{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "Random Numbers\n", "====" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Pseudorandom number generators (PRNG)\n", "----\n", "\n", "While psuedorandom numbers are generated by a deterministic algorithm, we can mostly treat them as if they were true random numbers and we will drop the \"pseudo\" prefix. Fundamentally, the algorithm generates random integers which are then normalized to give a floating point number from the standard uniform distribution. Random numbers from other distributions are in turn generated using these uniform random deviates, either via general (inverse transform, accept/reject, mixture representations) or specialized ad-hoc (e.g. Box-Muller) methods." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Generating standard uniform random numbers" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Linear congruential generators (LCG)\n", "\n", "$z_{i+1} = (az_i + c) \\mod m$\n", "\n", "Hull-Dobell Theorem: The LCG will have a full period for all seeds if and only if\n", "\n", "- $c$ and $m$ are relatively prime,\n", "- $a - 1$ is divisible by all prime factors of $m$\n", "- $a - 1$ is a multiple of 4 if $m$ is a multiple of 4.\n", "\n", "The number $z_0$ is called the *seed*, and setting it allows us to have a reproducible sequence of \"random\" numbers. The LCG is typically coded to return $z/m$, a floating point number in (0, 1). This can be scaled to any other range $(a, b)$.\n", "\n", "Note that most PRNGs now use the [Mersenne twister](http://www.math.sci.hiroshima-u.ac.jp/~m-mat/MT/ARTICLES/mt.pdf), but the LCG is presented because the LCG code much easier to understand and all we hope for is some appreciation for how apparently random sequences can be generated from a deterministic iterative scheme." ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def rng(m=2**32, a=1103515245, c=12345):\n", " rng.current = (a*rng.current + c) % m\n", " return rng.current/m\n", "\n", "# setting the seed\n", "rng.current = 1" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "[0.25693503906950355,\n", " 0.5878706516232342,\n", " 0.15432575810700655,\n", " 0.767266943352297,\n", " 0.9738139626570046,\n", " 0.5858681506942958,\n", " 0.8511155843734741,\n", " 0.6132153405342251,\n", " 0.7473867232911289,\n", " 0.06236015981994569]" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" } ], "source": [ "[rng() for i in range(10)]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## From standard uniform to other distributions" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Inverse transform method\n", "\n", "Once we have standard uniform numbers, we can often generate random numbers from other distribution using the inverse transform method. Recall that if $X$ is a continuous random variable with CDF $F_X$, then $Y = F_X(X)$ has the standard uniform distribution. Inverting this suggests that if $Y$ comes from a standard uniform distribution, then $F_X^{-1}(Y)$ has the same distribution as $X$. The inverse transform method is used below to generate random numbers from the exponential distribution." ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def expon_pdf(x, lmabd=1):\n", " \"\"\"PDF of exponential distribution.\"\"\"\n", " return lmabd*np.exp(-lmabd*x)" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def expon_cdf(x, lambd=1):\n", " \"\"\"CDF of exponetial distribution.\"\"\"\n", " return 1 - np.exp(-lambd*x)" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def expon_icdf(p, lambd=1):\n", " \"\"\"Inverse CDF of exponential distribution - i.e. quantile function.\"\"\"\n", " return -np.log(1-p)/lambd" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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rW7cuK1eu5NSpU9SvX58aNWrg7u6e73SbQuEghG1uiquwxnfu3Fk+JhQjx9mW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\nJous0BuNisuNgoLCk0Vhyex8Ffrg4GBq1arFH3/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jDzIzM0NODEHq1KnDjh07Cn1f586d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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import scipy.stats as stats\n", "\n", "dist = stats.expon()\n", "x = np.linspace(0,4,100)\n", "y = np.linspace(0,1,100)\n", "\n", "with plt.xkcd():\n", " plt.figure(figsize=(12,4))\n", " plt.subplot(121)\n", " plt.plot(x, expon_cdf(x))\n", " plt.axis([0, 4, 0, 1])\n", " for q in [0.5, 0.8]:\n", " plt.arrow(0, q, expon_icdf(q)-0.1, 0, head_width=0.05, head_length=0.1, fc='b', ec='b')\n", " plt.arrow(expon_icdf(q), q, 0, -q+0.1, head_width=0.1, head_length=0.05, fc='b', ec='b')\n", " plt.ylabel('1: Generate a (0,1) uniform PRNG')\n", " plt.xlabel('2: Find the inverse CDF')\n", " plt.title('Inverse transform method');\n", "\n", " plt.subplot(122)\n", " u = np.random.random(10000)\n", " v = expon_icdf(u)\n", " plt.hist(v, histtype='step', bins=100, normed=True, linewidth=2)\n", " plt.plot(x, expon_pdf(x), linewidth=2)\n", " plt.axis([0,4,0,1])\n", " plt.title('Histogram of exponential PRNGs');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Creating a random number generator for arbitrary distributions\n", "\n", "Suppose we have some random samples with an unknown distribution. We can still use the inverse transform method to create a random number generator from a random sample, by estimating the inverse CDF function using interpolation." ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from scipy.interpolate import interp1d\n", "from statsmodels.distributions.empirical_distribution import ECDF\n", "\n", "# Make up some random data\n", "x = np.concatenate([np.random.normal(0, 1, 10000), \n", " np.random.normal(4, 1, 10000)])\n", "\n", "ecdf = ECDF(x)\n", "inv_cdf = interp1d(ecdf.y, ecdf.x, bounds_error=False, assume_sorted=True)\n", "r = np.random.uniform(0, 1, 1000)\n", "ys = inv_cdf(r)\n", "\n", "plt.hist(x, 25, histtype='step', color='red', normed=True, linewidth=1)\n", "plt.hist(ys, 25, histtype='step', color='blue', normed=True, linewidth=1);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Rejection sampling (Accept-reject method)" ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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qlTh79izq1KljsDhW/7i7d+/CwsLCIEwbLWM6javVatkgjbpz6D8vfc+0fvbv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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Suppose we want to sample from the (truncated) T distribution witb 10 degrees of freedom\n", "# We use the uniform as a proposal distibution (highly inefficient)\n", "\n", "x = np.linspace(-4, 4)\n", "\n", "df = 10\n", "dist = stats.cauchy()\n", "upper = dist.pdf(0)\n", "\n", "with plt.xkcd():\n", " plt.figure(figsize=(12,4))\n", " plt.subplot(121)\n", " plt.plot(x, dist.pdf(x))\n", " plt.axhline(upper, color='grey')\n", " px = 1.0\n", " plt.arrow(px,0,0,dist.pdf(1.0)-0.01, linewidth=1,\n", " head_width=0.2, head_length=0.01, fc='g', ec='g')\n", " plt.arrow(px,upper,0,-(upper-dist.pdf(px)-0.01), linewidth=1, \n", " head_width=0.3, head_length=0.01, fc='r', ec='r')\n", " plt.text(px+.25, 0.2, 'Reject', fontsize=16)\n", " plt.text(px+.25, 0.01, 'Accept', fontsize=16)\n", " plt.axis([-4,4,0,0.4])\n", " plt.title('Rejection sampling concepts', fontsize=20)\n", "\n", " plt.subplot(122)\n", " n = 100000\n", " # generate from sampling distribution\n", " u = np.random.uniform(-4, 4, n)\n", " # accept-reject criterion for each point in sampling distribution\n", " r = np.random.uniform(0, upper, n)\n", " # accepted points will come from target (Cauchy) distribution\n", " v = u[r < dist.pdf(u)]\n", "\n", " plt.plot(x, dist.pdf(x), linewidth=2)\n", "\n", " # Plot scaled histogram \n", " factor = dist.cdf(4) - dist.cdf(-4)\n", " hist, bin_edges = np.histogram(v, bins=100, normed=True)\n", " bin_centers = (bin_edges[:-1] + bin_edges[1:]) / 2.\n", " plt.step(bin_centers, factor*hist, linewidth=2)\n", "\n", " plt.axis([-4,4,0,0.4])\n", " plt.title('Histogram of accepted samples', fontsize=20);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Mixture representations\n", "\n", "Sometimes, the target distribution from which we need to generate random numbers can be expressed as a mixture of \"simpler\" distributions that we already know how to sample from\n", "\n", "$$\n", "f(x) = \\int{g(x\\,|\\,y)p(y) dy}\n", "$$\n", "\n", "For example, if $y$ is drawn from the $\\chi_\\nu^2$ distribution, then $\\mathcal{N}(0, \\nu/y)$ is a sample from the Student's T distribution with $\\nu$ degrees of freedom." ] }, { "cell_type": "code", "execution_count": 23, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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vXhSvXr1aaD5IQVJSUsTExMRS0/7rr78KzT8oDWnexr59+7zuV9ScgeLIyMgQ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EFBQQgKCoJSqURoaChGjhyJkJAQhIaGQqPRkCpg8ODBCAgIgEqlgp+fH0Qi0SMPvkCb8XGZIMMw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\nrVu34tNPP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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "n = 10000\n", "df = 2\n", "dist = stats.t(df=df)\n", "y = stats.chi2(df=df).rvs(n)\n", "r = stats.norm(0, df/y).rvs(n)\n", "\n", "with plt.xkcd():\n", " plt.plot(x, dist.pdf(x), linewidth=2)\n", "\n", " # Plot scaled histogram \n", " factor = dist.cdf(4) - dist.cdf(-4)\n", " hist, bin_edges = np.histogram(v, bins=100, normed=True)\n", " bin_centers = (bin_edges[:-1] + bin_edges[1:]) / 2.\n", " plt.step(bin_centers, factor*hist, linewidth=2)\n", "\n", " plt.axis([-4,4,0,0.4])\n", " plt.title('Histogram of accepted samples', fontsize=20);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Ad-hoc methods - e.g. Box-Muller for generating normally distributed random numbers\n", "\n", "The Box-Muller transform starts with 2 random uniform numbers $u$ and $v$\n", "- Generate an exponentially distributed variable $r^2$ from $u$ using the inverse transform method\n", "- This means that $r$ is an exponentially distributed variable on $(0, \\infty)$\n", "- Generate a variable $\\theta$ uniformly distributed on $(0, 2\\pi)$ from $v$ by scaling\n", "- In polar coordinates, the vector $(r, \\theta)$ has an independent bivariate normal distribution\n", "- Hence the projection onto the $x$ and $y$ axes give independent univariate normal random numbers\n", "\n", "Note:\n", "\n", "- Normal random numbers can also be generated using the *general* inverse transform method (e.g. by approximating the inverse CDF with a polynomial) or the rejection method (e.g. using the exponential distribution as the sampling distribution). \n", "- There is also a variant of Box-Muller that does not require the use of (expensive) trigonometric calculations." ] }, { "cell_type": "code", "execution_count": 24, "metadata": { "collapsed": true }, "outputs": [], "source": [ "n = 1000\n", "u1 = np.random.random(n)\n", "u2 = np.random.random(n)\n", "r_squared = -2*np.log(u1)\n", "r = np.sqrt(r_squared)\n", "theta = 2*np.pi*u2\n", "x = r*np.cos(theta)\n", "y = r*np.sin(theta)" ] }, { "cell_type": "code", "execution_count": 25, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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HEURu5Ybtsu8bOQ4pnhdfd/ojWLOpGYvm12Pj1jZdy0XL+uKPjTcYIR6tZoEE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\n6y6lVFqs/I5vvO7Shs4zq5Uf1vp330nWEoyL82XoPlf/gS1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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "sns.jointplot(x, y, kind='scatter')\n", "pass" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Using the numpy.random and scipy.stats PRNGs\n", "\n", "From this part onwards, we will assume that there is a library of PRNGs that we can use - either from numpy.random or scipy.stats which are both based on the Mersenne Twister, a high-quality PRNG for random integers. The numpy versions simply generate random deviates while the scipy versions will also provide useful functions related to the distribution, e.g. PDF, CDF and quantiles." ] }, { "cell_type": "code", "execution_count": 35, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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aazdspfw+wC+AvYB1wNXW2jszErGIiGRcsi2D/wHOAL4AHARMBu7v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\nF+oAAAAASUVORK5CYII=\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import numpy.random as rng\n", "\n", "# Histogram of beta distribution\n", "rs = rng.beta(a=0.5, b=0.5, size=1000)\n", "plt.hist(rs, bins=20, histtype='step', normed=True, linewidth=1)\n", "\n", "# PDF for the beta distribution\n", "xs = np.linspace(0, 1, 100)\n", "plt.plot(xs, stats.beta.pdf(xs, a=0.5, b=0.5), color='red')\n", "pass" ] }, { "cell_type": "code", "execution_count": 27, "metadata": { "collapsed": true }, "outputs": [], "source": [ "%load_ext rpy2.ipython" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "##### Python analog of R random number functions" ] }, { "cell_type": "code", "execution_count": 30, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "[1] 1.0610330 0.6366198 1.0610330\n", "[1] 0.2048328 0.5000000 0.7951672\n", "[1] 0.02447174 0.50000000 0.97552826\n", "[1] 0.9685769 0.6340875 0.9386236 0.3633199 0.6934238\n" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "%%R\n", "\n", "n <- 5\n", "xs <- c(0.1, 0.5, 0.9)\n", "print(dbeta(xs, 0.5, 0.5))\n", "print(pbeta(xs, 0.5, 0.5))\n", "print(qbeta(xs, 0.5, 0.5))\n", "print(rbeta(n, 0.5, 0.5))" ] }, { "cell_type": "code", "execution_count": 33, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[ 1.06103295 0.63661977 1.06103295]\n", "[ 0.20483276 0.5 0.79516724]\n", "[ 0.02447174 0.5 0.97552826]\n", "[ 0.09332562 0.21171851 0.42106969 0.76274382 0.890998 ]\n" ] } ], "source": [ "# Using scipy\n", "\n", "n = 5\n", "xs = [0.1, 0.5, 0.9]\n", "rv = stats.beta(a=0.5, b=0.5)\n", "\n", "print(rv.pdf(xs)) # equivalent of dbeta\n", "print(rv.cdf(xs)) # equivalent of pbeta\n", "print(rv.ppf(xs)) # equvialent of qbeta\n", "print(rv.rvs(n)) # equivalent of rbeta" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.5.1" } }, "nbformat": 4, "nbformat_minor": 0 }