal}(y_{ij}\\ \\vert\\ \\theta_j, \\sigma^2) $$\n", "

\n", "where $\\mathrm{Normal}(\\theta_j\\ \\vert\\ \\mu, \\tau^2) = \\frac{1}{\\sqrt{2\\pi \\tau^2}}\\mathrm{exp}(-\\frac{(\\theta_j-\\mu)^2}{2\\tau^2})$.\n", "

\n", " 1. Now, find the MAP (Maximum A Posteriori) solution to this (find the solution to MAP for all these parameters). In other words, find $\\theta_j, \\mu, \\sigma, \\tau$ which maximizes the likelihood.

\n", "(Hint: The likelihood is given as $\\prod_{j=1}^J \\mathrm{Normal}(\\theta_j\\ \\vert\\ \\mu, \\tau^2) \\prod_{j=1}^J \\prod_{i=1}^{n_j} \\mathrm{Normal}(y_{ij}\\ \\vert\\ \\theta_j, \\sigma^2)$. Take the log of the likelihood and maximize it using scipy.optimize.fmin (https://docs.scipy.org/doc/scipy-0.19.1/reference/generated/scipy.optimize.fmin.html). Note that you need to make initial guesses on the parameters in order to use fmin. Make a reasonable guess! You can use a different in-built function to maximize the likelihood function.
\n", "Caveat: \"fmin\" minimizes a given function, so you should multiply the log-likelihood by $-1$ in order to maximize it using fmin.)" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "# Load data\n", "A = np.array([62, 60, 63, 59])\n", "B = np.array([63, 67, 71, 64, 65, 66])\n", "C = np.array([68, 66, 71, 67, 68, 68])\n", "D = np.array([56, 62, 60, 61, 63, 64, 63, 59])\n", "\n", "data = []\n", "data.append(A)\n", "data.append(B)\n", "data.append(C)\n", "data.append(D)\n", "\n", "data = np.array(data)" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "from scipy import optimize\n", "\n", "def minus_log_likelihood(param, y_i1=data[0], y_i2=data[1], y_i3=data[2], y_i4=data[3]):\n", " theta1, theta2, theta3, theta4, mu, sigma, tau = param\n", " return ..." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "..." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "You should find that the MAP solution is dependent on your initial guesses. The point is that the maximal likelihood estimator is biased, even though we have all the parameters. \n", "Hence, it is better to use the Monte Carlo simulation for the parameter estimation; we can also determine posterior quantiles with the Monte Carlo method. First, we will try the Gibbs sampler.

\n", "Starting points:
\n", "In this example, we can choose overdispersed starting points for each parameter $\\theta_j$ by simply taking random points from the data $y_{ij}$ from group $j$. We obtain 10 starting points for the simulations by drawing $θ_j$ independently in this way for each group. We also need starting points for $\\mu$, which can be taken as the average of the starting $θ_j$ values. No starting values are needed for $\\tau$ or $\\sigma$ as they can be drawn as the first steps in the Gibbs sampler.

\n", "Conditional posterior distribution of $\\sigma^2$:
\n", "The conditional posterior density for $\\sigma^2$ has the form corresponding to a normal variance with known mean; there are $n$ observations $y_{ij}$ with means $\\theta_j$. The conditional posterior distribution is
\n", "$$ \\sigma^2 | \\theta, \\mu, \\tau, y \\sim \\mathrm{Inv}\\mbox{-}\\chi^2(n, \\hat{\\sigma}^2) $$\n", "
\n", "where $$\\mathrm{Inv}\\mbox{-}\\chi^2(x|n, \\hat{\\sigma}^2) = \\mathrm{Inv\\mbox{-}gamma}\\Big(\\alpha = \\frac{n}{2}, \\beta = \\frac{n}{2}\\hat{\\sigma}^2 \\Big) = \\frac{\\beta^\\alpha}{\\Gamma(\\alpha)}x^{-(\\alpha+1)}\\mathrm{exp}(-\\beta/x)$$\n", "
\n", "$$ \\hat{\\sigma}^2 = \\frac{1}{n}\\sum_{j=1}^J \\sum_{i=1}^{n_j} (y_{ij}-\\theta_j)^2 $$\n", "

\n", "(Hint: You can take random samples from the inverse gamma function using scipy.stats.invgamma - https://docs.scipy.org/doc/scipy-0.14.0/reference/generated/scipy.stats.invgamma.html.
invgamma.rvs(alpha, scale = beta, size=1) will take one random sample from $\\mathrm{Inv\\mbox{-}gamma}(\\alpha, \\beta)$.)\n", "

\n", "Conditional posterior distribution of $\\tau^2$:
\n", "Conditional on $y$ and the other parameters in the model, $\\mu$ has a normal distribution determined by the $J$ values $\\theta_j$:
\n", "$$ \\tau^2 | \\theta, \\mu, \\sigma, y \\sim \\mathrm{Inv}\\mbox{-}\\chi^2(J-1, \\hat{\\tau}^2) $$\n", "
\n", "with $$ \\hat{\\tau}^2 = \\frac{1}{J-1} \\sum_{j=1}^J (\\theta_j - \\mu)^2. $$\n", "

\n", "Conditional posterior distribution of each $\\theta_j$:
\n", "The factors in the joint posterior density that involve $\\theta_j$ are the $N(\\mu, \\tau^2)$ prior distribution and the normal likelihood from the data in the $j$th group, $y_{ij}$ , $i = 1, ... , n_j$ . The conditional posterior distribution of each $\\theta_j$ given the other parameters in the model is
\n", "$$ \\theta_j | \\mu, \\sigma, \\tau, y \\sim \\mathrm{Normal}(\\hat{\\theta_j}, V_{\\theta_j}) $$\n", "

\n", "where the parameters of the conditional posterior distribution depend on $\\mu, \\sigma, \\tau$ as well as $y$:\n", "

\n", "$$ \\hat{\\theta_j} = \\frac{\\frac{1}{\\tau^2}\\mu + \\frac{n_j}{\\sigma^2}(\\frac{1}{n_j}\\sum_{i=1}^{n_j} y_{ij})}{\\frac{1}{\\tau^2} + \\frac{n_j}{\\sigma^2}} $$\n", "
\n", "$$ V_{\\theta_j} = \\frac{1}{\\frac{1}{\\tau^2} + \\frac{n_j}{\\sigma^2}} $$\n", "

\n", "These conditional distributions are independent; thus drawing the $\\theta_j$’s one at a time is equivalent to drawing the vector $\\theta$ all at once from its conditional posterior distribution.\n", "

\n", "Conditional posterior distribution of $\\mu$:
\n", "Conditional on $y$ and the other parameters in the model, $\\mu$ has a normal distribution determined by the $J$ values $\\theta_j$:
\n", "$$ \\mu | \\theta, \\sigma, \\tau, y \\sim \\mathrm{Normal}(\\hat{\\mu}, \\tau^2/J) $$\n", "
\n", "where $\\hat{\\mu} = \\frac{1}{J}\\sum_{j=1}^J \\theta_j$.\n", "\n", "

\n", " 2. Define a function which does the Gibbs sampling. Take 100 samples. Remove the first 50 sequences and store the latter half. Repeat this 10 times so that you get ten Gibbs sampler sequences, each of length 50. We have 7 parameters ($\\theta_1, ..., \\theta_4, \\mu, \\sigma, \\tau$), and for each parameter, you created 10 chains, each of length 50. " ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "..." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ " 3. Estimate posterior quantiles. Find 2.5%, 25%, 50%, 75%, 97.5% posterior percentiles of all parameters.
\n", "(Hint: You can use np.percentile - https://docs.scipy.org/doc/numpy-dev/reference/generated/numpy.percentile.html.)" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "..." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ " 4. Now, test for convergence using \"Gelman-Rubin statistic.\" For all seven parameters, compute $R$ and determine if the condition $R < 1.1$ is satisfied.

\n", "For a given parameter $\\theta$, the $R$ statistic compares the variance across chains with the variance within a chain. \n", "
Given chains $J=1,\\ldots,m$, each of length $n$,
\n", "Let $B=\\frac{n}{m-1} \\sum_j \\left(\\bar{\\theta}_j - \\bar{\\theta}\\right)^2$, where $\\bar{\\theta_j}$ is the average $\\theta$ for chain $j$ and $\\bar{\\theta}$ is the global average. This is proportional to the variance of the individual-chain averages for $\\theta$.
\n", "Let $W=\\frac{1}{m}\\sum_j s_j^2$, where $s_j^2$ is the estimated variance of $\\theta$ within chain $j$. This is the average of the individual-chain variances for $\\theta$.
\n", "Let $V=\\frac{n-1}{n}W + \\frac{1}{n}B$. This is an estimate for the overall variance of $\\theta$.\n", "

\n", "Finally, $R=\\sqrt{\\frac{V}{W}}$. We'd like to see $R\\approx 1$ (e.g. $R < 1.1$ is often used). Note that this calculation can also be used to track convergence of combinations of parameters, or anything else derived from them. " ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "..." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now, try the Metropolis algorithm. \n", "\n", " 5. Run ten parallel sequences of Metropolis algorithm simulations using the package \"emcee\" (http://dfm.io/emcee/current/). First, define the log of prior (already given to you), likelihood, and posterior (Hint: http://dfm.io/emcee/current/user/line/)
" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "import emcee" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def log_prior(param):\n", " theta1, theta2, theta3, theta4, mu, sigma, tau = param\n", " if sigma > 0 and tau > 0:\n", " return 0.0\n", " return -np.inf\n", "\n", "def log_likelihood(param, data0, data1, data2, data3):\n", " theta1, theta2, theta3, theta4, mu, sigma, tau = param\n", " return ...\n", "\n", "def log_posterior(param, data0, data1, data2, data3):\n", " return ..." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ " 6. Now, try different number of MCMC walkers and burn-in period, and number of MCMC steps. At which point do you obtain similar results to those obtained\n", "using Gibbs sampling? Run the MCMC chain and estimate posterior quantiles as in Part 3.
" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "emcee_trace = []\n", "for i in range(10):\n", " # Here we'll set up the computation. emcee combines multiple \"walkers\",\n", " # each of which is its own MCMC chain. The number of trace results will\n", " # be nwalkers * nsteps\n", "\n", " ndim = 7 # number of parameters in the model\n", " nwalkers = 50 # number of MCMC walkers\n", " nburn = 500 # \"burn-in\" period to let chains stabilize\n", " nsteps = 1000 # number of MCMC steps to take\n", "\n", " # set theta near the maximum likelihood, with \n", " np.random.seed(0)\n", " starting_guesses = np.random.random((nwalkers, ndim))\n", "\n", " # Here's the function call where all the work happens:\n", " # we'll time it using IPython's %time magic\n", "\n", " sampler = emcee.EnsembleSampler(nwalkers, ndim, log_posterior, args=[data[0], data[1], data[2], data[3]])\n", " sampler.run_mcmc(starting_guesses, nsteps)\n", "\n", " emcee_trace.append(sampler.chain[:, nburn:, :].reshape(-1, ndim).T)\n", "\n", "emcee_trace = np.array(emcee_trace)\n", " \n", " " ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "np.shape(emcee_trace)" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "..." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Using the package \"corner,\" you can also easily plot the 1-d and 2-d posterior (looks familiar?). Make a plot for one chain. Plots along the diagonal correspond to 1-d constraints. The dotted lines show 16%, 50%, and 84% percentile ranges. " ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "import corner\n", "fig = corner.corner(emcee_trace[0, :, :].T, labels=[\"$\\\\theta_1$\", \"$\\\\theta_2$\", \"$\\\\theta_3$\", \"$\\\\theta_4$\", \"$\\mu$\", \"$\\sigma$\", \"$\\\\tau$\"], quantiles=[0.16, 0.5, 0.84], range = 0.95*np.ones(7))\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ " 6. Test for convergence using Gelman-Rubin statistic as in Part 4.
" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "..." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ " 7. Using autocorrelation_plot from pandas (https://pandas.pydata.org/pandas-docs/stable/visualization.html#visualization-autocorrelation), plot the auto-correlation of six parameters and determine that it gets small for large lag.
\n" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "from pandas.tools.plotting import autocorrelation_plot" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true, "scrolled": false }, "outputs": [], "source": [ "..." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ " 7. Using the package \"daft\", plot a graphical model in this problem.
Note that we have $J$ experiments each with $n_j$ data, each its own mean $\\theta_j$, but common variance $\\sigma$. The mean $\\theta_j$ has a hyperprior, generated as a\n", "gaussian with some mean $\\mu$ and variance $\\tau$.
\n", "(Hint: https://github.com/KIPAC/StatisticalMethods/blob/8232a7b7e870b82088fe3589b8a796430e9076d6/examples/SDSScatalog/FirstPGM.ipynb)

" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "import daft\n", "from matplotlib import rc" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "..." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "***" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Problem 3 - Mixture Model for Outliers\n", "\n", "Suppose we have data that can be fit to a linear regression, apart from a few outlier points. It is always better to understand the underlying generative model of outliers.

\n", "Consider the following dataset, relating the observed variables $x$ and $y$, and the error of $y$ stored in $\\sigma_y$.

\n", "![alt text](eq3.png \"Title\")" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "# Load the data\n", "x = np.array([ 0, 3, 9, 14, 15, 19, 20, 21, 30, 35,\n", " 40, 41, 42, 43, 54, 56, 67, 69, 72, 88])\n", "y = np.array([33, 68, 34, 34, 37, 71, 37, 44, 48, 49,\n", " 53, 49, 50, 48, 56, 60, 61, 63, 44, 71])\n", "e = np.array([ 3.6, 3.9, 2.6, 3.4, 3.8, 3.8, 2.2, 2.1, 2.3, 3.8,\n", " 2.2, 2.8, 3.9, 3.1, 3.4, 2.6, 3.4, 3.7, 2.0, 3.5])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ " 1. Determine $\\theta = [\\theta_0, \\theta_1]$ which maximize the likelihood (or, equivalently, minimize the loss). As in Problem 2-1, you can use scipy.optimize.fmin. Plot the best-fit line (on top of data points) using $\\theta$ from the MAP solution.
" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "from scipy import optimize\n", "\n", "..." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Clearly, we get a poor fit to the data because the squared loss is overly sensitive to outliers." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "![alt text](eq11.png \"Title\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ " 2. As in Problem2-Part5, define log-prior (already given to you), log-likelihood and log-posterior.
" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def log_prior(theta):\n", " #g_i needs to be between 0 and 1\n", " if (all(theta[2:] > 0) and all(theta[2:] < 1)):\n", " return 0\n", " else:\n", " return -np.inf # recall log(0) = -inf\n", "\n", "def log_likelihood(theta, x, y, e, sigma_B):\n", " ...\n", "\n", "def log_posterior(theta, x, y, e, sigma_B):\n", " return ..." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now, run the MCMC samples." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "ndim = 2 + len(x) # number of parameters in the model\n", "nwalkers = 50 # number of MCMC walkers\n", "nburn = 10000 # \"burn-in\" period to let chains stabilize\n", "nsteps = 15000 # number of MCMC steps to take\n", "\n", "# set theta near the maximum likelihood, with \n", "np.random.seed(0)\n", "starting_guesses = np.zeros((nwalkers, ndim))\n", "starting_guesses[:, :2] = np.random.normal(theta1, 1, (nwalkers, 2))\n", "starting_guesses[:, 2:] = np.random.normal(0.5, 0.1, (nwalkers, ndim - 2))\n", "\n", "sampler = emcee.EnsembleSampler(nwalkers, ndim, log_posterior, args=[x, y, e, 50])\n", "sampler.run_mcmc(starting_guesses, nsteps)\n", "\n", "sample = sampler.chain # shape = (nwalkers, nsteps, ndim)\n", "sample = sampler.chain[:, nburn:, :].reshape(-1, ndim)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Once we have these samples, we can exploit a very nice property of the Markov chains. Because their distribution models the posterior, we can integrate out (i.e. marginalize) over nuisance parameters simply by ignoring them!

\n", "We can look at the (marginalized) distribution of slopes and intercepts by examining the first two columns of the sample:" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "plt.plot(sample[:, 0], sample[:, 1], ',k', alpha=0.1)\n", "plt.xlabel('intercept')\n", "plt.ylabel('slope')\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We allowed the model to have a nuisance parameter $0 < g_i < 1$ for each data point: $g_i = 0$ indicates an outlier. We can also allow sb to be a nuisance parameter to marginalize over (or just make it a large number). Now, let us define an outlier whenever posterior $E(g_i) < 0.5$.\n", "

\n", " 3. Using such cutoff at $g = 0.5$, identify an outlier and mark them on the plot. Also, plot the marginalized best model over the original data.
" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "..." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "***" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## To Submit\n", "Execute the following cell to submit.\n", "If you make changes, execute the cell again to resubmit the final copy of the notebook, they do not get updated automatically.
\n", "__We recommend that all the above cells should be executed (their output visible) in the notebook at the time of submission.__
\n", "Only the final submission before the deadline will be graded. \n" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "_ = ok.submit()" ] } ], "metadata": { "kernelspec": { "display_name": "Python 2", "language": "python", "name": "python2" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 2 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython2", "version": "2.7.13" } }, "nbformat": 4, "nbformat_minor": 2 }