{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Bayes' Rule" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$$P(A|B) = \\frac{P(B|A)\\cdot P(A)}{P(B)}$$\n", "\n", "$$\\text{Posterior} = \\frac{\\text{Likelihood } \\cdot \\text{ Prior}}{\\text{Evidence}}$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Back to the COVID example\n", "\n", "In this example, we have a prior belief about our chances of having COVID, $COVID^+$. We also know the sensitivity and specificity of the test we are taking, .8 and 1.0 respectively. These represent our true positive and true negative rate and will be crucial in helping us identify our posterior. To make Bayes' Rule applicable to our situation, let's change some of the symbols. Let $x$ represent the result we get on our test, either $+$ or $-$.\n", "\n", "$$ P(COVID^+|x) = \\frac{P(x|COVID^+) \\cdot P(COVID^+)}{P(x)} $$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now we have an equation that will help us to find our posterior no matter the value we observe for $x$, but before we can use it, we still have to determine the value for the likelihood function and the evidence. This is where we go back to the sensitivity and specificity of the test, and we can find all the probabilities $P(x|COVID)$ by assuming for a moment that we either have COVID-19 or that we don't have COVID-19.\n", "\n", "Assuming we do have COVID, $P(x|COVID^+)$:\n", "$$\\text{True Positive Rate: }P(+|COVID^+) = 0.8 \\text{ Sensitivity/Precision}$$\n", "$$\\text{False Negative Rate: }P(-|COVID^+) = 0.2$$\n", "Assuming we do not have COVID, $P(x|COVID^-)$:\n", "$$\\text{False Positive Rate: }P(+|COVID^-) = 0.0$$\n", "$$\\text{True Negative Rate: }P(-|COVID^-) = 1.0 \\text{ Specificity/Recall}$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now we almost have everything we need to start. The last thing is the probability of $x$, $P(x)$. Because we don't know if we have COVID or not, $P(x)$ actually depends on our prior. It is either $P(x|COVID^+)$ or $P(x|COVID^-)$, so we estimate the probability in this situation (which is easily done, luckily, because it is a binary situation) by multiplying these two probabilities by our priors.\n", "\n", "$$ P(x) = P(x|COVID^+) \\cdot P(COVID^+) + P(x|COVID^-) \\cdot P(COVID^-) $$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Now we can finish our example." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This time around we will assume that our true state of nature is $COVID^-$. This is nicer for us because there are no false positives in this situation. If we were $COVID^+$, then once we got a positive test result, there would be no more uncertainty. For us (the authors), it will be nice for us to see how the uncertainty of our hypothetical selves will decay." ] }, { "cell_type": "code", "execution_count": 33, "metadata": {}, "outputs": [], "source": [ "# Define our priors and conditional probabilities\n", "# We have to assume that our state of nature is COVID-\n", "prior = .5\n", "posCpos = .8\n", "negCpos = .2\n", "posCneg = .0\n", "negCneg = 1." ] }, { "cell_type": "code", "execution_count": 34, "metadata": {}, "outputs": [], "source": [ "posteriors = []\n", "posteriors.append(prior)\n", "for i in range(10):\n", " x = 0 # A negative test result; in other situations, this might be a random variable\n", " if x == 0:\n", " # chance of a negative result given a positive state * chance of a positive state + chance of a negative result ...\n", " px = negCpos * prior + negCneg * (1-prior)\n", " # posterior = likelihood * prior / evidence\n", " prior = negCpos * prior / px\n", " elif x == 1: # If a positive test result\n", " # chance of a positive result given a positive state * chance of a positive state + chance of a positive result ...\n", " px = posCpos * prior + posCneg * (1-prior)\n", " # posterior = likelihood * prior / evidence\n", " prior = posCpos * prior / px\n", " posteriors.append(prior)" ] }, { "cell_type": "code", "execution_count": 35, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[0.5,\n", " 0.16666666666666669,\n", " 0.03846153846153847,\n", " 0.00793650793650794,\n", " 0.0015974440894568696,\n", " 0.0003198976327575177,\n", " 6.399590426212724e-05,\n", " 1.2799836162097128e-05,\n", " 2.559993446416778e-06,\n", " 5.119997378561345e-07,\n", " 1.0239998951424113e-07]" ] }, "execution_count": 35, "metadata": {}, "output_type": "execute_result" } ], "source": [ "posteriors" ] }, { "cell_type": "code", "execution_count": 36, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "import matplotlib.pyplot as plt\n", "plt.plot(posteriors)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Thompson Sampling" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "For Thompson Sampling, we have to be able to apply this to continuous distributions instead of just binary problems. And just to make it easier on ourselves, we will modify Bayes' Rule to be a proportion instead of an equality.\n", "\n", "$$ \\text{Posterior } \\propto \\text{ Likelihood } \\cdot \\text{ Prior} $$\n", "\n", "We can do this because our evidence $P(x)$ is a constant." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "For this topic, we will also be modeling a Multi-Armed Bandit problem. Herbert Robbins and others intellectualized the problem of playing slot machines. Some have different probabilities of paying out and different amounts that pay out when you win. How do you discover most quickly which slot machine is best to play on?" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "So let's play on some slot machines. We will be simulating a Multi-Armed Bandit problem using a Bernoulli Thompson Sampler. Beta distributions are parameterized by $\\alpha$ and $\\beta$ and their probability density function is $f(\\mu; \\alpha, \\beta) \\propto \\mu^{\\alpha-1} \\cdot (1-\\mu)^{\\beta-1}$ Betas are super easy to update when we are using a binomial likelihood function (only two outcomes - success and failure). It looks like this: $L(\\mu) = \\mu^y \\cdot (1-\\mu)^{n-y}$. Put them together and our posterior becomes:\n", "\n", "\\begin{align}\n", "f(\\mu;\\alpha,\\beta|x) &\\propto (\\mu^x \\cdot (1-\\mu)^{1-x}) \\cdot \\mu^{\\alpha-1} \\cdot (1-\\mu)^{\\beta-1} \\\\\n", "f(\\mu;\\alpha,\\beta|x) &\\propto \\mu^{\\alpha-1+x} \\cdot (1-\\mu)^{\\beta-x} \\\\\n", "f(\\mu;\\alpha,\\beta|x) &\\propto f(\\mu;\\alpha+x,\\beta+1-x)\n", "\\end{align}\n", "\n", "In short, if we have a success (a payout), we add one to $\\alpha$. If we have a failure (the machine \"robs\" us of our money), we add one to $\\beta$.\n", "\n", "Let's say in this case that we have two slot machines. Machine 1 pays out \\\\$40 when we win. Machine 2 pays out \\\\$60 when we win. However, we do not know the average frequencies ($\\mu_1, \\mu_2$) with which they pay out. We are left to guess (to form our priors) at what these frequencies might be." ] }, { "cell_type": "code", "execution_count": 37, "metadata": {}, "outputs": [], "source": [ "from scipy.stats import beta" ] }, { "cell_type": "code", "execution_count": 38, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "mu = np.linspace(0,1,100)\n", "p1 = beta.pdf(mu,4,2)\n", "p2 = beta.pdf(mu,2,4)\n", "plt.plot(mu, p1, c='red')\n", "plt.plot(mu, p2, c='blue')\n", "plt.title('Multi-Armed Prior')\n", "plt.ylabel('Probability Density Function')\n", "plt.xlabel('Average Frequency')\n", "plt.legend(['Machine 1','Machine 2'])\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The priors used here are beta priors which (when using a binomial likelihood function as in this one) have really simple rules for updating (finding the posterior). Notice that these priors indicate we believe that Machine 1 (which pays less) pays out more frequently than Machine 2. This is to represent the possibility of believing the casino has made the average payout per game roughly equal throughout the establishment. (But really I just wanted to show the shape of two different beta distributions.)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The dilemma presented here is that we want to explore the possibility that one of these machines pays out more than the other on average, but we also do not want to rule one or the other out too quickly. This is called the explore-exploit dilemma. Thompson Sampling is an incredibly effective and quick method of learning the optimal strategies in a static environment. (Also note that there are ways to add the uncertainty of random walk drift to this problem which I know you would be interested in, Matt.)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To perform a Thompson Sampling, we simply have to pick randomly from our priors two average frequencies, one from each prior. Let's say we sample our priors (using a random number generator) and get .8 for Machine 1 and .2 for Machine 2. We always want to play the slot machine that we guess gives us the most payout so we'll multiply these average frequencies by the size of the payout and get \\\\$32 for Machine 1 and \\\\$12 for Machine 2 and we will pull Machine 1's lever." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Though this may be the more likely outcome, it does not eliminate the possibility of sampling, say, a .6 frequency for Machine 1 and a .5 frequency for Machine 2. In this case, we estimate an average payout of \\\\$24 for Machine 1 and \\\\$30 for Machine 2. In this somewhat more rare case, we will still play Machine 2. The beauty of Thompson Sampling is that we essentially leave all of the exploitation up to chance and simply update the probability distributions that we draw from." ] }, { "cell_type": "code", "execution_count": 52, "metadata": {}, "outputs": [], "source": [ "payout1 = 40\n", "payout2 = 60\n", "beta1 = [4,2]\n", "beta2 = [2,4]\n", "\n", "machine1 = .5\n", "machine2 = .3\n", "\n", "pulls = []\n", "payouts = []\n", "\n", "for _ in range(100):\n", " mu1 = beta.rvs(*beta1)\n", " mu2 = beta.rvs(*beta2)\n", " e1 = mu1*payout1\n", " e2 = mu2*payout2\n", " if e1 > e2:\n", " # Play Machine 1\n", " success = np.random.choice([1,0],p=[machine1, 1-machine1])\n", " payout = payout1*success\n", " if success:\n", " beta1[0] += 1\n", " else:\n", " beta1[1] += 1\n", " pulls.append(1)\n", " else:\n", " # Play Machine 2\n", " success = np.random.choice([1,0],p=[machine2, 1-machine2])\n", " payout = payout2*success\n", " if success:\n", " beta2[0] += 1\n", " else:\n", " beta2[1] += 1\n", " pulls.append(2)\n", " payouts.append(payout)" ] }, { "cell_type": "code", "execution_count": 54, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[39, 43]" ] }, "execution_count": 54, "metadata": {}, "output_type": "execute_result" } ], "source": [ "beta1" ] }, { "cell_type": "code", "execution_count": 55, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[6, 24]" ] }, "execution_count": 55, "metadata": {}, "output_type": "execute_result" } ], "source": [ "beta2" ] }, { "cell_type": "code", "execution_count": 56, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "mu = np.linspace(0,1,100)\n", "p1 = beta.pdf(mu,*beta1)\n", "p2 = beta.pdf(mu,*beta2)\n", "plt.plot(mu, p1, c='red')\n", "plt.plot(mu, p2, c='blue')\n", "plt.title('Multi-Armed Posterior - 100 Pulls')\n", "plt.ylabel('Probability Density Function')\n", "plt.xlabel('Average Frequency')\n", "plt.legend(['Machine 1','Machine 2'])\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": 57, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.plot(pulls)\n", "plt.title('Simulation Pulls')\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 58, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.plot(payouts)\n", "plt.title('Simulation Payouts')\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "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": "3.8.10" } }, "nbformat": 4, "nbformat_minor": 4 }