{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Chapter 6\n", "Original content created by Cam Davidson-Pilon\n", "\n", "Ported to Python 3 and PyMC3 by Max Margenot (@clean_utensils) and Thomas Wiecki (@twiecki) at Quantopian (@quantopian)\n", "\n", "\n", "---\n", "\n", "This chapter of [Bayesian Methods for Hackers](https://github.com/CamDavidsonPilon/Probabilistic-Programming-and-Bayesian-Methods-for-Hackers) focuses on the most debated and discussed part of Bayesian methodologies: how to choose an appropriate prior distribution. We also present how the prior's influence changes as our dataset increases, and an interesting relationship between priors and penalties on linear regression." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Getting our priorities straight\n", "\n", "\n", "Up until now, we have mostly ignored our choice of priors. This is unfortunate as we can be very expressive with our priors, but we also must be careful about choosing them. This is especially true if we want to be objective, that is, not to express any personal beliefs in the priors. \n", "\n", "### Subjective vs Objective priors\n", "\n", "Bayesian priors can be classified into two classes: *objective* priors, which aim to allow the data to influence the posterior the most, and *subjective* priors, which allow the practitioner to express his or her views into the prior. \n", "\n", "What is an example of an objective prior? We have seen some already, including the *flat* prior, which is a uniform distribution over the entire possible range of the unknown. Using a flat prior implies that we give each possible value an equal weighting. Choosing this type of prior is invoking what is called \"The Principle of Indifference\", literally we have no prior reason to favor one value over another. Calling a flat prior over a restricted space an objective prior is not correct, though it seems similar. If we know $p$ in a Binomial model is greater than 0.5, then $\\text{Uniform}(0.5,1)$ is not an objective prior (since we have used prior knowledge) even though it is \"flat\" over [0.5, 1]. The flat prior must be flat along the *entire* range of possibilities. \n", "\n", "Aside from the flat prior, other examples of objective priors are less obvious, but they contain important characteristics that reflect objectivity. For now, it should be said that *rarely* is a objective prior *truly* objective. We will see this later. \n", "\n", "#### Subjective Priors\n", "\n", "On the other hand, if we added more probability mass to certain areas of the prior, and less elsewhere, we are biasing our inference towards the unknowns existing in the former area. This is known as a subjective, or *informative* prior. In the figure below, the subjective prior reflects a belief that the unknown likely lives around 0.5, and not around the extremes. The objective prior is insensitive to this." ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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ja9GRm5cBqO1RMtu0An47fxq2byd4536OvfoBJ/xKcX+TOnQZNZwS9R5gl7n4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\nol1TPv30U9566y2OHz8OQEFBAWfOnHFsL0vUAXx9fQHIz8/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MnwVKqWSlVKJS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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "%matplotlib inline\n", "import numpy as np\n", "import scipy.stats as stats\n", "from IPython.core.pylabtools import figsize\n", "import matplotlib.pyplot as plt\n", "\n", "figsize(12.5,3)\n", "colors = [\"#348ABD\", \"#A60628\", \"#7A68A6\", \"#467821\"]\n", "\n", "x = np.linspace(0,1)\n", "y1, y2 = stats.beta.pdf(x, 1,1), stats.beta.pdf(x, 10,10)\n", "\n", "p = plt.plot(x, y1, \n", " label='An objective prior \\n(uninformative, \\n\"Principle of Indifference\")')\n", "plt.fill_between(x, 0, y1, color = p[0].get_color(), alpha = 0.3)\n", "\n", "p = plt.plot(x,y2 ,\n", " label = \"A subjective prior \\n(informative)\")\n", "plt.fill_between(x, 0, y2, color = p[0].get_color(), alpha = 0.3)\n", "\n", "p = plt.plot(x[25:], 2*np.ones(25), label = \"another subjective prior\")\n", "plt.fill_between(x[25:], 0, 2, color = p[0].get_color(), alpha = 0.3)\n", "\n", "plt.ylim(0,4)\n", "\n", "plt.ylim(0, 4)\n", "leg = plt.legend(loc = \"upper left\")\n", "leg.get_frame().set_alpha(0.4)\n", "plt.title(\"Comparing objective vs. subjective priors for an unknown probability\");" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The choice of a subjective prior does not always imply that we are using the practitioner's subjective opinion: more often the subjective prior was once a posterior to a previous problem, and now the practitioner is updating this posterior with new data. A subjective prior can also be used to inject *domain knowledge* of the problem into the model. We will see examples of these two situations later." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Decision, decisions...\n", "\n", "The choice, either *objective* or *subjective* mostly depends on the problem being solved, but there are a few cases where one is preferred over the other. In instances of scientific research, the choice of an objective prior is obvious. This eliminates any biases in the results, and two researchers who might have differing prior opinions would feel an objective prior is fair. Consider a more extreme situation:\n", "\n", "> A tobacco company publishes a report with a Bayesian methodology that retreated 60 years of medical research on tobacco use. Would you believe the results? Unlikely. The researchers probably chose a subjective prior that too strongly biased results in their favor.\n", "\n", "Unfortunately, choosing an objective prior is not as simple as selecting a flat prior, and even today the problem is still not completely solved. The problem with naively choosing the uniform prior is that pathological issues can arise. Some of these issues are pedantic, but we delay more serious issues to the Appendix of this Chapter (TODO)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We must remember that choosing a prior, whether subjective or objective, is still part of the modeling process. To quote Gelman [5]:\n", "\n", ">... after the model has been fit, one should look at the posterior distribution\n", "and see if it makes sense. If the posterior distribution does not make sense, this implies\n", "that additional prior knowledge is available that has not been included in the model,\n", "and that contradicts the assumptions of the prior distribution that has been used. It is\n", "then appropriate to go back and alter the prior distribution to be more consistent with\n", "this external knowledge.\n", "\n", "If the posterior does not make sense, then clearly one had an idea what the posterior *should* look like (not what one *hopes* it looks like), implying that the current prior does not contain all the prior information and should be updated. At this point, we can discard the current prior and choose a more reflective one.\n", "\n", "Gelman [4] suggests that using a uniform distribution with large bounds is often a good choice for objective priors. Although, one should be wary about using Uniform objective priors with large bounds, as they can assign too large of a prior probability to non-intuitive points. Ask yourself: do you really think the unknown could be incredibly large? Often quantities are naturally biased towards 0. A Normal random variable with large variance (small precision) might be a better choice, or an Exponential with a fat tail in the strictly positive (or negative) case. \n", "\n", "If using a particularly subjective prior, it is your responsibility to be able to explain the choice of that prior, else you are no better than the tobacco company's guilty parties. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Empirical Bayes\n", "\n", "While not a true Bayesian method, *empirical Bayes* is a trick that combines frequentist and Bayesian inference. As mentioned previously, for (almost) every inference problem there is a Bayesian method and a frequentist method. The significant difference between the two is that Bayesian methods have a prior distribution, with hyperparameters $\\alpha$, while empirical methods do not have any notion of a prior. Empirical Bayes combines the two methods by using frequentist methods to select $\\alpha$, and then proceeds with Bayesian methods on the original problem. \n", "\n", "A very simple example follows: suppose we wish to estimate the parameter $\\mu$ of a Normal distribution, with $\\sigma = 5$. Since $\\mu$ could range over the whole real line, we can use a Normal distribution as a prior for $\\mu$. How to select the prior's hyperparameters, denoted ($\\mu_p, \\sigma_p^2$)? The $\\sigma_p^2$ parameter can be chosen to reflect the uncertainty we have. For $\\mu_p$, we have two options:\n", "\n", "1. Empirical Bayes suggests using the empirical sample mean, which will center the prior around the observed empirical mean:\n", "\n", "$$\\mu_p = \\frac{1}{N} \\sum_{i=0}^N X_i$$\n", "\n", "2. Traditional Bayesian inference suggests using prior knowledge, or a more objective prior (zero mean and fat standard deviation).\n", "\n", "Empirical Bayes can be argued as being semi-objective, since while the choice of prior model is ours (hence subjective), the parameters are solely determined by the data.\n", "\n", "Personally, I feel that Empirical Bayes is *double-counting* the data. That is, we are using the data twice: once in the prior, which will influence our results towards the observed data, and again in the inferential engine of MCMC. This double-counting will understate our true uncertainty. To minimize this double-counting, I would only suggest using Empirical Bayes when you have *lots* of observations, else the prior will have too strong of an influence. I would also recommend, if possible, to maintain high uncertainty (either by setting a large $\\sigma_p^2$ or equivalent.)\n", "\n", "Empirical Bayes also violates a theoretical axiom in Bayesian inference. The textbook Bayesian algorithm of:\n", "\n", ">*prior* $\\Rightarrow$ *observed data* $\\Rightarrow$ *posterior* \n", "\n", "is violated by Empirical Bayes, which instead uses \n", "\n", ">*observed data* $\\Rightarrow$ *prior* $\\Rightarrow$ *observed data* $\\Rightarrow$ *posterior*\n", "\n", "Ideally, all priors should be specified *before* we observe the data, so that the data does not influence our prior opinions (see the volumes of research by Daniel Kahneman *et. al* about [anchoring](http://en.wikipedia.org/wiki/Anchoring_and_adjustment))." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Useful priors to know about\n", "\n", "### The Gamma distribution\n", "\n", "A Gamma random variable, denoted $X \\sim \\text{Gamma}(\\alpha, \\beta)$, is a random variable over the positive real numbers. It is in fact a generalization of the Exponential random variable, that is:\n", "\n", "$$\\text{Exp}(\\beta) \\sim \\text{Gamma}(1, \\beta)$$\n", "\n", "This additional parameter allows the probability density function to have more flexibility, hence allowing the practitioner to express his or her subjective priors more accurately. The density function for a $\\text{Gamma}(\\alpha, \\beta)$ random variable is:\n", "\n", "$$f(x \\mid \\alpha, \\beta) = \\frac{\\beta^{\\alpha}x^{\\alpha-1}e^{-\\beta x}}{\\Gamma(\\alpha)}$$\n", "\n", "where $\\Gamma(\\alpha)$ is the [Gamma function](http://en.wikipedia.org/wiki/Gamma_function), and for differing values of $(\\alpha, \\beta)$ looks like:" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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s2YiNjUVYWBieeuop+VhJSUnyEoWlpaW4++67ERYWhvHjx6OoqAgpKSnQarUA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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "figsize(12.5, 5)\n", "gamma = stats.gamma\n", "\n", "parameters = [(1, 0.5), (9, 2), (3, 0.5), (7, 0.5)]\n", "x = np.linspace(0.001 ,20, 150)\n", "for alpha, beta in parameters:\n", " y = gamma.pdf(x, alpha, scale=1./beta)\n", " lines = plt.plot(x, y, label = \"(%.1f,%.1f)\"%(alpha,beta), lw = 3)\n", " plt.fill_between(x, 0, y, alpha = 0.2, color = lines[0].get_color())\n", " plt.autoscale(tight=True)\n", " \n", "plt.legend(title=r\"$\\alpha, \\beta$ - parameters\");" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### The Wishart distribution\n", "\n", "Until now, we have only seen random variables that are scalars. Of course, we can also have *random matrices*! Specifically, the Wishart distribution is a distribution over all [positive semi-definite matrices](http://en.wikipedia.org/wiki/Positive-definite_matrix). Why is this useful to have in our arsenal? (Proper) covariance matrices are positive-definite, hence the Wishart is an appropriate prior for covariance matrices. We can't really visualize a distribution of matrices, so I'll plot some realizations from the $5 \\times 5$ (above) and $20 \\times 20$ (below) Wishart distribution:" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "\n", "n = 4\n", "for i in range(10):\n", " ax = plt.subplot(2, 5, i+1)\n", " if i >= 5:\n", " n = 15\n", " plt.imshow(stats.wishart.rvs(n+1, np.eye(n)), interpolation=\"none\", \n", " cmap = \"hot\")\n", " ax.axis(\"off\")\n", " \n", "plt.suptitle(\"Random matrices from a Wishart Distribution\");" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "One thing to notice is the symmetry of these matrices. The Wishart distribution can be a little troubling to deal with, but we will use it in an example later." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### The Beta distribution\n", "\n", "You may have seen the term beta in previous code in this book. Often, I was implementing a Beta distribution. The Beta distribution is very useful in Bayesian statistics. A random variable $X$ has a $\\text{Beta}$ distribution, with parameters $(\\alpha, \\beta)$, if its density function is:\n", "\n", "$$f_X(x | \\; \\alpha, \\beta ) = \\frac{ x^{(\\alpha - 1)}(1-x)^{ (\\beta - 1) } }{B(\\alpha, \\beta) }$$\n", "\n", "where $B$ is the [Beta function](http://en.wikipedia.org/wiki/Beta_function) (hence the name). The random variable $X$ is only allowed in [0,1], making the Beta distribution a popular distribution for decimal values, probabilities and proportions. The values of $\\alpha$ and $\\beta$, both positive values, provide great flexibility in the shape of the distribution. Below we plot some distributions:" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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Lt0TCU3saV2nonLR8/tAVV413BzbFZCTh2tEYTMaA3E8SaSGEEEKIc9zVJ2k4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vSwh7oDXv2Yx3BP1b1QwoHoXhhz1L1wpZBCYLd2UejcRLF7C/mebQ/WG75P4v5t0n3XSfdfJzF8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\nT1r40z7YaGAyGpi84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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "figsize(12.5, 5)\n", "\n", "params = [(2, 5), (1, 1), (0.5, 0.5), (5, 5), (20, 4), (5, 1)]\n", "\n", "x = np.linspace(0.01, .99, 100)\n", "beta = stats.beta\n", "for a, b in params:\n", " y = beta.pdf(x, a, b)\n", " lines = plt.plot(x, y, label = \"(%.1f,%.1f)\"%(a,b), lw = 3)\n", " plt.fill_between(x, 0, y, alpha = 0.2, color = lines[0].get_color())\n", " plt.autoscale(tight=True)\n", "plt.ylim(0)\n", "plt.legend(loc = 'upper left', title=\"(a,b)-parameters\");" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "One thing I'd like the reader to notice is the presence of the flat distribution above, specified by parameters $(1,1)$. This is the Uniform distribution. Hence the Beta distribution is a generalization of the Uniform distribution, something we will revisit many times.\n", "\n", "There is an interesting connection between the Beta distribution and the Binomial distribution. Suppose we are interested in some unknown proportion or probability $p$. We assign a $\\text{Beta}(\\alpha, \\beta)$ prior to $p$. We observe some data generated by a Binomial process, say $X \\sim \\text{Binomial}(N, p)$, with $p$ still unknown. Then our posterior *is again a Beta distribution*, i.e. $p | X \\sim \\text{Beta}( \\alpha + X, \\beta + N -X )$. Succinctly, one can relate the two by \"a Beta prior with Binomial observations creates a Beta posterior\". This is a very useful property, both computationally and heuristically.\n", "\n", "In light of the above two paragraphs, if we start with a $\\text{Beta}(1,1)$ prior on $p$ (which is a Uniform), observe data $X \\sim \\text{Binomial}(N, p)$, then our posterior is $\\text{Beta}(1 + X, 1 + N - X)$. \n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "##### Example: Bayesian Multi-Armed Bandits\n", "*Adapted from an example by Ted Dunning of MapR Technologies*\n", "\n", "> Suppose you are faced with $N$ slot machines (colourfully called multi-armed bandits). Each bandit has an unknown probability of distributing a prize (assume for now the prizes are the same for each bandit, only the probabilities differ). Some bandits are very generous, others not so much. Of course, you don't know what these probabilities are. By only choosing one bandit per round, our task is devise a strategy to maximize our winnings.\n", "\n", "Of course, if we knew the bandit with the largest probability, then always picking this bandit would yield the maximum winnings. So our task can be phrased as \"Find the best bandit, and as quickly as possible\". \n", "\n", "The task is complicated by the stochastic nature of the bandits. A suboptimal bandit can return many winnings, purely by chance, which would make us believe that it is a very profitable bandit. Similarly, the best bandit can return many duds. Should we keep trying losers then, or give up? \n", "\n", "A more troublesome problem is, if we have found a bandit that returns *pretty good* results, do we keep drawing from it to maintain our *pretty good score*, or do we try other bandits in hopes of finding an *even-better* bandit? This is the exploration vs. exploitation dilemma.\n", "\n", "### Applications\n", "\n", "\n", "The Multi-Armed Bandit problem at first seems very artificial, something only a mathematician would love, but that is only before we address some applications:\n", "\n", "- Internet display advertising: companies have a suite of potential ads they can display to visitors, but the company is not sure which ad strategy to follow to maximize sales. This is similar to A/B testing, but has the added advantage of naturally minimizing strategies that do not work (and generalizes to A/B/C/D... strategies)\n", "- Ecology: animals have a finite amount of energy to expend, and following certain behaviours has uncertain rewards. How does the animal maximize its fitness?\n", "- Finance: which stock option gives the highest return, under time-varying return profiles.\n", "- Clinical trials: a researcher would like to find the best treatment, out of many possible treatment, while minimizing losses. \n", "- Psychology: how does punishment and reward affect our behaviour? How do humans learn?\n", "\n", "Many of these questions above are fundamental to the application's field.\n", "\n", "It turns out the *optimal solution* is incredibly difficult, and it took decades for an overall solution to develop. There are also many approximately-optimal solutions which are quite good. The one I wish to discuss is one of the few solutions that can scale incredibly well. The solution is known as *Bayesian Bandits*.\n", "\n", "\n", "### A Proposed Solution\n", "\n", "\n", "Any proposed strategy is called an *online algorithm* (not in the internet sense, but in the continuously-being-updated sense), and more specifically a reinforcement learning algorithm. The algorithm starts in an ignorant state, where it knows nothing, and begins to acquire data by testing the system. As it acquires data and results, it learns what the best and worst behaviours are (in this case, it learns which bandit is the best). With this in mind, perhaps we can add an additional application of the Multi-Armed Bandit problem:\n", "\n", "- Psychology: how does punishment and reward affect our behaviour? How do humans learn?\n", "\n", "\n", "The Bayesian solution begins by assuming priors on the probability of winning for each bandit. In our vignette we assumed complete ignorance of these probabilities. So a very natural prior is the flat prior over 0 to 1. The algorithm proceeds as follows:\n", "\n", "For each round:\n", "\n", "1. Sample a random variable $X_b$ from the prior of bandit $b$, for all $b$.\n", "2. Select the bandit with largest sample, i.e. select $B = \\text{argmax}\\;\\; X_b$.\n", "3. Observe the result of pulling bandit $B$, and update your prior on bandit $B$.\n", "4. Return to 1.\n", "\n", "That's it. Computationally, the algorithm involves sampling from $N$ distributions. Since the initial priors are $\\text{Beta}(\\alpha=1,\\beta=1)$ (a uniform distribution), and the observed result $X$ (a win or loss, encoded 1 and 0 respectfully) is Binomial, the posterior is a $\\text{Beta}(\\alpha=1+X,\\beta=1+1âˆ’X)$.\n", "\n", "To answer our question from before, this algorithm suggests that we should not discard losers, but we should pick them at a decreasing rate as we gather confidence that there exist *better* bandits. This follows because there is always a non-zero chance that a loser will achieve the status of $B$, but the probability of this event decreases as we play more rounds (see figure below).\n", "\n", "Below we implement Bayesian Bandits using two classes, Bandits that defines the slot machines, and BayesianStrategy which implements the above learning strategy." ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": false }, "outputs": [], "source": [ "rand = np.random.rand\n", "\n", "class Bandits(object):\n", " \"\"\"\n", " This class represents N bandits machines.\n", "\n", " parameters:\n", " p_array: a (n,) Numpy array of probabilities >0, <1.\n", "\n", " methods:\n", " pull( i ): return the results, 0 or 1, of pulling \n", " the ith bandit.\n", " \"\"\"\n", " def __init__(self, p_array):\n", " self.p = p_array\n", " self.optimal = np.argmax(p_array)\n", " \n", " def pull(self, i):\n", " #i is which arm to pull\n", " return np.random.rand() < self.p[i]\n", " \n", " def __len__(self):\n", " return len(self.p)\n", "\n", " \n", "class BayesianStrategy(object):\n", " \"\"\"\n", " Implements a online, learning strategy to solve\n", " the Multi-Armed Bandit problem.\n", " \n", " parameters:\n", " bandits: a Bandit class with .pull method\n", " \n", " methods:\n", " sample_bandits(n): sample and train on n pulls.\n", "\n", " attributes:\n", " N: the cumulative number of samples\n", " choices: the historical choices as a (N,) array\n", " bb_score: the historical score as a (N,) array\n", " \"\"\"\n", " \n", " def __init__(self, bandits):\n", " \n", " self.bandits = bandits\n", " n_bandits = len(self.bandits)\n", " self.wins = np.zeros(n_bandits)\n", " self.trials = np.zeros(n_bandits)\n", " self.N = 0\n", " self.choices = []\n", " self.bb_score = []\n", "\n", " \n", " def sample_bandits(self, n=1):\n", " \n", " bb_score = np.zeros(n)\n", " choices = np.zeros(n)\n", " \n", " for k in range(n):\n", " #sample from the bandits's priors, and select the largest sample\n", " choice = np.argmax(np.random.beta(1 + self.wins, 1 + self.trials - self.wins))\n", " \n", " #sample the chosen bandit\n", " result = self.bandits.pull(choice)\n", " \n", " #update priors and score\n", " self.wins[choice] += result\n", " self.trials[choice] += 1\n", " bb_score[k] = result \n", " self.N += 1\n", " choices[k] = choice\n", " \n", " self.bb_score = np.r_[self.bb_score, bb_score]\n", " self.choices = np.r_[self.choices, choices]\n", " return " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Below we visualize the learning of the Bayesian Bandit solution." ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": false }, "outputs": [], "source": [ "figsize(11.0, 10)\n", "\n", "beta = stats.beta\n", "x = np.linspace(0.001,.999,200)\n", "\n", "def plot_priors(bayesian_strategy, prob, lw = 3, alpha = 0.2, plt_vlines = True):\n", " ## plotting function\n", " wins = bayesian_strategy.wins\n", " trials = bayesian_strategy.trials\n", " for i in range(prob.shape[0]):\n", " y = beta(1+wins[i], 1 + trials[i] - wins[i])\n", " p = plt.plot(x, y.pdf(x), lw = lw)\n", " c = p[0].get_markeredgecolor()\n", " plt.fill_between(x,y.pdf(x),0, color = c, alpha = alpha, \n", " label=\"underlying probability: %.2f\" % prob[i])\n", " if plt_vlines:\n", " plt.vlines(prob[i], 0, y.pdf(prob[i]) ,\n", " colors = c, linestyles = \"--\", lw = 2)\n", " plt.autoscale(tight = \"True\")\n", " plt.title(\"Posteriors After %d pull\" % bayesian_strategy.N +\\\n", " \"s\"*(bayesian_strategy.N > 1))\n", " plt.autoscale(tight=True)\n", " return" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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al8A0NqEhIucCtwAXisinIrJRRJa03SfIGLMS2C0iO4A/Al8NY5Ujlit2IKOu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\nAW7MIKyXFlAUNqDWum9lyLYXs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fI2B3jwwcN3/P9z8uRJXnjhBQAK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hdXaeaOb3dpSmzfNy+NRNCya1j6NhPHohVuvzNcAmEUkVS0tvAY6McI9i4585VIai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\nreNU1jlo6Whg8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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "hidden_prob = np.array([0.85, 0.60, 0.75])\n", "bandits = Bandits(hidden_prob)\n", "bayesian_strat = BayesianStrategy(bandits)\n", "\n", "draw_samples = [1, 1, 3, 10, 10, 25, 50, 100, 200, 600]\n", "\n", "for j,i in enumerate(draw_samples):\n", " plt.subplot(5, 2, j+1) \n", " bayesian_strat.sample_bandits(i)\n", " plot_priors(bayesian_strat, hidden_prob)\n", " #plt.legend()\n", " plt.autoscale(tight = True)\n", "plt.tight_layout()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Note that we don't really care how accurate we become about the inference of the hidden probabilities — for this problem we are more interested in choosing the best bandit (or more accurately, becoming *more confident* in choosing the best bandit). For this reason, the distribution of the red bandit is very wide (representing ignorance about what that hidden probability might be) but we are reasonably confident that it is not the best, so the algorithm chooses to ignore it.\n", "\n", "From the above, we can see that after 1000 pulls, the majority of the \"blue\" function leads the pack, hence we will almost always choose this arm. This is good, as this arm is indeed the best.\n", "\n", "Below is a D3 app that demonstrates our algorithm updating/learning three bandits. The first figure are the raw counts of pulls and wins, and the second figure is a dynamically updating plot. I encourage you to try to guess which bandit is optimal, prior to revealing the true probabilities, by selecting the arm buttons." ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "\n", " \n", " \n", " \n", "\n", " \n", "\n", "\n", " \n", "
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\n", "\n", "\n" ], "text/plain": [ "" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from IPython.core.display import HTML\n", "\n", "#try executing the below command twice if the first time doesn't work\n", "HTML(filename = \"BanditsD3.html\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Deviations of the observed ratio from the highest probability is a measure of performance. For example,in the long run, optimally we can attain the reward/pull ratio of the maximum bandit probability. Long-term realized ratios less than the maximum represent inefficiencies. (Realized ratios larger than the maximum probability is due to randomness, and will eventually fall below). \n", "\n", "### A Measure of *Good*\n", "\n", "We need a metric to calculate how well we are doing. Recall the absolute *best* we can do is to always pick the bandit with the largest probability of winning. Denote this best bandit's probability by $w_{opt}$. Our score should be relative to how well we would have done had we chosen the best bandit from the beginning. This motivates the *total regret* of a strategy, defined:\n", "\n", "\\begin{align}\n", "R_T & = \\sum_{i=1}^{T} \\left( w_{opt} - w_{B(i)} \\right)\\\\\\\\\n", "& = Tw^* - \\sum_{i=1}^{T} \\; w_{B(i)} \n", "\\end{align}\n", "\n", "\n", "where $w_{B(i)}$ is the probability of a prize of the chosen bandit in the $i$ round. A total regret of 0 means the strategy is matching the best possible score. This is likely not possible, as initially our algorithm will often make the wrong choice. Ideally, a strategy's total regret should flatten as it learns the best bandit. (Mathematically, we achieve $w_{B(i)}=w_{opt}$ often)\n", "\n", "\n", "Below we plot the total regret of this simulation, including the scores of some other strategies:\n", "\n", "1. Random: randomly choose a bandit to pull. If you can't beat this, just stop. \n", "2. Largest Bayesian credible bound: pick the bandit with the largest upper bound in its 95% credible region of the underlying probability. \n", "3. Bayes-UCB algorithm: pick the bandit with the largest *score*, where score is a dynamic quantile of the posterior (see [4] )\n", "3. Mean of posterior: choose the bandit with the largest posterior mean. This is what a human player (sans computer) would likely do. \n", "3. Largest proportion: pick the bandit with the current largest observed proportion of winning. \n", "\n", "The code for these are in the other_strats.py, where you can implement your own very easily." ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "collapsed": false }, "outputs": [], "source": [ "figsize(12.5, 5)\n", "from other_strats import *\n", "\n", "#define a harder problem\n", "hidden_prob = np.array([0.15, 0.2, 0.1, 0.05])\n", "bandits = Bandits(hidden_prob)\n", "\n", "#define regret\n", "def regret(probabilities, choices):\n", " w_opt = probabilities.max()\n", " return (w_opt - probabilities[choices.astype(int)]).cumsum()\n", "\n", "#create new strategies\n", "strategies= [upper_credible_choice, \n", " bayesian_bandit_choice, \n", " ucb_bayes , \n", " max_mean,\n", " random_choice]\n", "algos = []\n", "for strat in strategies:\n", " algos.append(GeneralBanditStrat(bandits, strat))" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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9xKZNm7BYLCQlJbF9+3YuXLhAlSpVaNSokfV8du3aZe0htz1fW5YtW0ZkZCQJ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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "#train 10000 times\n", "for strat in algos:\n", " strat.sample_bandits(10000)\n", " \n", "#test and plot\n", "for i,strat in enumerate(algos):\n", " _regret = regret(hidden_prob, strat.choices)\n", " plt.plot(_regret, label = strategies[i].__name__, lw = 3)\n", "\n", "plt.title(\"Total Regret of Bayesian Bandits Strategy vs. Random guessing\")\n", "plt.xlabel(\"Number of pulls\")\n", "plt.ylabel(\"Regret after $n$ pulls\");\n", "plt.legend(loc = \"upper left\");" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Like we wanted, Bayesian bandits and other strategies have decreasing rates of regret, representing we are achieving optimal choices. To be more scientific so as to remove any possible luck in the above simulation, we should instead look at the *expected total regret*:\n", "\n", "$$\\bar{R}_T = E[ R_T ]$$\n", "\n", "It can be shown that any *sub-optimal* strategy's expected total regret is bounded below logarithmically. Formally,\n", "\n", "$$E[R_T] = \\Omega \\left( \\;\\log(T)\\; \\right)$$\n", "\n", "Thus, any strategy that matches logarithmic-growing regret is said to \"solve\" the Multi-Armed Bandit problem [3].\n", "\n", "Using the Law of Large Numbers, we can approximate Bayesian Bandit's expected total regret by performing the same experiment many times (500 times, to be fair):" ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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QQpsAaVqJLqUsnGqchZaaDbU2ZrMZh8Ph2c7Nza3VQC4uLqa8vNzTwM7IyCA1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\nE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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "#this can be slow, so I recommend NOT running it. \n", "\n", "trials = 500\n", "expected_total_regret = np.zeros((10000, 3))\n", "\n", "for i_strat, strat in enumerate(strategies[:-2]):\n", " for i in range(trials):\n", " general_strat = GeneralBanditStrat(bandits, strat)\n", " general_strat.sample_bandits(10000)\n", " _regret = regret(hidden_prob, general_strat.choices)\n", " expected_total_regret[:,i_strat] += _regret\n", " plt.plot(expected_total_regret[:,i_strat]/trials, lw =3, label = strat.__name__)\n", " \n", "plt.title(\"Expected Total Regret of Multi-armed Bandit strategies\")\n", "plt.xlabel(\"Number of pulls\")\n", "plt.ylabel(\"Exepected Total Regret \\n after $n$ pulls\");\n", "plt.legend(loc = \"upper left\");" ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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0009z9OhRi2vCw8N56aWX2LBhAx07dgSgV69e5vaW9Lvmpl69ely5coUmTZoA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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.figure()\n", "[pl1, pl2, pl3] = plt.plot(expected_total_regret[:, [0,1,2]], lw = 3)\n", "plt.xscale(\"log\")\n", "plt.legend([pl1, pl2, pl3], \n", " [\"Upper Credible Bound\", \"Bayesian Bandit\", \"UCB-Bayes\"],\n", " loc=\"upper left\")\n", "plt.ylabel(\"Exepected Total Regret \\n after $\\log{n}$ pulls\");\n", "plt.title( \"log-scale of above\" );\n", "plt.ylabel(\"Exepected Total Regret \\n after $\\log{n}$ pulls\");" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Extending the algorithm \n", "\n", "\n", "Because of the Bayesian Bandits algorithm's simplicity, it is easy to extend. Some possibilities:\n", "\n", "- If interested in the *minimum* probability (eg: where prizes are a bad thing), simply choose $B = \\text{argmin} \\; X_b$ and proceed.\n", "\n", "- Adding learning rates: Suppose the underlying environment may change over time. Technically the standard Bayesian Bandit algorithm would self-update itself (awesome) by noting that what it thought was the best is starting to fail more often. We can motivate the algorithm to learn changing environments quicker by simply adding a *rate* term upon updating:\n", "\n", " self.wins[choice] = rate*self.wins[choice] + result\n", " self.trials[choice] = rate*self.trials[choice] + 1\n", "\n", " If rate < 1, the algorithm will *forget* its previous wins quicker and there will be a downward pressure towards ignorance. Conversely, setting rate > 1 implies your algorithm will act more risky, and bet on earlier winners more often and be more resistant to changing environments. \n", "\n", "- Hierarchical algorithms: We can setup a Bayesian Bandit algorithm on top of smaller bandit algorithms. Suppose we have $N$ Bayesian Bandit models, each varying in some behavior (for example different rate parameters, representing varying sensitivity to changing environments). On top of these $N$ models is another Bayesian Bandit learner that will select a sub-Bayesian Bandit. This chosen Bayesian Bandit will then make an internal choice as to which machine to pull. The super-Bayesian Bandit updates itself depending on whether the sub-Bayesian Bandit was correct or not. \n", "\n", "- Extending the rewards, denoted $y_a$ for bandit $a$, to random variables from a distribution $f_{y_a}(y)$ is straightforward. More generally, this problem can be rephrased as \"Find the bandit with the largest expected value\", as playing the bandit with the largest expected value is optimal. In the case above, $f_{y_a}$ was Bernoulli with probability $p_a$, hence the expected value for a bandit is equal to $p_a$, which is why it looks like we are aiming to maximize the probability of winning. If $f$ is not Bernoulli, and it is non-negative, which can be accomplished apriori by shifting the distribution (we assume we know $f$), then the algorithm behaves as before:\n", "\n", " For each round, \n", " \n", " 1. Sample a random variable $X_b$ from the prior of bandit $b$, for all $b$.\n", " 2. Select the bandit with largest sample, i.e. select bandit $B = \\text{argmax}\\;\\; X_b$.\n", " 3. Observe the result,$R \\sim f_{y_a}$, of pulling bandit $B$, and update your prior on bandit $B$.\n", " 4. Return to 1\n", "\n", " The issue is in the sampling of $X_b$ drawing phase. With Beta priors and Bernoulli observations, we have a Beta posterior — this is easy to sample from. But now, with arbitrary distributions $f$, we have a non-trivial posterior. Sampling from these can be difficult.\n", "\n", "- There has been some interest in extending the Bayesian Bandit algorithm to commenting systems. Recall in Chapter 4, we developed a ranking algorithm based on the Bayesian lower-bound of the proportion of upvotes to total votes. One problem with this approach is that it will bias the top rankings towards older comments, since older comments naturally have more votes (and hence the lower-bound is tighter to the true proportion). This creates a positive feedback cycle where older comments gain more votes, hence are displayed more often, hence gain more votes, etc. This pushes any new, potentially better comments, towards the bottom. J. Neufeld proposes a system to remedy this that uses a Bayesian Bandit solution.\n", "\n", "His proposal is to consider each comment as a Bandit, with the number of pulls equal to the number of votes cast, and number of rewards as the number of upvotes, hence creating a $\\text{Beta}(1+U,1+D)$ posterior. As visitors visit the page, samples are drawn from each bandit/comment, but instead of displaying the comment with the $\\max$ sample, the comments are ranked according to the ranking of their respective samples. From J. Neufeld's blog [7]:\n", "\n", " > [The] resulting ranking algorithm is quite straightforward, each new time the comments page is loaded, the score for each comment is sampled from a $\\text{Beta}(1+U,1+D)$, comments are then ranked by this score in descending order... This randomization has a unique benefit in that even untouched comments $(U=1,D=0)$ have some chance of being seen even in threads with 5000+ comments (something that is not happening now), but, at the same time, the user is not likely to be inundated with rating these new comments. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Just for fun, though the colors explode, we watch the Bayesian Bandit algorithm learn 15 different options. " ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[ 6.78509844e-03 9.68721665e-02 3.16101371e-02 8.88059449e-02\n", " 3.32812651e-02 6.59572621e-02 7.91635546e-02 5.97822577e-02\n", " 1.17088549e-01 1.29945195e-05 3.66798062e-02 5.77077187e-02\n", " 4.32774140e-02 6.94914246e-02 1.22741733e-01 5.13528129e-02\n", " 3.29414904e-01 5.13320236e-02 5.35031763e-02 1.57610420e-02\n", " 1.94570205e-02 1.11759388e-01 3.23349076e-02 2.04068995e-02\n", " 1.47822753e-01 8.24022697e-03 3.20395660e-04 4.45643230e-03\n", " 6.42090321e-03 7.29322919e-02 8.18486095e-02 5.05066236e-03\n", " 1.73946201e-01 6.48018322e-02 7.70657954e-03]\n" ] }, { "data": { "image/png": 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+dbFctq6h1KculivGXt/1qYtl69/fhlCf2vr9LWuvpk+fbvN9p5Cydgc9hIeH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\n3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JOPVvyP/lmXU3awkFI5j5763jw4/X/k/jOHBF8xaxNuZtrvXmi5vdZCCCTf80jKGoSU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\nQkxEiYoYQhXYJtmwTrNh0WxYRBZWqWJJCLSoR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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "figsize(12.0, 8)\n", "beta = stats.beta\n", "hidden_prob = beta.rvs(1,13, size = 35)\n", "print(hidden_prob)\n", "bandits = Bandits(hidden_prob)\n", "bayesian_strat = BayesianStrategy(bandits)\n", "\n", "for j,i in enumerate([100, 200, 500, 1300]):\n", " plt.subplot(2, 2, j+1) \n", " bayesian_strat.sample_bandits(i)\n", " plot_priors(bayesian_strat, hidden_prob, lw = 2, alpha = 0.0, plt_vlines=False)\n", " #plt.legend()\n", " plt.xlim(0, 0.5)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Eliciting expert prior\n", "\n", "Specifying a subjective prior is how practitioners incorporate domain knowledge about the problem into our mathematical framework. Allowing domain knowledge is useful for many reasons:\n", "\n", "- Aids speeds of MCMC convergence. For example, if we know the unknown parameter is strictly positive, then we can restrict our attention there, hence saving time that would otherwise be spent exploring negative values.\n", "- More accurate inference. By weighing prior values near the true unknown value higher, we are narrowing our eventual inference (by making the posterior tighter around the unknown) \n", "- Express our uncertainty better. See the *Price is Right* problem in Chapter 5.\n", "\n", "plus many other reasons. Of course, practitioners of Bayesian methods are not experts in every field, so we must turn to domain experts to craft our priors. We must be careful with how we elicit these priors though. Some things to consider:\n", "\n", "1. From experience, I would avoid introducing Betas, Gammas, etc. to non-Bayesian practitioners. Furthermore, non-statisticians can get tripped up by how a continuous probability function can have a value exceeding one.\n", "\n", "2. Individuals often neglect the rare *tail-events* and put too much weight around the mean of distribution. \n", "\n", "3. Related to above is that almost always individuals will under-emphasize the uncertainty in their guesses.\n", "\n", "Eliciting priors from non-technical experts is especially difficult. Rather than introduce the notion of probability distributions, priors, etc. that may scare an expert, there is a much simpler solution. \n", "\n", "### Trial roulette method \n", "\n", "\n", "The *trial roulette method* [8] focuses on building a prior distribution by placing counters (think casino chips) on what the expert thinks are possible outcomes. The expert is given $N$ counters (say $N=20$) and is asked to place them on a pre-printed grid, with bins representing intervals. Each column would represent their belief of the probability of getting the corresponding bin result. Each chip would represent an $\\frac{1}{N} = 0.05$ increase in the probability of the outcome being in that interval. For example [9]:\n", "\n", "> A student is asked to predict the mark in a future exam. The figure below shows a completed grid for the elicitation of a subjective probability distribution. The horizontal axis of the grid shows the possible bins (or mark intervals) that the student was asked to consider. The numbers in top row record the number of chips per bin. The completed grid (using a total of 20 chips) shows that the student believes there is a 30% chance that the mark will be between 60 and 64.9.\n", "\n", "\n", "\n", "\n", "From this, we can fit a distribution that captures the expert's choice. Some reasons in favor of using this technique are:\n", "\n", "1. Many questions about the shape of the expert's subjective probability distribution can be answered without the need to pose a long series of questions to the expert - the statistician can simply read off density above or below any given point, or that between any two points.\n", "\n", "2. During the elicitation process, the experts can move around the chips if unsatisfied with the way they placed them initially - thus they can be sure of the final result to be submitted.\n", "\n", "3. It forces the expert to be coherent in the set of probabilities that are provided. If all the chips are used, the probabilities must sum to one.\n", "\n", "4. Graphical methods seem to provide more accurate results, especially for participants with modest levels of statistical sophistication." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "##### Example: Stock Returns\n", "\n", "\n", "Take note stock brokers: you're doing it wrong. When choosing which stocks to pick, an analyst will often look at the *daily return* of the stock. Suppose $S_t$ is the price of the stock on day $t$, then the daily return on day $t$ is :\n", "\n", "$$r_t = \\frac{ S_t - S_{t-1} }{ S_{t-1} }$$\n", "\n", "The *expected daily return* of a stock is denoted $\\mu = E[ r_t ]$. Obviously, stocks with high expected returns are desirable. Unfortunately, stock returns are so filled with noise that it is very hard to estimate this parameter. Furthermore, the parameter might change over time (consider the rises and falls of AAPL stock), hence it is unwise to use a large historical dataset. \n", "\n", "Historically, the expected return has been estimated by using the sample mean. This is a bad idea. As mentioned, the sample mean of a small sized dataset has enormous potential to be very wrong (again, see Chapter 4 for full details). Thus Bayesian inference is the correct procedure here, since we are able to see our uncertainty along with probable values.\n", "\n", "For this exercise, we will be examining the daily returns of the AAPL, GOOG, MSFT and AMZN. Before we pull in the data, suppose we ask our a stock fund manager (an expert in finance, but see [10] ), \n", "\n", "> What do you think the return profile looks like for each of these companies?\n", "\n", "Our stock broker, without needing to know the language of Normal distributions, or priors, or variances, etc. creates four distributions using the trial roulette method above. Suppose they look enough like Normals, so we fit Normals to them. They may look like: " ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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KyJHyzw+7HatpfNnJGYrptGMrMAGISHkUIkN2DRvKGeNlzf8ppYa8Mn/OK+UE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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "figsize(11., 5)\n", "colors = [\"#348ABD\", \"#A60628\", \"#7A68A6\", \"#467821\"]\n", "\n", "normal = stats.norm\n", "x = np.linspace(-0.15, 0.15, 100)\n", "\n", "expert_prior_params = {\"AAPL\":(0.05, 0.03),\n", " \"GOOG\":(-0.03, 0.04), \n", " \"TSLA\": (-0.02, 0.01), \n", " \"AMZN\": (0.03, 0.02), \n", " }\n", "\n", "for i, (name, params) in enumerate(expert_prior_params.items()):\n", " plt.subplot(2, 2, i+1)\n", " y = normal.pdf(x, params[0], scale = params[1])\n", " #plt.plot( x, y, c = colors[i] )\n", " plt.fill_between(x, 0, y, color = colors[i], linewidth=2,\n", " edgecolor = colors[i], alpha = 0.6)\n", " plt.title(name + \" prior\")\n", " plt.vlines(0, 0, y.max(), \"k\",\"--\", linewidth = 0.5)\n", " plt.xlim(-0.15, 0.15)\n", "plt.tight_layout()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Note that these are subjective priors: the expert has a personal opinion on the stock returns of each of these companies, and is expressing them in a distribution. He's not wishful thinking -- he's introducing domain knowledge.\n", "\n", "In order to better model these returns, we should investigate the *covariance matrix* of the returns. For example, it would be unwise to invest in two stocks that are highly correlated, since they are likely to tank together (hence why fund managers suggest a diversification strategy). We will use the *Wishart distribution* for this, introduced earlier." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's get some historical data for these stocks. We will use the covariance of the returns as a starting point for our Wishart random variable. This is not empirical bayes (as we will go over later) because we are only deciding the starting point, not influencing the parameters." ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "collapsed": false }, "outputs": [], "source": [ "# I wish I could have used Pandas as a prereq for this book, but oh well.\n", "import datetime\n", "import collections\n", "import ystockquote as ysq\n", "import pandas as pd\n", "\n", "n_observations = 100 # we will truncate the the most recent 100 days.\n", "\n", "stocks = [\"AAPL\", \"GOOG\", \"TSLA\", \"AMZN\"]\n", "\n", "enddate = \"2015-04-27\"\n", "startdate = \"2012-09-01\"\n", "\n", "CLOSE = 6\n", "\n", "stock_closes = pd.DataFrame()\n", "\n", "for stock in stocks:\n", " x = np.array(ysq.get_historical_prices(stock, startdate, enddate))\n", " stock_series = pd.Series(x[1:,CLOSE].astype(float), name=stock)\n", " stock_closes[stock] = stock_series\n", "\n", "stock_closes = stock_closes[::-1]\n", "stock_returns = stock_closes.pct_change()[1:][-n_observations:]\n", " \n", "dates = list(map(lambda x: datetime.datetime.strptime(x, \"%Y-%m-%d\"), x[1:n_observations+1,0]))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "And here let's form our basic model:" ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Applied log-transform to c and added transformed c_log_ to model.\n", "Added new variable c to model diagonal of Wishart.\n", "Added new variable z to model off-diagonals of Wishart.\n" ] } ], "source": [ "import pymc3 as pm\n", "import theano.tensor as tt\n", "from theano.tensor.nlinalg import matrix_inverse, diag, matrix_dot\n", "\n", "prior_mu = np.array([x[0] for x in expert_prior_params.values()])\n", "prior_std = np.array([x[1] for x in expert_prior_params.values()])\n", "\n", "init = stock_returns.cov()\n", "\n", "with pm.Model() as model:\n", " cov_matrix = pm.WishartBartlett(\"covariance\", np.diag(prior_std**2), 10, testval = init)\n", "\n", " mu = pm.Normal(\"returns\", mu=prior_mu, sd=1, shape=4)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here are the returns for our chosen stocks:" ] }, { "cell_type": "code", "execution_count": 17, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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9x7dyJGMfmsbvxzt37M6rd9umd0ZCQgKxsbGNzjdv7wrBSa21V719zkC61trf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7HmNjwix/B+nZVsq5601Bh+eO/QrWzdZht7yjvYUdJO7jnxJ756NQviA1icGEhyqOGyn3ub3crT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\nIOk7wDXAKEmy/TfgubKo/xD4aRk3yPY75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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "figsize(12.5, 4)\n", "\n", "cum_returns = np.cumprod(1 + stock_returns) - 1\n", "cum_returns.index = dates[::-1]\n", "cum_returns.plot()\n", "\n", "plt.legend(loc = \"upper left\")\n", "plt.title(\"Return space\")\n", "plt.ylabel(\"Return of $1 on first date, x100%\");" ] }, { "cell_type": "code", "execution_count": 18, "metadata": { "collapsed": false, "scrolled": true }, "outputs": [ { "data": { "image/png": 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WfYWqbjZYNAYq49fqydJXXQFpcPi97GqgM4uV7nRPV3rpwFpfB3n76/rVVx1SqSsekXQY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\nByKfPGWNoZFfGS4EfmZmofg+/xJCWBunWCIi0samHd4qIiL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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "figsize(11., 5 )\n", "\n", "for i, _stock in enumerate(stocks):\n", " plt.subplot(2,2,i+1)\n", " plt.hist(stock_returns[_stock], bins=20,\n", " normed = True, histtype=\"stepfilled\",\n", " color=colors[i], alpha=0.7)\n", " plt.title(_stock + \" returns\")\n", " plt.xlim(-0.15, 0.15)\n", "\n", "plt.tight_layout()\n", "plt.suptitle(\"Histogram of daily returns\", size =14);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Below we perform the inference on the posterior mean return and posterior covariance matrix. " ] }, { "cell_type": "code", "execution_count": 19, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " [-------100%-------] 5000 of 5000 in 40.4 sec. | SPS: 123.8 | ETA: 0.0" ] } ], "source": [ "with model:\n", " obs = pm.MvNormal(\"observed returns\", mu=mu, cov=cov_matrix, observed=stock_returns)\n", " step = pm.NUTS()\n", " trace = pm.sample(5000, step=step)" ] }, { "cell_type": "code", "execution_count": 20, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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uQPijbP1Rtv4oW3+UrT/K1q/uMI76okWLmDNnDrNnz2bJkiXs2rWr+b3evXtz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\niIiEkGrU85TqzvxRtv4oW39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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "figsize(12.5,4)\n", "\n", "#examine the mean return first.\n", "mu_samples = trace[\"returns\"]\n", "\n", "for i in range(4):\n", " plt.hist(mu_samples[:,i], alpha = 0.8 - 0.05*i, bins = 30,\n", " histtype=\"stepfilled\", normed=True, \n", " label = \"%s\" % stock_returns.columns[i])\n", "\n", "plt.vlines(mu_samples.mean(axis=0), 0, 500, linestyle=\"--\", linewidth = .5)\n", "\n", "plt.title(\"Posterior distribution of$\\mu$, daily stock returns\")\n", "plt.legend();" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "(Plots like these are what inspired the book's cover.)\n", "\n", "What can we say about the results above? Clearly TSLA has been a strong performer, and our analysis suggests that it has an almost 1% daily return! Similarly, most of the distribution of AAPL is negative, suggesting that its *true daily return* is negative.\n", "\n", "\n", "You may not have immediately noticed, but these variables are a whole order of magnitude *less* than our priors on them. For example, to put these one the same scale as the above prior distributions:" ] }, { "cell_type": "code", "execution_count": 21, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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k6WHgJknnAU8BZ7UykWYD9cS3rmFt55JWJ8OspepdB8L6kEJ/uhRiBI+BKJIU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\ndUmaVbbv65LmSJoh6X8l7VL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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "figsize(11.0,3)\n", "for i in range(4):\n", " plt.subplot(2,2,i+1)\n", " plt.hist(mu_samples[:,i], alpha = 0.8 - 0.05*i, bins = 30,\n", " histtype=\"stepfilled\", normed=True, color = colors[i],\n", " label = \"%s\" % stock_returns.columns[i])\n", " plt.title(\"%s\" % stock_returns.columns[i])\n", " plt.xlim(-0.15, 0.15)\n", " \n", "plt.suptitle(\"Posterior distribution of daily stock returns\")\n", "plt.tight_layout()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Why did this occur? Recall how I mentioned that finance has a very very low signal to noise ratio. This implies an environment where inference is much more difficult. One should be careful about over-interpreting these results: notice (in the first figure) that each distribution is positive at 0, implying that the stock may return nothing. Furthermore, the subjective priors influenced the results. From the fund managers point of view, this is good as it reflects his updated beliefs about the stocks, whereas from a neutral viewpoint this can be too subjective of a result. \n", "\n", "Below we show the posterior correlation matrix, and posterior standard deviations. An important caveat to know is that the Wishart distribution models the *inverse covariance matrix*, so we must invert it to get the covariance matrix. We also normalize the matrix to acquire the *correlation matrix*. Since we cannot plot hundreds of matrices effectively, we settle by summarizing the posterior distribution of correlation matrices by showing the *mean posterior correlation matrix* (defined on line 2)." ] }, { "cell_type": "code", "execution_count": 22, "metadata": { "collapsed": false, "scrolled": true }, "outputs": [ { "data": { "image/png": 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YzC7u0w1yzuXqmdVrmDZvZbOr0edOGTPMG9m94Hd8rIGPk52fVriqrpjDazRk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\niend4rykJ4BnzOw14DVJdwF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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "cov_samples = trace[\"covariance\"]\n", "mean_covariance_matrix = cov_samples.mean(axis=0)\n", "\n", "def cov2corr(A):\n", " \"\"\"\n", " covariance matrix to correlation matrix.\n", " \"\"\"\n", " d = np.sqrt(A.diagonal())\n", " A = ((A.T/d).T)/d\n", " #A[ np.diag_indices(A.shape[0]) ] = np.ones( A.shape[0] )\n", " return A\n", "\n", "\n", "plt.subplot(1,2,1)\n", "plt.imshow(cov2corr(mean_covariance_matrix) , interpolation=\"none\", \n", " cmap = \"hot\") \n", "plt.xticks(np.arange(4), stock_returns.columns)\n", "plt.yticks(np.arange(4), stock_returns.columns)\n", "plt.colorbar(orientation=\"vertical\")\n", "plt.title(\"(mean posterior) Correlation Matrix\")\n", "\n", "plt.subplot(1,2,2)\n", "plt.bar(np.arange(4), np.sqrt(np.diag(mean_covariance_matrix)),\n", " color = \"#348ABD\", alpha = 0.7)\n", "plt.xticks(np.arange(4) + 0.5, stock_returns.columns);\n", "plt.title(\"(mean posterior) standard deviations of daily stock returns\")\n", "\n", "plt.tight_layout();\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Looking at the above figures, we can say that likely TSLA has an above-average volatility (looking at the return graph this is quite clear). The correlation matrix shows that there are not strong correlations present, but perhaps GOOG and AMZN express a higher correlation (about 0.30). \n", "\n", "With this Bayesian analysis of the stock market, we can throw it into a Mean-Variance optimizer (which I cannot stress enough, do not use with frequentist point estimates) and find the minimum. This optimizer balances the tradeoff between a high return and high variance.\n", "\n", "$$w_{opt} = \\max_{w} \\frac{1}{N}\\left( \\sum_{i=0}^N \\mu_i^T w - \\frac{\\lambda}{2}w^T\\Sigma_i w \\right)$$\n", "\n", "where$\\mu_i$and$\\Sigma_i$are the$i$th posterior estimate of the mean returns and the covariance matrix. This is another example of loss function optimization." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Protips for the Wishart distribution\n", "\n", "If you plan to be using the Wishart distribution, read on. Else, feel free to skip this. \n", "\n", "In the problem above, the Wishart distribution behaves pretty nicely. Unfortunately, this is rarely the case. The problem is that estimating an$NxN$covariance matrix involves estimating$\\frac{1}{2}N(N-1)$unknowns. This is a large number even for modest$N$. Personally, I've tried performing a similar simulation as above with$N = 23$stocks, and ended up giving considering that I was requesting my MCMC simulation to estimate at least$\\frac{1}{2}23*22 = 253$additional unknowns (plus the other interesting unknowns in the problem). This is not easy for MCMC. Essentially, you are asking you MCMC to traverse 250+ dimensional space. And the problem seemed so innocent initially! Below are some tips, in order of supremacy:\n", "\n", "1. Use conjugancy if it applies. See section below.\n", "\n", "2. Use a good starting value. What might be a good starting value? Why, the data's sample covariance matrix is! Note that this is not empirical Bayes: we are not touching the prior's parameters, we are modifying the starting value of the MCMC. Due to numerical instability, it is best to truncate the floats in the sample covariance matrix down a few degrees of precision (e.g. instability can cause unsymmetrical matrices, which can cause PyMC3 to cry.). \n", "\n", "3. Provide as much domain knowledge in the form of priors, if possible. I stress *if possible*. It is likely impossible to have an estimate about each$\\frac{1}{2}N(N-1)$unknown. In this case, see number 4.\n", "\n", "4. Use empirical Bayes, i.e. use the sample covariance matrix as the prior's parameter.\n", "\n", "5. For problems where$N$is very large, nothing is going to help. Instead, ask, do I really care about *every* correlation? Probably not. Further ask yourself, do I really really care about correlations? Possibly not. In finance, we can set an informal hierarchy of what we might be interested in the most: first a good estimate of$\\mu$, the variances along the diagonal of the covariance matrix are secondly important, and finally the correlations are least important. So, it might be better to ignore the$\\frac{1}{2}(N-1)(N-2)$correlations and instead focus on the more important unknowns.\n", "\n", "**Another thing** to note is that the implementation of the Wishart distribution has changed in from PyMC to PyMC3. Wishart distribution matrices are required to have certain mathematical characteristics that are very restrictive. This makes it so that it is impossible for MCMC methods to propose matrices that will be accepted in our sampling procedure. With our model here we sample the Bartlett decomposition of a Wishart distribution matrix and use that to calculate our samples for the covariance matrix (http://en.wikipedia.org/wiki/Wishart_distribution#Bartlett_decomposition)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Conjugate Priors\n", "\n", "Recall that a$\\text{Beta}$prior with$\\text{Binomial}$data implies a$\\text{Beta}$posterior. Graphically:\n", "\n", "$$\\underbrace{\\text{Beta}}_{\\text{prior}} \\cdot \\overbrace{\\text{Binomial}}^{\\text{data}} = \\overbrace{\\text{Beta}}^{\\text{posterior} }$$ \n", "\n", "Notice the$\\text{Beta}$on both sides of this equation (no, you cannot cancel them, this is not a *real* equation). This is a really useful property. It allows us to avoid using MCMC, since the posterior is known in closed form. Hence inference and analytics are easy to derive. This shortcut was the heart of the Bayesian Bandit algorithm above. Fortunately, there is an entire family of distributions that have similar behaviour. \n", "\n", "Suppose$X$comes from, or is believed to come from, a well-known distribution, call it$f_{\\alpha}$, where$\\alpha$are possibly unknown parameters of$f$.$f$could be a Normal distribution, or Binomial distribution, etc. For particular distributions$f_{\\alpha}$, there may exist a prior distribution$p_{\\beta}$, such that:\n", "\n", "$$\\overbrace{p_{\\beta}}^{\\text{prior}} \\cdot \\overbrace{f_{\\alpha}(X)}^{\\text{data}} = \\overbrace{p_{\\beta'}}^{\\text{posterior} }$$ \n", "\n", "where$\\beta'$is a different set of parameters *but$p$is the same distribution as the prior*. A prior$p$that satisfies this relationship is called a *conjugate prior*. As I mentioned, they are useful computationally, as we can avoided approximate inference using MCMC and go directly to the posterior. This sounds great, right?\n", "\n", "Unfortunately, not quite. There are a few issues with conjugate priors.\n", "\n", "1. The conjugate prior is not objective. Hence only useful when a subjective prior is required. It is not guaranteed that the conjugate prior can accommodate the practitioner's subjective opinion.\n", "\n", "2. There typically exist conjugate priors for simple, one dimensional problems. For larger problems, involving more complicated structures, hope is lost to find a conjugate prior. For smaller models, Wikipedia has a nice [table of conjugate priors](http://en.wikipedia.org/wiki/Conjugate_prior#Table_of_conjugate_distributions).\n", "\n", "Really, conjugate priors are only useful for their mathematical convenience: it is simple to go from prior to posterior. I personally see conjugate priors as only a neat mathematical trick, and offer little insight into the problem at hand. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Jefferys Priors\n", "\n", "Earlier, we talked about objective priors rarely being *objective*. Partly what we mean by this is that we want a prior that doesn't bias our posterior estimates. The flat prior seems like a reasonable choice as it assigns equal probability to all values. \n", "\n", "But the flat prior is not transformation invariant. What does this mean? Suppose we have a random variable$\\textbf X$from Bernoulli($\\theta$). We define the prior on$p(\\theta) = 1$. " ] }, { "cell_type": "code", "execution_count": 23, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "figsize(12.5, 5)\n", "\n", "x = np.linspace(0.000 ,1, 150)\n", "y = np.linspace(1.0, 1.0, 150)\n", "lines = plt.plot(x, y, color=\"#A60628\", lw = 3)\n", "plt.fill_between(x, 0, y, alpha = 0.2, color = lines[0].get_color())\n", "plt.autoscale(tight=True)\n", "plt.ylim(0, 2);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now, let's transform$\\theta$with the function$\\psi = log \\frac{\\theta}{1-\\theta}$. This is just a function to stretch$\\theta$across the real line. Now how likely are different values of$\\psi$under our transformation." ] }, { "cell_type": "code", "execution_count": 24, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "figsize(12.5, 5)\n", "\n", "psi = np.linspace(-10 ,10, 150)\n", "y = np.exp(psi) / (1 + np.exp(psi))**2\n", "lines = plt.plot(psi, y, color=\"#A60628\", lw = 3)\n", "plt.fill_between(psi, 0, y, alpha = 0.2, color = lines[0].get_color())\n", "plt.autoscale(tight=True)\n", "plt.ylim(0, 1);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Oh no! Our function is no longer flat. It turns out flat priors do carry information in them after all. The point of Jeffreys Priors is to create priors that don't accidentally become informative when you transform the variables you placed them originally on.\n", "\n", "Jeffreys Priors are defined as:\n", "\n", "$$p_J(\\theta) \\propto \\mathbf{I}(\\theta)^\\frac{1}{2}$$\n", "$$\\mathbf{I}(\\theta) = - \\mathbb{E}\\bigg[\\frac{d^2 \\text{ log } p(X|\\theta)}{d\\theta^2}\\bigg]$$\n", "\n", "$\\mathbf{I}$being the *Fisher information*" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Effect of the prior as$N$increases\n", "\n", "In the first chapter, I proposed that as the amount of our observations or data increases, the influence of the prior decreases. This is intuitive. After all, our prior is based on previous information, and eventually enough new information will shadow our previous information's value. The smothering of the prior by enough data is also helpful: if our prior is significantly wrong, then the self-correcting nature of the data will present to us a *less wrong*, and eventually *correct*, posterior. \n", "\n", "We can see this mathematically. First, recall Bayes Theorem from Chapter 1 that relates the prior to the posterior. The following is a sample from [What is the relationship between sample size and the influence of prior on posterior?](http://stats.stackexchange.com/questions/30387/what-is-the-relationship-between-sample-size-and-the-influence-of-prior-on-poste)[1] on CrossValidated.\n", "\n", ">The posterior distribution for a parameter$\\theta$, given a data set${\\textbf X}$can be written as \n", "\n", "$$p(\\theta | {\\textbf X}) \\propto \\underbrace{p({\\textbf X} | \\theta)}_{{\\textrm likelihood}} \\cdot \\overbrace{ p(\\theta) }^{ {\\textrm prior} }$$\n", "\n", "\n", "\n", ">or, as is more commonly displayed on the log scale, \n", "\n", "$$\\log( p(\\theta | {\\textbf X}) ) = c + L(\\theta;{\\textbf X}) + \\log(p(\\theta))$$\n", "\n", ">The log-likelihood,$L(\\theta;{\\textbf X}) = \\log \\left( p({\\textbf X}|\\theta) \\right)$, **scales with the sample size**, since it is a function of the data, while the prior density does not. Therefore, as the sample size increases, the absolute value of$L(\\theta;{\\textbf X})$is getting larger while$\\log(p(\\theta))$stays fixed (for a fixed value of$\\theta$), thus the sum$L(\\theta;{\\textbf X}) + \\log(p(\\theta))$becomes more heavily influenced by$L(\\theta;{\\textbf X})$as the sample size increases. \n", "\n", "There is an interesting consequence not immediately apparent. As the sample size increases, the chosen prior has less influence. Hence inference converges regardless of chosen prior, so long as the areas of non-zero probabilities are the same. \n", "\n", "Below we visualize this. We examine the convergence of two posteriors of a Binomial's parameter$\\theta\$, one with a flat prior and the other with a biased prior towards 0. As the sample size increases, the posteriors, and hence the inference, converge." ] }, { "cell_type": "code", "execution_count": 25, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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wWiFES5IOuHCWkpISCgsLpQPuxjw8PIiKimr039AlcsCVUpuB17TW2+pvb24O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