{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Chapter 6\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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mzJl08pOSkqze87///e+cOnWKJk2a4OHhQdeuXenWrZu1DRFx+fhwVTltvKXN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\nODss4aJq8kh4TWHYug3T6tUorbH074d+6AEwVVQFqhCitOsZCS/3J1J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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "%matplotlib inline\n", "import numpy as np\n", "from IPython.core.pylabtools import figsize\n", "import matplotlib.pyplot as plt\n", "import scipy.stats as stats\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", "\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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yLzV49OhR7rjjDnr16sXQoUPJyckhNTUVu921y3ppaSmff/45N954Y8v+gLBw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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": [ "import pymc as pm\n", "\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(pm.rwishart(n + 1, np.eye(n)), interpolation=\"none\",\n", " cmap=plt.cm.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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ZkkQLv5J9W4U3JG6ENyRuhLcaxo7bA4UjZqDo9IGYUrtl6D8K9K79le0Xc3GU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WAAAg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\ncESAU8oTYCNn9GRZaZ/oxZIJs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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 a 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": [ "from pymc import rbeta\n", "\n", "\n", "class Bandits(object):\n", "\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", "\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", " \"\"\"\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", " 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(rbeta(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", "\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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20r9tJwN7GyFMbkPerCryF9VQsGgBeZfPQvLyho75FI4NQNOFPJr6hBMD3u/6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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 shows 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 of $w_{opt}$. 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 as:\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 $i$th round. A total regret of 0 means the strategy is attaining 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 strategy very easily." ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "collapsed": false }, "outputs": [], "source": [ "figsize(12.5, 5)\n", "from other_strats import GeneralBanditStrat, bayesian_bandit_choice, max_mean, lower_credible_choice, \\\n", " upper_credible_choice, random_choice, ucb_bayes, Bandits\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", "\n", "\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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2bWrVqsW0adOIj4+33Gvdk58RU6dOpVatWrRp04aqVasybdo0ix+DbRqdOnVi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\n1jrZWXgJhl9ARWAtUE1bFWDWrFn6mWe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3cpQ6GzqOV+VC60vzooe2U7Psp4S2LAU7nrbd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\nVEop1fFJPEp03wZCm5cQXP8sdu2xtDKOPufiHXcFnjGX4z5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IlTHmGaAKiAH3SjFcylBK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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 that 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": 14, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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znMgRwfj5980j+5DJGCillFJKKXU0jDHUHGygvKTG+WqpBag+0NDl8IaHBhAx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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# this can be slow, so I recommend NOT running it.\n", "trials = 200\n", "expected_total_regret = np.zeros((1000, 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(1000)\n", " _regret = regret(hidden_prob, general_strat.choices)\n", " expected_total_regret[:, i_strat] += _regret\n", "\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": 15, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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9/vx5nn76aZo1a4aPjw+tWrXimWee4cwZW7+65s2b4+XlhY+PD/7+/gwZMoTo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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 are:\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 a priori 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,$R \\sim f_{y_b}$, 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 the $X_b$ 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 the total number of 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 $(U=0,D=0)$ 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 35 different options. " ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[ 0.0431 0.0745 0.1187 0.0098 0.0945 0.0438 0.0442 0.0059 0.0749\n", " 0.023 0.0543 0.025 0.1231 0.0148 0.0164 0.2688 0.0073 0.0564\n", " 0.0031 0.0698 0.0478 0.1657 0.0091 0.0384 0.2236 0.1548 0.0562\n", " 0.0209 0.024 0.0197 0.0788 0.0572 0.1207 0.0405 0.0679]\n" ] }, { "data": { "image/png": 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NnWAQ5M2pzLQ4WYNreS3e3U301jdRvGpWTqWTUygUmSd8cicA5slLht0f6vLR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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)" ] }, { "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, for example:\n", "\n", "- Aids the speed 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", "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 the 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, TSLA 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": 17, "metadata": { "collapsed": false }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/Users/camerondavidson-pilon/.virtualenvs/data/lib/python2.7/site-packages/matplotlib/axes/_subplots.py:69: MatplotlibDeprecationWarning: The use of 0 (which ends up being the _last_ sub-plot) is deprecated in 1.4 and will raise an error in 1.5\n", " mplDeprecation)\n" ] }, { "data": { "image/png": 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WxwiEvKRTebZteovdodSNk8qwFbQBoZSNIs+8QnZsAl/POlze5hgfWwv+jd3k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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": "code", "execution_count": 18, "metadata": { "collapsed": false }, "outputs": [], "source": [ "import pymc as pm\n", "\n", "n_observations = 100 # we will truncate the the most recent 100 days.\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", "inv_cov_matrix = pm.Wishart(\"inv_cov_matrix\", n_observations, np.diag(prior_std ** 2))\n", "mu = pm.Normal(\"returns\", prior_mu, 1, size=4)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Next we pull historical data for these stocks:" ] }, { "cell_type": "code", "execution_count": 19, "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 ystockquote as ysq\n", "\n", "stocks = [\"AAPL\", \"GOOG\", \"TSLA\", \"AMZN\"]\n", "\n", "enddate = \"2015-04-27\"\n", "startdate = \"2012-09-01\"\n", "\n", "stock_closes = {}\n", "stock_returns = {}\n", "CLOSE = 6\n", "\n", "for stock in stocks:\n", " x = np.array(ysq.get_historical_prices(stock, startdate, enddate))\n", " stock_closes[stock] = x[1:, CLOSE].astype(float)\n", "\n", "# create returns:\n", "\n", "for stock in stocks:\n", " _previous_day = np.roll(stock_closes[stock], -1)\n", " stock_returns[stock] = ((stock_closes[stock] - _previous_day) / _previous_day)[:n_observations]\n", "\n", "dates = list(map(lambda x: datetime.datetime.strptime(x, \"%Y-%m-%d\"), x[1:n_observations + 1, 0]))" ] }, { "cell_type": "code", "execution_count": 20, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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07pFSai5wJ9Dm7MLr1q1j9erVhIeHA+Dt7c3YsWOJioqySEMvNGVlZaSkpDSX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\n12jCuk2r+GHJLH5ZOZ/MrLyX+ZQtXY4D6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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "figsize(12.5, 4)\n", "\n", "for _stock, _returns in stock_returns.items():\n", " p = plt.plot((1 + _returns)[::-1].cumprod() - 1, '-o', label=\"%s\" % _stock,\n", " markersize=4, markeredgecolor=\"none\")\n", "\n", "plt.xticks(np.arange(100)[::-8],\n", " list(map(lambda x: datetime.datetime.strftime(x, \"%Y-%m-%d\"), dates[::8])),\n", " rotation=60);\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": 21, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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5RbbL+R/CXcNy6hTVERI9c+/9/4qZjSDMsrEnYYDQ7939cjO7gjDgbHmS9XJ31616EZEI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\nKU/aT1OdPn06AM3NzTQ1NQ36iaMyMDH1qY4pVo2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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "figsize(11., 5)\n", "returns = np.zeros((n_observations, 4))\n", "\n", "for i, (_stock, _returns) in enumerate(stock_returns.items()):\n", " returns[:, i] = _returns\n", " plt.subplot(2, 2, i+1)\n", " plt.hist(_returns, 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": 22, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " [-----------------100%-----------------] 150000 of 150000 complete in 195.3 sec" ] }, { "name": "stderr", "output_type": "stream", "text": [ "/Users/camerondavidson-pilon/.virtualenvs/data/lib/python2.7/site-packages/pymc/Model.py:93: UserWarning: The MCMC() syntax is deprecated. Please pass in nodes explicitly via M = MCMC(input).\n", " 'The MCMC() syntax is deprecated. Please pass in nodes explicitly via M = MCMC(input).')\n" ] } ], "source": [ "obs = pm.MvNormal(\"observed returns\", mu, inv_cov_matrix, observed=True, value=returns)\n", "\n", "model = pm.Model([obs, mu, inv_cov_matrix])\n", "mcmc = pm.MCMC()\n", "\n", "mcmc.sample(150000, 100000, 3)" ] }, { "cell_type": "code", "execution_count": 23, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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dlUYHPJ2yYZPLY60Qj9uw7FNY2lGIFFt/FNto0ci6iIiIiEhIKWe9wCgPzS/F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\nM/sb4F3gKgDn3Btm9hDwBtAB3OSCDN2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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 = mcmc.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\" % list(stock_returns.keys())[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": 24, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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BX3/9dYYMGQJAv379GDFiBKNHJzObNTY2AvT6dG5bveSnUulp06ZlsvxUnvWRH5Vn98sv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\nYVD0/cC97t7lnQV3f42k4rg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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\" % list(stock_returns.keys())[i])\n", " plt.title(\"%s\" % list(stock_returns.keys())[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": 25, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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mNt/MDjCzsWZ2fsybY2Zz4v+3xu0HmtkMM1szKKfhtEyZ1tAuGq7b/KhMrHHy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\nx3FawDunKcjSapoXWVpN8yJLq2leFNk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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "inv_cov_samples = mcmc.trace(\"inv_cov_matrix\")[:]\n", "mean_covariance_matrix = np.linalg.inv(inv_cov_samples.mean(axis=0))\n", "\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=plt.cm.hot)\n", "plt.xticks(np.arange(4), stock_returns.keys())\n", "plt.yticks(np.arange(4), stock_returns.keys())\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.keys());\n", "plt.title(\"(mean posterior) variances of daily stock returns\")\n", "\n", "plt.tight_layout();" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Looking at the above figures, we can say that it is likely that TSLA has an above-average volatility (looking at the return graph this is quite clear). The correlation matrix shows that there are no 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 to 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 a 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 a 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 PyMC 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. Furthermore 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" ] }, { "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 it is 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$\\bf X$from Bernoulli($\\theta$). We define the prior on$p(\\theta) = 1$. " ] }, { "cell_type": "code", "execution_count": 26, "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": 27, "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${\\bf X}$can be written as \n", "\n", "$$p(\\theta | {\\bf X}) \\propto \\underbrace{p({\\bf X} | \\theta)}_{{\\rm likelihood}} \\cdot \\overbrace{ p(\\theta) }^{ {\\rm prior} }$$\n", "\n", "\n", "\n", ">or, as is more commonly displayed on the log scale, \n", "\n", "$$\\log( p(\\theta | {\\bf X}) ) = c + L(\\theta;{\\bf X}) + \\log(p(\\theta))$$\n", "\n", ">The log-likelihood,$L(\\theta;{\\bf X}) = \\log \\left( p({\\bf X}|\\theta) \\right)$, **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$L(\\theta;{\\bf X})$is getting larger while$\\log(p(\\theta))$stays fixed (for a fixed value of$\\theta$), thus the sum$L(\\theta;{\\bf X}) + \\log(p(\\theta))$becomes more heavily influenced by$L(\\theta;{\\bf X})$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": 28, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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3UZmb32BdQzsfwob1w3TdUEzXDSU4sbukpQjRikjHW7iD1prs7GzMZvOVKwuP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\nvQTdTaC1ZkOunT9uKOLR7aW1g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1gBmh94R9JwXKUDo+tvkJWVReEtC5vbL6WT\nSTVlUvhjorO74bLMWh3lvn4Y/fwpCQymNDCYksBgSgJDKAkMpjgoBJPnSW64ygFymn+13FUIwEcH\nvjpBXmk2w4K0+OoEAXoNgR6CAL3tK1CvwVtnexFSlI5IY/DE0Lcnhr49GyyXFgvmnHxMOfmYs/Mw\n5eRhzimwfc8twFJUgrW5n5xJibW8AsorOLF8Tcdx0JRJxrc7AAio+XI3subLsVvFlRa5snn1JJob\neJ/2OlbPnj35oWtdBbvBgwczZMiQZj6d0tFNS0wkTI2PFnLC5eV2J0mccS5DYk9+Zc8ClNa+8igK\n8MILL1BsPfUUfh2GAMK9IDwKBkWhw/YCr+Y/cZx6HVIak5iY2CC9xMeneTczN2tWEyHEGOAxKeWU\nmvb9gPX4GywVRVEURVEURbFp7t0SW4F4IUQPIYQHcCXwdet1S1EURVEURVE6lmalmkgpzUKI24Gf\nsE0n+Gb9GU0URVEURVEURWmoz