{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Sampling In Continuous Graphical Models\n", "As we know inference is asking conditional probability questions to the models, the exact solution of these problems quickly becomes intractable. Sampling algorithms can be used to get approximate inference results by generating a large\n", "number of coherent samples that converge to original distribution. In this notebook we take a look at some of the \n", "sampling algorithms that can be used to sample from continuous case models.\n", "\n", "1. Hamiltonian Monte Carlo\n", "2. No-U-Turn Sample\n", "\n", "## Hamiltonian Monte Carlo\n", "Hamiltonian Monte Carlo (HMC) is a Markov Chain Monte Carlo (MCMC) that proposes future states in Markov Chain using\n", "Hamiltonian Dynamics. Before understanding the HMC algorithm lets first understand Hamiltonian Dynamics.\n", "\n", "### Hamiltonian Dynamics\n", "Hamiltonian dynamics are used to describe how objects move throughout a\n", "system. Hamiltonian dynamics is defined in terms of object location $x$\n", "and its momentum $p$ (equivalent to object's mass times velocity) at some\n", "time $t$. For each location of object there is an associated potential\n", "energy $U(x)$ and with momentum there is associated \n", "kinetic energy $K(p)$. The total energy of system is constant and is called as Hamiltonian \n", "$H(x, p)$, defined as the sum of potential energy and kinetic energy:\n", "\n", "$$H(x, p) = U(x) + K(p)$$\n", "\n", "The partial derivatives of the Hamiltonian determines how position $x$ and\n", "momentum $p$ change over time $t$, according to Hamiltonian's equations:\n", "\n", "$$\\frac{dx_i}{dt} = \\frac{\\partial H}{\\partial p_i} = \\frac{\\partial K(p)}{\\partial p_i}$$\n", "\n", "$$\\frac{dp_i}{dt} = -\\frac{\\partial H}{\\partial x_i} = -\\frac{\\partial U(x)}{\\partial x_i}$$\n", "\n", "The above equations operates on a *d-dimensional position vector $x$* and\n", "a *d-dimensional momentum vector $p$*, for $i = 1, 2, \\cdots, d$.\n", "\n", "Thus, if we can evaluate $\\frac{\\partial U(x)}{\\partial x_i}$ and \n", "$\\frac{\\partial K(p)}{\\partial p_i}$ and have a set of initial conditions i.e\n", "an initial position and initial momentum at time $t_0$, then we can predict\n", "the location and momentum of object at any future time $t = t_0 + T$ by\n", "simulating dynamics for a time duration $T$.\n", "### Discretizing Hamiltonian's Equations\n", "\n", "The Hamiltonian's equations describes an object's motion in regard to time,\n", "which is a continuous variable. For simulating dynamics on a computer,\n", "Hamiltonian's equations must be numerically approximated by discretizing time.\n", "This is done by splitting the time interval $T$ into small intervals of size\n", "$\\epsilon$.\n", "\n", "#### Euler's Method\n", "For Hamiltonian's equations, this method performs the following steps, for\n", "each component of position and momentum (indexed by $i=1, ...,d$)\n", "\n", "$$p_i(t + \\epsilon) = p_i(t) + \\epsilon \\frac{dp_i}{dt}(t) = p_i(t) - \\epsilon \\frac{\\partial U}{\\partial x_i(t)}$$\n", "\n", "$$x_i(t + \\epsilon) = x_i(t) + \\epsilon \\frac{dx_i}{dt} = x_i(t) + \\epsilon \\frac{\\partial K}{\\partial p_i(t)}$$\n", "\n", "Even better results can be obtained if we use updated value of momentum\n", "in later equation\n", "\n", "$$x_i(t + \\epsilon) = x_i(t) + \\epsilon \\frac{\\partial K}{\\partial p_i(t + \\epsilon)}$$\n", "\n", "This method is called as **Modified Euler's method**.\n", "\n", "#### Leapfrog Method\n", "Unlike Euler's method where we take full steps for updating position and\n", "momentum in leapfrog method we take half steps to update momentum value.\n", "\n", "$$p_i(t + \\epsilon / 2) = p_i(t) - (\\epsilon / 2) \\frac{\\partial U}{\\partial x_i(t)}$$\n", "\n", "$$x_i(t + \\epsilon) = x_i(t) + \\epsilon \\frac{\\partial K}{\\partial p_i(t + \\epsilon /2)}$$\n", "\n", "$$p_i(t + \\epsilon) = p_i(t) - (\\epsilon / 2) \\frac{\\partial U}{\\partial x_i(t + \\epsilon)}$$\n", "\n", "Leapfrog method yields even better result than Modified Euler Method.\n", "\n", "#### Example: Simulating Hamiltonian dynamics of a simple pendulum\n", "\n", "Imagine a bob of mass $m = 1$ attached to a string of length $l=1.5$\n", "whose one end is fixed at point $(x=0, y=0)$.\n", "The equilibrium position of the pendulum is at $x = 0$. Now keeping string\n", "stretched we move it some distance horizontally say $x_0$. The corresponding\n", "change in potential energy is given by\n", "\n", "$U(h) = mg\\Delta h$, where $\\Delta h$ is change in height and $g$ is gravity of earth.\n", "\n", "Using simple trigonometry one can derive relationship between $x$ and \n", "$\\Delta h$.\n", "\n", "$$U(x) = mgl(1 - cos(sin^{-1}(x/l)))$$\n", "\n", "Kinetic energy of bob can be written in terms of momentum as\n", "\n", "$$K(v) = \\frac{mv^2}{2} = \\frac{(mv)^2}{2m} = \\frac{p^2}{2m} = K(p)$$\n", "\n", "Further, partial derivatives of potential and kinetic energy can be written as:\n", "\n", "$$\\frac{\\partial U}{\\partial x} = \\frac{mglx}{\\sqrt{l^2 - x^2}}$$\n", "\n", "and\n", "\n", "$$\\frac{\\partial K}{\\partial p} = \\frac{p}{m}$$\n", "\n", "Here is a animation that uses these equations to simulate the dynamics of simple pendulum\n", "\n", "The sub-plot in the right upper half of the output demonstrates the energies. The\n", "red portion of first bar plot represents potential energy and black represents\n", "kinetic energy. The second bar plot represents the Hamiltonian. The lower right sub-plot shows the phase space\n", "showing how momentum and position are varying. We can see that phase space\n", "maps out an ellipse without deviating from its path. In case of Euler\n", "method the particle doesn't fully trace a ellipse instead diverges slowly \n", "towards infinity. One can clearly see that value of position and momentum are not completely\n", "random, but takes a deterministic circular kind of trajectory.\n", "If we use Leapfrog method to propose future states than we can avoid\n", "random-walk behavior which we saw in Metropolis-Hastings algorithm. This is the main reason for good performance\n", "of HMC algorithm.\n", "\n", "### Hamiltonian and Probability: Canonical Distributions\n", "\n", "Now having a bit of understanding what is Hamiltonian and how we can simulate\n", "Hamiltonian dynamics, we now need to understand how we can use these\n", "Hamiltonian dynamics for MCMC. We need to develop some relation between\n", "probability distribution and Hamiltonian so that we can use Hamiltonian\n", "dynamics to explore the distribution. To relate $H(x, p)$ to target\n", "distribution $P(x)$ we use a concept from statistical mechanics known as\n", "the canonical distribution. For any energy function $E(q)$, defined over a set of variables $q$, we\n", "can find corresponding $P(q)$\n", "\n", "$$P(q) = \\frac{1}{Z} exp \\left( \\frac{-E(q)}{T} \\right)$$\n", "\n", ", where $Z$ is normalizing constant called Partition function and $T$ is\n", "temperature of system. For our use case we will consider $T=1$.\n", "\n", "Since, the Hamiltonian is an energy function for the joint state of \"position\",\n", "$x$ and \"momentum\", $p$, so we can define a joint distribution for them\n", "as follows:\n", "\n", "$$P(x, p) = \\frac{e^{-H(x, p)}}{Z}$$\n", "\n", "Since $H(x, p) = U(x) + K(p)$, we can write above equation as\n", "\n", "$$P(x, p) = \\frac{e^{-U(x)-K(p)}}{z}$$\n", "\n", "$$P(x, p) = \\frac{e^{-U(x)}e^{-K(p)}}{Z}$$\n", "\n", "Furthermore we can associate probability distribution with each of the\n", "potential and kinetic energy ($P(x)$ with potential energy and $P(p)$,\n", "with kinetic energy). Thus, we can write above equation as:\n", "\n", "$$P(x, p) = \\frac{P(x)P(p)}{Z'}$$\n", "\n", ",where $Z'$ is new normalizing constant. Since joint distribution factorizes\n", "over $x$ and $p$, we can conclude that $P(x)$ and $P(p)$ are independent.\n", "Because of this independence we can choose any distribution\n", "from which we want to sample the momentum variable. A common choice is to use\n", "a zero mean and unit variance Normal distribution $N(0, I)$ \n", "The target distribution of interest $P(x)$ from which we actually want to\n", "sample from is associated with potential energy.\n", "\n", "$$U(x) = - log (P(x))$$\n", "\n", "Thus, if we can calculate $\\frac{\\partial log(P(x))}{\\partial x_i}$, then\n", "we are in business and we can use Hamiltonian dynamics to generate samples.\n", "\n", "### Hamiltonian Monte Carlo Algorithm\n", "Given initial state $x_0$, stepsize $\\epsilon$, number of steps $L$, \n", "log density function $U$, number of samples to be drawn $M$, we can write HMC algorithm as:\n", "\n", "- set $m = 0$\n", "- repeat until $m = M$\n", "\n", " 1. set $m \\leftarrow m + 1$\n", "\n", " 2. Sample new initial momentum $p_0$ ~ $N(0, I)$\n", " \n", " 3. Set $x_m \\leftarrow x_{m-1}, x' \\leftarrow x_{m-1}, p' \\leftarrow p_0$\n", "\n", " 4. repeat for $L$ steps\n", "\n", " - Set $x', p' \\leftarrow Leapfrog(x', p', \\epsilon)$\n", "\n", " 5. Calculate acceptance probability $\\alpha = min \\left(1, \\frac{exp( U(x') - (p'.p')/2 )}{exp( U(x_{m-1}) - (p_0.p_0)/2 )} \\right)$\n", "\n", " 6. Draw a random number u ~ Uniform(0, 1)\n", " \n", " 7. if $u \\leq \\alpha$ then $x_m \\leftarrow x', p_m \\leftarrow -p'$\n", "\n", "$Leapfrog$ is a function that runs a single iteration of Leapfrog method.\n", "\n", "In practice sometimes instead of explicitly giving number of steps $L$, \n", "we use **trajectory length** which is product of number of steps $L$,\n", "and stepsize $\\epsilon$.\n", "\n", "### Hamiltonian Monte Carlo in pgmpy\n", "In pgmpy one can use Hamiltonian Monte Carlo algorithm by importing HamiltonianMC from pgmpy.inference.continuous " ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "from pgmpy.sampling import HamiltonianMC as HMC" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Lets use the HamiltonianMC implementation and draw some samples from a multivariate disrtibution $P(x) = N(\\mu, \\Sigma)$, where\n", "$$\n", "\\mu = [0, 0], \\qquad\n", "\\Sigma = \\left[\n", " \\begin{array}{cc}\n", " 1 & 0.97 \\\\\n", " 0.97 & 1\n", " \\end{array}\n", " \\right]\n", "$$" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/home/utgup/anaconda3/lib/python3.5/site-packages/ipykernel/__main__.py:18: MatplotlibDeprecationWarning: pyplot.hold is deprecated.\n", " Future behavior will be consistent with the long-time default:\n", " plot commands add elements without first clearing the\n", " Axes and/or Figure.\n", "/home/utgup/anaconda3/lib/python3.5/site-packages/matplotlib/__init__.py:917: UserWarning: axes.hold is deprecated. Please remove it from your matplotlibrc and/or style files.\n", " warnings.warn(self.msg_depr_set % key)\n", "/home/utgup/anaconda3/lib/python3.5/site-packages/matplotlib/rcsetup.py:152: UserWarning: axes.hold is deprecated, will be removed in 3.0\n", " warnings.warn(\"axes.hold is deprecated, will be removed in 3.0\")\n", "/home/utgup/anaconda3/lib/python3.5/site-packages/ipykernel/__main__.py:21: MatplotlibDeprecationWarning: pyplot.hold is deprecated.\n", " Future behavior will be consistent with the long-time default:\n", " plot commands add elements without first clearing the\n", " Axes and/or Figure.\n" ] }, { "data": { "image/png": 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6IUHrww7TetEiMw+YiDvItCZC1I2/KUwAbbPZ9BWXXqr10Udr3b691jt3erZX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\nQSGEW12vuFZjgg8+qmlDEbvc47ncY6Y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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "%matplotlib inline\n", "from pgmpy.factors.distributions import GaussianDistribution as JGD\n", "from pgmpy.sampling import LeapFrog, GradLogPDFGaussian\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "\n", "np.random.seed(77777)\n", "# Defining a multivariate distribution model\n", "mean = np.array([0, 0])\n", "covariance = np.array([[1, 0.97], [0.97, 1]])\n", "model = JGD(['x', 'y'], mean, covariance)\n", "\n", "# Creating a HMC sampling instance\n", "sampler = HMC(model=model, grad_log_pdf=GradLogPDFGaussian, simulate_dynamics=LeapFrog)\n", "# Drawing samples\n", "samples = sampler.sample(initial_pos=np.array([7, 0]), num_samples = 1000,\n", " trajectory_length=10, stepsize=0.25)\n", "plt.figure(figsize=(7, 7)); plt.hold(True)\n", "plt.scatter(samples['x'], samples['y'], label='HMC samples', color='k')\n", "plt.plot(samples['x'][0:100], samples['y'][0:100], 'r-', label='First 100 samples')\n", "plt.legend(); plt.hold(False)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "One, can change the values of parameters stepsize and trajectory_length and see the convergence towards target distribution. For example set the value of stepsize = 0.5 and let rest parameters have the same value and see the output. With this you might get a feel that performance of HMC critically depends upon choice of these parameters.\n", "\n", "The stepsize parameter for HamiltonianMC implementation is optional, but should be use only as starting point value.\n", "One should hand-tune the model using this stepsize value for good performance.\n", "\n", "### Hamiltonian Monte Carlo with dual averaging\n", "In pgmpy we have implemented an another variant of HMC in which we adapt the stepsize during the course of sampling thus\n", "completely eliminates the need of specifying stepsize (but still requires\n", "trajectory_length to be specified by user). This variant of HMC is known as Hamiltonian Monte Carlo with dual averaging (HamiltonianMCda in pgmpy). One can also use Modified Euler to simulate dynamics instead of leapfrog, or even can plug-in one's own implementation for simulating dynamics using base class for it." ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " x y\n", "0 7.000000e+00 0.000000\n", "1 3.458460e-323 0.000000\n", "2 3.458460e-323 0.000000\n", "3 3.458460e-323 0.000000\n", "4 3.458460e-323 0.000000\n", "5 3.614684e+00 0.780326\n", "6 1.316832e+00 0.643645\n", "7 1.316832e+00 0.643645\n", "8 -1.111247e-01 -0.306480\n", "9 1.163398e+00 1.357304\n", "\n", "Acceptance rate: 0.5\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "/home/utgup/anaconda3/lib/python3.5/site-packages/pgmpy-0.1.6-py3.5.egg/pgmpy/sampling/HMC.py:111: RuntimeWarning: divide by zero encountered in double_scalars\n", " return (1/(acceptance_prob ** a)) > (2**(-a))\n" ] } ], "source": [ "from pgmpy.sampling import HamiltonianMCDA as HMCda, ModifiedEuler\n", "# Using modified euler instead of Leapfrog for simulating dynamics\n", "sampler_da = HMCda(model, GradLogPDFGaussian, simulate_dynamics=ModifiedEuler)\n", "# num_adapt is number of iteration to run adaptation of stepsize\n", "samples = sampler_da.sample(initial_pos=np.array([7, 0]), num_adapt=10, num_samples=10, trajectory_length=10)\n", "print(samples)\n", "print(\"\\nAcceptance rate:\",sampler_da.acceptance_rate)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The values returned by HamiltonianMC and HamiltonianMCda depends upon the installation available in the working environment. In working env has a installation of pandas, it returns a pandas.DataFrame object otherwise it returns a\n", "numpy.recarry (numpy recorded arrays).\n", "\n", "Lets now use base class for simulating hamiltonian dynamics and write our own Modified Euler method" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " x y\n", "0 0.000000 0.000000\n", "1 0.624716 0.680638\n", "2 0.928227 1.143031\n", "3 -0.234847 -0.118653\n", "4 -1.633648 -1.977647\n", "5 -1.282438 -1.442565\n", "6 -1.734446 -1.282935\n", "7 -1.552439 -1.300669\n", "8 0.729025 0.793016\n", "9 -0.489195 -0.430182\n", "Total accepted proposal: 10.0\n" ] } ], "source": [ "from pgmpy.sampling import BaseSimulateHamiltonianDynamics\n", "\n", "class ModifiedEulerMethod(BaseSimulateHamiltonianDynamics):\n", " def __init__(self, model, position, momentum, stepsize, grad_log_pdf, grad_log_position=None):\n", "\n", " BaseSimulateHamiltonianDynamics.__init__(self, model, position, momentum,\n", " stepsize, grad_log_pdf, grad_log_position)\n", "\n", " self.new_position, self.new_momentum, self.new_grad_logp = self._get_proposed_values()\n", "\n", " def _get_proposed_values(self):\n", " new_momentum = self.momentum + self.stepsize * self.grad_log_position\n", " new_position = self.position + self.stepsize * new_momentum\n", "\n", " grad_log, _ = self.grad_log_pdf(new_position, self.model).get_gradient_log_pdf()\n", "\n", " return new_position, new_momentum, grad_log\n", "\n", "hmc_sampler = HMC(model, GradLogPDFGaussian, simulate_dynamics=ModifiedEulerMethod)\n", "samples = hmc_sampler.sample(initial_pos=np.array([0, 0]), num_samples=10, trajectory_length=10, stepsize=0.2)\n", "print(samples)\n", "print(\"Total accepted proposal:\", hmc_sampler.accepted_proposals)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## No-U-Turn Sampler\n", "Both (HMC and HMCda) of these algorithms requires some hand-tuning from user,\n", "which can be time consuming especially for high dimensional complex model.\n", "No-U-Turn Sampler(NUTS) is an extension of HMC that eliminates the need to specify the\n", "trajectory length but requires user to specify stepsize.\n", "\n", "NUTS, removes the need of parameter number of steps by considering a metric\n", "to evaluate whether we have ran Leapfrog algorithm for long enough, that\n", "is when running the simulation for more steps would no longer increase\n", "the distance between the proposal value of $x$ and initial value of\n", "$x$\n", "\n", "At high level, NUTS uses the leapfrog method to trace out a path forward\n", "and backward in fictitious time, first running forwards or backwards\n", "1 step, the forwards and backwards 2 steps, then forwards or backwards\n", "4 steps etc. This doubling process builds a balanced binary tree whose\n", "leaf nodes correspond to position-momentum states. The doubling process is\n", "halted when the sub-trajectory from the leftmost to the rightmost nodes of\n", "any balanced subtree of the overall binary tree starts to double back on\n", "itself (i.e., the fictional particle starts to make a \"U-Turn\"). At\n", "this point NUTS stops the simulation and samples from among the set of\n", "points computed during the simulation, taking are to preserve detailed\n", "balance.\n", "\n", "Lets use NUTS and draw some samples." ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/home/utgup/anaconda3/lib/python3.5/site-packages/pgmpy-0.1.6-py3.5.egg/pgmpy/sampling/NUTS.py:130: RuntimeWarning: invalid value encountered in true_divide\n", " if np.random.rand() < candidate_set_size2 / (candidate_set_size2 + candidate_set_size):\n", "/home/utgup/anaconda3/lib/python3.5/site-packages/ipykernel/__main__.py:13: MatplotlibDeprecationWarning: pyplot.hold is deprecated.\n", " Future behavior will be consistent with the long-time default:\n", " plot commands add elements without first clearing the\n", " Axes and/or Figure.\n", "/home/utgup/anaconda3/lib/python3.5/site-packages/matplotlib/__init__.py:917: UserWarning: axes.hold is deprecated. Please remove it from your matplotlibrc and/or style files.\n", " warnings.warn(self.msg_depr_set % key)\n", "/home/utgup/anaconda3/lib/python3.5/site-packages/matplotlib/rcsetup.py:152: UserWarning: axes.hold is deprecated, will be removed in 3.0\n", " warnings.warn(\"axes.hold is deprecated, will be removed in 3.0\")\n", "/home/utgup/anaconda3/lib/python3.5/site-packages/ipykernel/__main__.py:18: MatplotlibDeprecationWarning: pyplot.hold is deprecated.\n", " Future behavior will be consistent with the long-time default:\n", " plot commands add elements without first clearing the\n", " Axes and/or Figure.\n" ] }, { "data": { "image/png": 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oqqpCTU1NSiGD4zjq6cwQnudhsVhgsVgAzIXQ6elpccekUCgEs9ksLkxK5wMC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G/hiqLFDTSrEE5LgUUrpBQjftWE2HjCIL8t0O3A6JgUiKgaiGU5EJ5RZSEBmiKtdJns/BN2/4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OMIudy+l/p8++ZG97N9Ihg8YkynLMuUlpZSWlqKbdskEgkikQi9vb0IgpC3ZPL5fLNWBZ0L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\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1QkxiEhsbG7O6CaD9Udz72wu4QAfRXKnB/3x9G2ozEIyL7jC+8KtpVFUoIJdK4A7GYNIo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\nZmYiIyMDAQEBDh/YemNZFufOnYOHh4dT7lG1pBt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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from pgmpy.sampling import NoUTurnSampler as NUTS\n", "mean = np.array([1, 2, 3])\n", "covariance = np.array([[2, 0.4, 0.5], [0.4, 3, 0.6], [0.5, 0.6, 4]])\n", "model = JGD(['x', 'y', 'z'], mean, covariance)\n", "\n", "# Creating sampling instance of NUTS\n", "NUTS_sampler = NUTS(model=model, grad_log_pdf=GradLogPDFGaussian)\n", "samples = NUTS_sampler.sample(initial_pos=[10, 10, 0], num_samples=2000, stepsize=0.25)\n", "\n", "from mpl_toolkits.mplot3d import Axes3D\n", "fig = plt.figure(figsize=(9, 9))\n", "ax = Axes3D(fig)\n", "plt.hold(True)\n", "ax.scatter(samples['x'], samples['y'], samples['z'], label='NUTS Samples')\n", "ax.plot(samples['x'][:50], samples['y'][:50], samples['z'][:50], 'r-', label='Warm-up period')\n", "plt.legend()\n", "plt.title(\"Scatter plot of samples\")\n", "plt.hold(False)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The **Warm-up period** a.k.a **Burn-in period** of Markov chain , is the amount of time it takes for the markov chain\n", "to reach the target stationary distribution. The samples generated during this period of Markov chain are usually thrown away because they don't show the characteristics of distribution from which they are sampled.\n", "\n", "Since it is difficult to visualize more than 3-Dimensions we generally use a trace-plot of Markov chain to determine this\n", "warm-up period." ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/home/utgup/anaconda3/lib/python3.5/site-packages/ipykernel/__main__.py:2: MatplotlibDeprecationWarning: pyplot.hold is deprecated.\n", " Future behavior will be consistent with the long-time default:\n", " plot commands add elements without first clearing the\n", " Axes and/or Figure.\n", " from ipykernel import kernelapp as app\n", "/home/utgup/anaconda3/lib/python3.5/site-packages/matplotlib/__init__.py:917: UserWarning: axes.hold is deprecated. Please remove it from your matplotlibrc and/or style files.\n", " warnings.warn(self.msg_depr_set % key)\n", "/home/utgup/anaconda3/lib/python3.5/site-packages/matplotlib/rcsetup.py:152: UserWarning: axes.hold is deprecated, will be removed in 3.0\n", " warnings.warn(\"axes.hold is deprecated, will be removed in 3.0\")\n", "/home/utgup/anaconda3/lib/python3.5/site-packages/ipykernel/__main__.py:9: MatplotlibDeprecationWarning: pyplot.hold is deprecated.\n", " Future behavior will be consistent with the long-time default:\n", " plot commands add elements without first clearing the\n", " Axes and/or Figure.\n" ] }, { "data": { "image/png": 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d7tl8DwZHq7GTa8ynw7C/UxUIhI60pp/g+rR+b8XvJ5SdnhI65KGqCAlXZV6x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\nJzVzLruvqvjvHTsAAOcvWIB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ALL/3r21bbZ3pxyUMukvLKMSno282cMW9wFmvDt/RULOJ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49UfkpnvEJOBKBXzglK13jjnoJCNxUZWvFt1VLX+M+0VdOd2vaOH6gdSWMFA8ATzwIKYvKrfTr8\n9mZafmwsccyWodJRDaBu/pJzaJ6puvpBti0eP1reSkfMAzpF1Hks2LXiTxxkBdWukHSSlaxnZUMz\nm4Fv/7Rza4Va7/JWQJsolQphJzh3+0fZtHrImR7i3BVUcMps9VMJy7/YPcUcl15d03eYnc03D3xi\n43nAs/4zoDRvXtG68umIsQzg/BDp+Nthg7xUW3O5s1dI3uB3jLx0UfOKoHQ4aTLaD0VJko6ATTn5\na3VeNt0v8GJxi7dfn64Cx5adCOQUFkHqxnM8bNKMMdSqiNLhvFebMYg6kjL57Aau018W5dLTc3z+\nVsoxd7Kyt/uMI2dBFirmtt+21dOdse+hPwF2/DVwpDIXFgBKPcT8wMafF5jf/TPoDEi8j1pW3qzL\ntsOZzeE9FulAoPiVehi++O1DXPGpy7G6M95p4ePSslM6lIM8jPF6jtJhBpV6IG1jRhkT6fAPDsqy\nn3rmFeWnEeqlnhcVtm93H0z29oUJAQz7fgNOTCGdFdWWWTJOx8Y+kepvPMTth/7Re2QHneY9FxY1\npO2gjiQO1FCZV0Kbd8U/HpG0Sef+5sttgpBxfg0Sz1jREaWj7+3coX4XBEFyZImdK+PLxjk0Rkb+\njjF1hSqAYKLySx0qfOLiiwWRbKMOncoVNOvPEO524CZVpgwA2PZJQY7ImJE0z8R8nSTfpFg70U12\nRBwtM2hRz/IPmPqWxQnTKaVw2spEgELRvFLdt+aVtALssaWs+gdNvCazkDEmuj3mGAa2TS6sA6Cw\n5ugVhKkf+sBDZzk+9/9BeM9TOo72joKrZ/Z0mP3A2m3rMZVCBY8xLTulg1KWM5JEjnnFKh2d+g55\niJEjku5+TlqOlCOp1kzD9wL2KGQMbG7yXY/7d/nVdmBeyaDFBYWbb3IHy+Eq6xDVfiV/zeO/xD5T\nUJjobyS3aZ1wK1//sLUS/bKPLrPiSu5e8c0rCUXYBiELzSt5E29ITJuQeLBIh3ZZTJF6FMvhkI60\nMl4YhCeMHCmgRR6VJXAaewZPrHxezWFzcHVeShdc2h78tvLhV37YZ5JNjU3e+0YOutlCgx/DBFz5\ndDD5Vb6DOUcKCrP7TkukaspdYFxLOi2VDVo2dxegawBJ2SPlzy4Ae742kgwAmEMedaB07J/bL3w+\n5h2GCsfgSK3WtOyUDu04ko6LdPgrEas5+0oHN/FbPpEO/dgPpeXIOtTIW8H5jqRB+5NWTs3TqSA0\nBQ+vl2X7weWWWxQ239XIMKNWYeFpR4HLDkdy2QKtnVR7f0NSSmGyfya5Q9KuvlBAEei3LTEoB41t\nee7UOp3WCZ8OaaUn5CltbAvymB8gRhw1HBOR7yfEKSTjIHS0HtOKf6GAJ2afEFillQ6tgYnk6o3/\nHhzSEfbZhM+C0zc4pWMQLB6edfqzWlSxK2Nf03GJR5LOOzfBkjiStg0TTuk1q/8j+BeRIiKzwrB3\nF1NnWdGxkZpYrQKfeYjaUx+/yWfMlGW9jvx2Lb9XUU4AD/6hcEqxQZti4xj3XbxTZvfN8uZ3VnEq\nXYT5e0XLTulYOp+O5uuo2rximRPlw1FyGCqFs6cBAXINEnmXXGH+Pe+9HTQmXaYCML3Cv8uvtkvt\nKR0ZXueDfgQlsCu0e/4TnvKNU8Ln1uwV8R63HVlBYXqfee8jCDuxH1OBQTp6wz46dtW2uJaUAWGd\nLFHMvAJcf8OweUreqdeTEJPc8iwxJpT6WvLpaIkUcj4dOs2n3vQVOHt615J5xd7ewcXqsJp0KIOM\ndOT0OfpcgvntvX7Q15UbUCjO/5x/61zWSkcVeIHlsXZdup00XWh0peP8iReG77z5XVW4/pHbalU/\nSX9HyaejW22Vj56NRKgzdJ3f+dTV3cJvq7F3rBdkTJ8ydZ63bZo8I0jH6snV2De3Twh+xsx9w+Ik\n0nHsyEw64zhv6QHpleZLDY4C/cPAGm8ZEUMjFvcn5YxSDkzqNTrtQ/vKT5PYMqsUJh2kQwPiaaup\ngE4MaSUOljU9eRMe717eXO/+sknuhaa3f5ldM4UqcPati8AdvwzsYMxAXe9gJz1Ad0gcElWJ/nCA\nDudF31phNL/PeDmb7HU/ZR1JXb7Vao9+yxFNhkpSLAD3mxHlqLW+ThXBfDmL6OIgD+kAgM6nt8sP\nmd1ECkJPyNm9oiS5pPfwlA4ouP4zhB77DHD7LzbXq85zHvftzKFlpaNNvK5xlI6Kh1fYPsYBMskk\nFDg5QSYOfKt9uhJIR6w3BEUGvzghzbMyDCoYlG3k5hUHDulolI4NKzdUSgeQNx6VJ80rx4ac8WuJ\nfDrMRDelJoA9ZwBdMoHVTppeo3ngD4FN7wjvB8KmyM+fHk1484q53vADwETcJKLgBcgJyqWToG9L\nz1E6mk2SAU17oZNtZ9r+3821r3TYDt4oHfP9KiaCUqrSB4/cb9KnYfJ1R5/fXK/ch8GQmFfIpJo0\nr5h07G+OlOfTYZFhv4yVT4vzkcp79FPkmY90SChI2/7DIR0ZMDQ5QFHmKfA4vLN51S575LBhzQ11\nmt2qGB6LxZTr6GnUK5ppYxPr3O2ThpoJwF+RzgGzjzLyVjSotQVS7sQ6J82hSWEXTU3UvDIiGmz4\nBPL3p5l07cqoAgimEsXPXslFOvynHdYfxSAdQOXfNJU+hVuV8tkyVuCS9pkgCfOMtKONKzeK5pWC\nMycOiuVhXlFKPVUp9S9KqfuUUvcqpd6+FIKNTroZZ5bKpwN2QmBOzKn7nPdg8QlgRg6UZUVNUnL7\nHrdK8GFqNA14ww8BPyhsg9NN8tAmKNitdwyAvd8gj3JatQImZgNWcTIDTOmZV+rHjdLx3+/6K1OK\nZ8ZJwuTeJHTqo8a8Em4L1j5vnmHiOaGi2r3irxzZlWQWkTwH7wUWSZyNLPOK+27vOj2wt4XlRO/5\nSZo0O3dYFCLhX8F9vyNU6YiYMhnKRjqSymrG8rHrOigopdDvMcpDBr/N9xMEVgi3uWP675MiLYVP\nR4VaenXxxLPaMglRKJWxKv/aB6KPGwU+gXR4zW5S+Q5tDM86c0RZYJEO37wCJk3kHpkPNq7amDCv\neFQsLg+lA8AAwDu11pcCeBGAtyqlLl0CviNRAKCOqsSTgWA4qJiExycbn46YlhorXyvg8H0pQXi+\nsTQUuq2JXK8VYhoYJ6VSl8HqRw+FVUVvBfDAfwa29m1Cnrcv73T8iPaQbGe1CJT3fox5RSkSi0Dx\nsQCClTTtq0Uf/eGA3b0CjQxTRw7sbsut3ufoEZfn3NwYaJ0lVXjFx5QOVyxLl05nOAw75oL8oeX3\n3is98d+dRxzqrtbhlA6bh6z8rKOhFrbM5vQ58bMIM6Xv0wHV8AgOlIsPWp+63m5TLcVDbXPIvhbr\nTJvLg6uIlkrH//jhG4B73VhDqZ2H/+HKXwYeJqcjF6H5NCuqKRBUdx2R2GVWFROwjGhGrE+HS08+\nqc0GRG4O4cxvROlYuRF37L4DD0z992BxqhhzIvZdtDyUDq31bq31Heb3EQD3A3jKuHyXgsZCOsgk\nprU9M0QafEJN3X0eoTvfCmz5eEyQBAMwZXvQWsE0QI6mqvgNB+b2B6UeOCBMoLPm/ITbDLSdo3R8\n5aPAPuFgLJ9sZ7JogxTxdHA0uFWoohm8nndNXh14u1f6wz4KC7cSuFPrjLNXMnZe0LIAxo4dHByX\nSY6VJAxu5l7T3SsmY28taF10c7Yf1oquJo52gPcjvK59nGl9WiQpsR21M2xCcXSZ7Q71w9AMoAA8\nxAT0Dc0rnE9HeMspj9Jjn2bi7QAa5rv4SkcCefi759zTpBMPFpHksxNZo5DT05g5empHOkwPpkrH\ncxT46RddiR96rrslO6UwTBdr3BvMUQWN4pKKVuteTiiuPhSXNM6w5LZxu+bGu+7S+OIXR1sbb6Bx\nTNYz/kw+HTxv+fl0KKXOA3AFgFuZZ29WSt2ulLp9H39++ZIQRaPHitNBBwKjRSvoEItjzRutC5Mf\nJR1Jw/J14DgKuD4e6RX60IFMgXIomFf84E8ppWPbZ4FD5wMHnw68VwOD+IBX08Ju4KbHgXv+oynH\nvI99ly3XBPIp6pi5fhvYwdFTDJSndCz2B2w4Zq0VZk8/M7jvpRLKYUjFtl2O2b4e+qR3QwrrT8oi\nO3UAYIJZSYZEw3rn2dOrbJE0vnll06+6zztlnaS76c0cA0cOaipT0PiXb3JF5iAd0jfx7t/288DW\na4MJSCkFbeu0HADfuQGY3crzkEgPZaUjQ1G1SSY6cRRrMiaPb15xH2bJ0y2KYEj6xjf4tJZuv8Xz\nG2G2TDdbZtvNA902SkdMQRxORNJYE0wXjz8umbjiDsxxZZF558EycyRVSq0G8HkA79BaBwEXtNYf\n11o/T2v9vI0bpUBD45Mm/7d3hCNU9gkfg3RozVoyUsh58llsgAh2xmSaV+g9Vgnh2DRpyujER39b\nrT5T6dg9RrCcr24D5ncwMgAYzgKHH3BuOaul2Y1hHoacPKrE3ff1m90r9KyUrIGshbIQhEmGcM3Q\n7Db5We8gcPAe7/PlxOlwy55gVpIB2W+vNZzgYOzERJEOQUHh6njmbi/NRANmLEqh0GFMTNookE3Z\n/MIkA+nweYt5zfXQUzqgoG2dbn8h8Cc/Dhy8w2TJnBn0OOYVgnQUccW/iCx8ArSvhX/I6sObcfG0\nVR5cPt/9bjzv4oK/VZ98A1OPDcd4H9r+hOu83oHc1jljnEiceaUGOsy9/hqZS8KUXkTQR6dd9w4B\nN/8YUC4TR1IAUEpNoFI4Pq21/sJS8ByVNFEMqi2zI64Sy17z0RcrHWrV3A4vEfXpGKGcDM9+HD3D\nu8HZ/lLmFcAZOBOrVgWNgcdycTHuKd48S7RqPRN/HiXOKVQeUBxH0uGk0IldchZMqkRvMGgGIaIk\nlsFW4RTFVou68qcRTqBNtq2dfxfec9ADXzOOmFfAf+duTuhkzSAdmVv5GjmjCcNbRaN08L4pbjtR\nJK6M5Aqch3QIIkrK1Y6rGB6mXfU7ley1ScpXCqU+NYJ5hXzUxrwSP+Mk+lV0atUl09N2XoMHXvhC\ntoypqXhbKIL4QOTbP1HBJLlbZrHWG9e5Nmt9OuKcXOICJ+7YZQtpitPSDqI4wsadfk0SNvn1oD76\nYFkgHapaGn4CwP1a6w+OL9J45H6mccwrBOk4sgu4/Rdwzr5vhemsT8dYFMm/+Q3APAmSlWvfpwNX\nMXDzBeFGQ/I7wWJPGPjamld834s2VadTE7F77xvfINNKdyGrMB/pQMHH6SizVv6RiT4o2Do3tkQ6\nbnwNsOcr4f2ejUGiqmO2I8d1s0iHcsteO+nFNOHI8eloMbRo4LlnXSHA4AmIXnXjXcJTThfmXPOK\nsMT0rhO7VzjzlE87XwT85Q1NDqVQ2joawnwfIXS81KfGQjqaqkkerBZlUv8nPRQpZv5ekVA6Nt3p\n9UnaR/2IpC3nAUcurz8GTrcRZEeXpq0VZOfXl78J3PZzzjet1slhXT1l6hKbgnKtf3Uii8fzp64k\naZs8ywXpuArAGwG8TCm1yfx7TSrTsSLaB8ZzJCXOU0oBs1uqIEZiPxJWONH27k3YLNsucP+PR0UN\nyvY7RmfophGVDl3/GfoTZtTnAI0GLg2Qj3y0Ujh0xCntA8mN+XEZvGe/+a4Chy2wMjEv1/OWa4Cd\nFUBXFL7S0W98OlTTictWPg5IKovrT6mCg7FHiIziSLpIHO0G3nbXWJwOwZQwlVgNO3nbylsqPLHN\nM7maQ+CScH0xmQC9bD80Kz9v9Zl14FsK6aAKVlC3JC/xk6l2r5g2NDDv2hbp0AQd2/vP/kM+T/1Y\n4aPm4Og00pEwr7SJR0P5krr3FZAU0rEw6ysdoYnru7uMjSapAPuKBFd2G0dSjy9ViPpDYO4xtzjN\n+3S85cyP4+9e56GYBOmImVd++YzPsveXhdKhtb5Ra6201s/WWl9u/jFLr+NDmvyfvWWKI6p0mEZY\nqCJskNa8MlaAnZjSAaSbup/fH6y9gSEJlWsMPZ6iI6mVzc7BwfY/Q49/HrjpR6pbVcgAACAASURB\nVOPFPpJ4T2e1nlHfWmHLFot0zIN3zCqqo6sf/TNAa5Slp3R0F5ktdDoP6WhBz3tBVb/Bp2kTgIwS\n9SEYTHlNhGkvLDX3W+9esUNL8mA8AKXCzh0QBnungPBW/5QGnInmtxN6890WB/OsP2jr4GC55MnX\nXTAO9Q/aSUlAOjpcsC2TzLIczrUW5y//svr7svN/OJouaV4JwtfnjYV00vRZrJDCwljyd4Ywit/O\nw9ZskvhYAXrBJgLAbJmNxcgoY33GzcdtmVVQmO763z7PvDKlVjdyEN7LQuk40WjJfDq0h3TAICfc\neK0BnPYigU+kDCkiYVBAgiEXP8RxXiqQdIbz+AyDYoSti9pXOtKtuiiAF7wAePObrayGBqmRnEM6\nFLDruen0E3O8QuRFH9y9iz4rge4C6yWehXRooc44SYsK6dClYr7nCG341IcNYwWc9ojLI2pesbuC\n3CydHAWeRot1tsxqBO+gvTYUTF5WWYnIDQBHnk5YpZQOg3SYDMOyx0P8OUjHNAm25gyjguM3c/bK\nitltwK1vAP7ZmL/qKK4tHEnpDhiu3AxaO5VhOhOoqj9hGnkwDnjTuve/Q7eTaG++v4QzAVfvXu/K\naX20PWNeCQ58c8vyOJj/M8pVdpkc8tHQePBBqYy4eUU7i9WTSscxJQ2gWyvB4yIdjbkBEOCsrKBT\nCYoNMuwW3URZTEyCLGSgLsrbMgu4qxeOVb1IS7fqsgQ6HeDnfs6TK6V0SD4dT1zmpSMDvc0zdZg/\nPyYYrHykYwETtXd/U+bcauYwulBg4TcjRlG1gflgwcp8yzZUh8eOmKY4B0zl1oW4ZdZpJ9S80qLv\nRefYxLt3teuGIuW38U6cXSQ876w4HU8lJ5NSZSnaz9xJVgPAwq7Gf2brtdVR6E98PcKDClo2RxrE\nDpZMypKbkhEheF1y48g5/H3LN1AyG/rcWbEzq4ANp6bNK93giIZcUsDHv4Nzbvyf5FZVXrfN6bm2\nXx24LVqa6EiqNd75ThlFEs0rM5u979JcJA/ROw607JQOoIHAltSnQ+I3dRSjTwo5A7MP/eUoOL55\nJRfpaMoItsyu28EkJPLVu8MGWYpHt2ur1eQfKgf65okO7iROx0P/BvjY3cC+73OT0zNepg7zSEfH\nx3E9paOziMnAvEJWpTOpMy4yqfaZUe5fleHXYInWu+8cOHUkkk/Y8kmRDijg9l9IlC85knLtnDAv\nhXRKeU1bAwcuAG75t8BNrwX2TQJ/cUEc6fAdPkgbK6DyLAEpnw5ny2keShWYfrUC+ofMUeipM90N\nlbo5B2ro5ZGUn5HMwLGJVbnf2tFBU7vkZMXnu+vCYH813fe7KPzdYwNqDq8aVLfjm60A3Mltq2a+\nxa7n49Qnfqx5Zr5xoHTEHElr2UjfYxqc5EiqoRFuN88wr2x6e6Vc0JNwv/onAE4iHceEnOlwLJ8O\nsmW2XiwVfgEYeyW6FJQMPMVB9nEKHEndAsMMFOnIUDo6HReQUcMc+F5Io4sq9HKvcp48b+1F1X1q\n95WUDuekWR/dMUhHp1I6lB0wps9u0hy+NyJvbp1r1HE6anOElSGzfd3yk8DNP0HydRr5Nv9Monhp\npU58Oooi7TfgIEJ2wAsh3oBKo1ywK1+vHeoC6D0JDA4DP/UDwM0b8pCOYqJCfcpOfW/D9Ma8MOjs\nFhGSj+5OEBFGFWm/dhxpS7rS3oH2SIeWJ3yf4s992anSSqaXYYg6OI6kbcbqxf3QQ0/puOcGclHJ\n0Km3zBLeXzwbePcFUfalQVzX0KCnRomfaIN01Eg5j2LQn5xPh0ZlcnX40S2zEfNKvw84feiB1wI4\nqXQcE6LAbgU/jagQMD4dBRhHUqlLZjo6pimxymUba/N/RSrNh+Q5ckTj4sOnZqQHWJ+OjJV5rXTU\nbGYRBkLzKWNwA/BTF/wi8IW/Ap68CI55hVM6vNM5nTI6PaAoiXmFo4xBJ0mqenfFTUwphdE86x2o\nJuKaTJ0s7AV2PS9evIR09Fc2UoiKK7m35mJziyIdGXUQi0jqfGfN9pkmTkeiP61/jvFvqaiQsNAs\nZZG2E4KEZSqaCsqdaLLGAo/KErj1IWDf9cDu0X33cyT+6rOfzecNfHEogkUmRQbFjPl0xEmHPh3D\nAbDvOvO4GkeGtTmVIjEKmI37sAz6lSzr6NBg0M5ysc18YtOmx0MO6Xjve7nIwRnmFTBKh6mvk+aV\nY0C0I49zkFG1WreaKjGvBJaM9igCyZxOMuXDjGnzSqB0mGiMuXTfvcCPvrID7E1sraXkIB3pTjas\nd/vZOl7MUDqoCHQ7qtuMV3RWApvfCGcVVpRZCIzzTSaqlX3qbIqIkHnJOt36sL1QjBGRNIt06KFw\nBgQhSenorWrutpoUqepPIF6JxM/uvzvlS+7WSKQki0zcZBce+MYJSM1wnl/QzGahfGllPyLSoTUw\n2wPue08VkTcvU3gnqvRVkr10vRDtVQPBNGL7MVUMUkgHx1r8dDpEOhy0qMrYtyZyZ3UDxnfMvR4O\nqNJhx49K/n/6chvzireFXDP+f4Y969OhGCU7MzhYzz+iyih9J5GOY0DVsFR9GNXSa1kmg3SI/I6h\neeXI6RAdKIV7Q9VnemyOjB4cKGVx7ttOaZ8NkaPZv/zlnk+HHqSVDnHiszyqPw8/LCQLPPwTZI5K\n7yjuiOoMaqOMKgOlcuYVOrDd92W/EIEf2QnBHDbmJSbsiK2CxPfQrRR4gnRo8N+NW+Vz/Ut7F4zT\na55PR8hUHB3G2T2kS+D+/8zczzHjtKSxtukTy0yyu2p0he+vocJJ3Z4gPUfQUkbxdRW+Fu0rcAi2\nLOw4UL3QoPbL85COhCl30C8wPQ02Zs7MQT/OEGc68U2DcaRS8umQlGxLonnls1+skA7q02FQp5NI\nxzEgZ12U0OCTdPSh6u/eym4fgrFj+nTkLOznvDDo3IDo3dOsDbpN/NvUoMu8r93ilvLp+MqfVsk9\n80qW0sE5kkIFE9GNN1K+NE+ix/m7Lszpmh3jud4eOGurdADBIOP7dNx0H3DXOzP4EaQjGKC9MqZo\naHoqc1Ovp09KikvcXp1FYj/13j1pXsmUj3DnHEmDVSe3mqVibP2E+8xx6uTLDxCWUcwr0V1CiRXD\n2bfXSkcKmFSI+Fw4kVQN/5Vm58ksCfg2jB893+7tGaQDvhzAwC4yqOwlQqTDe7cSCpOT7u1JswPl\n8AX+ieBy+2qe0MM2w8rW4RDepI3sXhQXwU9eHJpXzBh5Euk4BqQBLBqfqkceVq3G/YCOPgLc8Gpg\n550AbHAwP9GYis0xIHb8ytkBkV1XzCr1STPQzj8elnX3bwMAztr3M8B3fgUA2b1Smz3bIh1UBrcZ\nd0RAKkPNp7NQp8Ioi1ggsFFXm+98Np59iBxNrYZokA4A5/0A8LaHQ6VDF8Di3jR/R+nwFIb5He71\nbhrnhCAdRhl4xtwdWJM4idQljWZoyZgU2TNT/NWi/S0rHW3NqdWSgeEXnGfCzgjNz4U91T8AgXIv\n+G0opTDySp+KNYqyAgCdAS69FNi+vUIda/qty8K00YW6V/6DXzMnOgM4+pTmPnMOiXuiczskbTjk\ntnlbHiVefeGr8YFXfKAuyZE35bSuCxT2KBzzfmse+Qjw2qtQdj0zVo6/lROY0TejKhnp4DTiHPPK\ncNKYV0KlA/jen7+y/JQOrcnKZwkUgnIB9uMpzpF0SXw62uR3016ufwH+QCdDdZm8aZyLpAwmzbdn\nqmPH998QKh0Hvu2mBYd0DNshHTGlw+mLdMBJqfkaTrj3wiIdlqEn3+KTze991/P8RFI4fW4VubT2\nXyLvTz6OShHx/FeG8821ZDKiSseTz3CfPfRB4O7fbK4HJOqhDutVa93SKVsTaDcnubA4CHbuLDXS\nwW+ZHfpKR+kbyKvczfNIaH8ufS0Zr5C0o7ZIh6H7fhKvfS3w0Y8Cm+8i9+9dG6aNnTKr0ZjF9l0P\nPPBV4JZfr66fIFvYGaXDiUgalzYotBx4Ey5FXLTGV97wFVx+5nNsSUQOAJzCQllBNUqHlU8PgcMT\nUMMwOnGMU1Ooua7HlzzTS1gzROnwzSt3/xZw288DgymDdNBszTt/r00sy0/pqP8DxkYhjpxlmFKl\ngyYgSsNdvxbn9cQ35WfR4GC0nJA23ck8U3VGwmcExSiB0Lpl6ubYceEAqdXzz6x/+1tmqw7ZAulg\nJkdLXcevj04OGb2tQ9LUSIewyn+A2O45hSZ6pg7wsp3nVr/3P8aevVCRP/EqD74X8lmlY8+zgF3P\nd5+VC8CB7xBZGGVONWhFqUvMz7exuVu5QUbulu2PU1qEvhB1JI18gyCkdZ3Fy0OVvEZAkiHDzu/l\nUVB46cafri6OnomRxqpR1zqfvA74/KexeTPwgQ94fForP9bETPLf+qvAe7Xrx5F0JA3LlVfkGsMo\nWuFlVJ58QV5/GiRIh+cvVmjfzBgzr2QgHTYt60jKmFeIAjhzyJP7wK3A3DZgOBn6dJAx8nttYlme\nSkd9MabSUWvnFZ89u73qWnluFZtAl8D87jaSGf65A3Iw8maQn24cn47Icy4OA419YUwrAHDunl+t\nfwdIBzAi0kF8OowsHckaEgm6dGr37IpnwSkdQjc5tImIkzqJNKTf+c0C2LEFgIa2K6AUkuYjHRJZ\nmWdzIqcKZOp1bl5j1apEWodK2KFFPiyMQcuS6TgbN3hk8973MvndDAq8SSbw6RgmYmBEkQ7+/ZVS\n+Lnz3g38wWF0FjeMNlYJPi71M4keuwoYTuHzn88TNyqZs2skEl4/8MFwFQ1O6Th4QCwUwwFnXrHo\nnv8SHtIR7F4pg8sA6bAXvkNs7OyVejyjPh3hjB/16YggHb/6Ntm88sEPEjk888pJpONYkBOF0Pua\n73yOn1omq3SYxrP5Lq+6pg0SsuIsoH8wzqs3Iz9rg0IETm5hZ50uzxyxDA/yE7Mk7I90kibQdEGa\nWxCRFDoK41ZJePPKX3ws5tNBkQ5Z6fjJM34b0B1gltSdVTpM9MMVd/66k+fZ+36fjExmMHF6dBzp\ncC512fCi4Zs5n44cBdIOwAko2SQm/Alvc2BVr0cPcovQve+p/i6sJfWSMZnScPWBXL7CnYF09GeA\n/dexRRXbmsPNFPgmF5hXOBTLaYoZSgf7jgrorUkfbhZlvQQmZOf7S+UIIjhnxni86IFnmlE6yKze\nldBEvlCUQbtWjk+HI0kK6dj1JeeyNxcqHXMmLl4xlA9gC8RkkQ5vxjdriiyfDu3dkyI4Wx+untHa\n9n71JNJxLEkDWLPGwkpMh2yz4K+VDrsK5RxJTams3ZfQAoeE5CIdkYGFyVpgEuj5nSPnxYUVS7RQ\n5h3u+KVkSaFPR4Z5hZsclcL0tFs/DjBB20BkxXrByucCB84HqM3WcyQtjjwVuOen6sfPPPA7oTzD\nYTXpAa2USU19OhzzlILzPejq8chDEY4mXesdXMy3zY2fYts4mYia0v26SCEdTLvSAM68K0jZJk6H\n6tHj5fkVduBImorTESAdVGYB6YDCLbdUv6tjQwi/LfFTX92iIt/3u28B/pe3xTrVJlmkQ86zuIgm\nUm3vgCuP0/fiW2YLtDknRUA6alOILy/9VnCRjkevDsbunVsQOJLOzlpOfrk5fZy0n8Lz6Vj5JB4Z\nCqb3g0835Zu0Aw/hZB2w0SgdgyPA9S+vTtE2aVetOulIuuSktcaKFRTp8BO0YGaVjoIqHZFOTu3k\nQbkcpmU14XFMH8yg2dK2HbBWqa2lzD2qgR95ADh4B5eo/jWKT8fKlXzdd/3z4KVvlDJLlAAK8h5m\ny2zXKB3aW8k517XSUZJBLAfpqKa+ZpuzAiaIM1/BmFcA4I/uATa9XeZfIx2ZSANHZqXKrth4RgG/\nceLzge7mofz9UqNiuQ+L/ZfV96TBLwzUFIHQAWAQOSekTu6iNEop/PZv299wv8HhpyCLUp/j6EPA\nzq2cMDKflmae2aOq8iV48P3A1mvkhJx5hTSOCc4PbI00DmmUfrvurwSOmgA9Pc8u48cRWRSC4dW8\nQqTD1ov2x8as3StUFg9mOOcWXNv/YVeKLcaWuf8SVH1gADzyZ8DN73GZnREq4FV5NBIsmbsAHD0K\nnJoZbPpY0fJTOkC6lAjZtqR6FSohHfkhxt1bPNKh+j3g4DYxG8+D3tKMIpMjo2kO66xtVKorOgmm\n0JrmPu3E3a5d4VGzTFzGc+hYTOJ0LJSzTlHuOJBnXimUqlAB2iMM0qGo0kFWF7zSMSQr33yTVhmc\ns2CoOwm2vg8vVg6hHxdOsNz7tWrwvSXD/8MRxyJIqO3XXRUJLuYoRKHSUVWo8j+Kx8NXLpyH5Dff\nPmqko+D6mHtvxa3vrn9Lu1fCLbPgTwpd2FOZlOa2s3K5BR8SH7lmRgD9TAeaaJwOQz6cz/IRfhuK\nKY6HZ8zDPV8xyjZNTPte3Kejw50Ie4lwSKHW0KU3dS2sr07p/e5bKmdKWjrlrRWw4J8s7dGAUTrq\n7H59yvaoxmRCkQ4/v/LSAnjrFcDrvt9N9vgXgKP73MXdjquYsgWSUJHvAZ04kiwRedN3cKeVecVq\npcrVFuVCY5MM24Iz8omFiVRCh4N8DtKx1jgdBrvCMvL6ozc7UjFIh7NXP/5x3ABFTXn76xgJ5okk\nbsohUMNFOsw7FYLS4QpnyyBIR7TelPO3r4xJxg+ipAoEW2YBsFtsKS3urQ6Bi58QzpCdwQHMPA0A\n8MypV7VjQUw6KmvlzKR55u8CRRdOexeqs41LVOWfo+tSOfNK6NPBhNBXChjMAvuZrdLcYYmr9kIy\nPRSFe03Dz0epjCGvplwaoIvel4idQ+U8hw5lLuI4pUMllI4Y+f1w/pTqGx1lTI5dUp8ZW2bRQ7h7\nxVKgNGQgHdzCyg/oSC8XusB+Mwg7bcbbti6Y4diI9SeVjmNHSaSDayN3CiOzgddr84p4VHMbpYFQ\nKYUEZJSG+lGmeWWcUM433g1c8j+BUyWfAQcvNH8khYEvt1Y6JppDxfDUm6JiSUrHlad7qwIRLpaV\nGqVQTZZMkykQQTpq508SU7oV0gFAAQvF/uqH7x1feAONLf/Zn24yRylHBsLjS9cG97t6JfIojKoq\nSpd72Bk3gceShE+dK2qJU+C3zZa+0jF3Wn2CcXvSwNaXAPf8O+++b4IaBelA2t/mht8J7/n1LSGD\n3p0Lb7gbOLrFeTbj+8eLpro40tH1j6qPUdENy/Hq7BWvAH769ZY5+XbBu3vfett/A7YtQim3rdha\nGPjb7rPMK0TRELbM1mm/5M9FntJBF3dMnQLAxRdz7E+cqf7EkWSJqNrv3A5xUNuEnSUdzzYvmley\nJAtv+RChlYf871B/RWLAqGjQHTIPWgi+eAj4AX8Dv8BLRGtC+en2xHr3ylPNCairLwBe9KdRsZxV\nqe3s+y7FM041QYimh44kl17qyUEHCM8JU9XmlfCdbZyOqmkJg6pVOoYl4rsZrCyuTIudJyul1ucv\nKR2MQyVLnZzAVYQG4VaKbMcz0bwyDuUrHVmOpCSNb92rc/hKx6OvAI6c497b8ENVm/WF4IT7+2uB\n3mrvtqd00DpjvgHPG8CLPhJ5iIxzdzyKfOtV+2aAI/c59x5+yK/0FkqHs3ulhZyqE06ij7mmhq9/\nHbj+OsOfbuG37zcQ/K62fwoow4ikNRW5MVnQKAjrzI7JoiuauyyX4oiv1FATVccrj6/rOmTAPT9N\n+Jw4U/2JI8kSkdMEOE2wjc3SKh1JR1I72MYGSG5JxSMdWrr46geBD/i7YEK+ZYczr7TYJ5U8o4S5\nJ2131XwnYeN0JMiFwhu+9Yrkgsq348ip1d+VwQLd+l0sAJvd80tqp9YOo3SYblIdElkAd/wyLrvp\nVtenY/GJ6u89j7ZHOgAMsAB2C1zREeuwKiLRhbsJkxLgDWy2mKbM++6PZg5vEWW621GyorbpHSaO\nS6whUIVrBKTDe0hXr3OzqlGED91Z3w8jkiZEBBonxiHjN1TXZcOEdnnfD1pawQakVVqpDNoH23mj\nj+3uFc0isDGUivy+8KsMX6p0tDCvqG74XotMJFVLhefTAQDDyBhHw6D79NdfzJCP1BcArL2EPPPH\nYbeQyYlYfRbyOEvInqmDz/21WM73kpan0mE7RjmBoBdxZzeJSocZQJKOpImOLFHdcbzVWABSRAYF\nEYwYGZIBkHI+4ybBFoMRRlQ6BPOKP2gPu2Vzn4ti6vtJWHmHCuhySAf1Bi+AI/dj5dG5Jh8A9A8B\n1/0wcOfDQGHssWsvlV+mLqbKr+uzVzikQ9gyC4Tpfeq2dCRlJqDdu7wbIoVIx9o1UvvQwMxdVYj8\n6DuMi3S4RNNsny5x8IkCuP0XgXsaB9MhB+2kmD/wh8Cdb0vH6zEUIB2c0yUJrAeAnO9imcQKILuh\nPHrBC5R7gmrCvOKSHwDMV4LzO7UbBj1yvpFPnNIhxawAANp/g0/LQV2V0rFrV/gIW30/ihgMyPAW\nzCs9ozt2g9fwfTpk+thrPoa3Pv+tcnDEE4SWp9JhGwK7YoggFT7ZVUTKkTTFR6KYTwdLnOxCJ/eV\njjbHuqu+x8OXhxuU0+/urGy6Yyod9UzDrRSrdEH8A2fydt+hRjq64bvZ3SvVXGT5KWb3iomYuer8\nvBdyJBuA/ZaqcL9lW5h0IkfpiK90s0mHPh1TkzkfWUWUZ+/irjeGSUb06QCAD30IwK6es5269JUO\nrTLm4gXg8L1MmcTcSybkqHnFxrTwt+Df+TavzIhQtr8LSoDY9yKLKq01r6yPSK4jaZuZUoflRlFt\n2r5tf+XQaZu8RFEAX/gCTS+9p/z+bMAvwbzyV39VpT3q776OOZJ69EvP/yV89DUfbZCOE5SWndIB\noIljX3aB77zVe8hkkCZM1rzCFchKkRa07ijZTJnbmUpHG/MKEpAtDaYz0g4c4NAhb+Aj8v3mpfx+\n/6R5xXsUDKx1nYRRPWtH0il6v2IwYezNulTOIMTvWFTpQHFUfG2h2CHYraOST4cno0hzG+LPJbna\nP2yITIbyya/0nVogHftC9KiN0sHuSLjmu8A1zZbY8Gh79kNnkmbHFzp3i0iHX99+nBkN4PDZQrEy\n0tGUyRTD1OXCYB4H5w8apSPVBjIV2Lt+DW5wMGEqevQx93rLx4GZzWE6JvgYK5Ot9yJiAj3t4XBM\nEVnHZnheoXGvK9n22oOjY+O77mQt7izScX77tc9xoWWndDgH55QMDMcs0ofP4A4hQOP8lUI6ypzV\nZMz2zQ1yEvkafmZ5rZQOq40LcnCTqrhltrlPB5lXvlJWOi5eeyVbbK55RVGkg9u9olSwYqvjdJwd\nfstuwTi51Xwp0oGqjUTigbCkgFINwHbHogN2y2wgB0M3/QZw55vayWL5jTTH2tUjhc2FNt6WJ1D1\nC2YHWfaBb9/+qapNWFj/b813ndsI7L2iTjYc+n1nDHu449ieiXREFyOeXJ/7G+GZRTrCNqVUDGUM\nH9y/7z6c95HzzMp9CcwrB+8ADm1yD3yTI7W51zs+a8rxx/XI5O8wt2VGQvtPHUZRAKfkHFvEKh22\nQXJIB6/slHXfiZTFIR19P/J049Mx0XIX8vGi5ad0ANU5FsD45pXbftlkoT4dTP6tn4jzkcoVzSuR\nfLlIx6S37S7lHEpp7bY4LO8oHflIBx3o1q71lY70Fgln1VwHsdKB0kEipHsPyODPlVcCWEfrqWJg\nlQ43IqlnXqETbg7S4cXpqCKS5iAd/kuRgdtvC/e9TlaUAeBvzgGuPd+DcAO2+cTUqYx0UFJ8v3IE\nMr8Z232gdHBK+5GHgcV9Jo2pE6qHO7oNswhoZQv0FXAG6fDjdDircWm28E2mqCJxskmFAwQz2Db8\nm8XH4cXDRunwE49hXsnaWk3a1HbSN/33iplXnLOg/DTMy08fQFFYxMBbXPhkHcgZYs0rgmP3QJsj\nF/w93P7uFb8tfWh7wMsiHSeVjuNEmvyfu3tFJDYMOpPuf/2Red5yNWdXbbUtOIOkIvrett/CG5zb\nIB1nbALOupPc8GHemId+fSPI69hwI46kbasxUDpMiOQQSrfaCGdeUaKNvDGvoB4EVD2ZM4NEGwWv\nbrGCT0fKvOKsmH1ZEt376guBT5/LiSOImvlhSMjrWulIRSQVn3kXzDs55zuKDKq/FdIRt9P/0Xd/\nK5RvDLCjUUgbJt+5tXka9ANp1R4oQ0XkGwuVYk/YzXkfi9jRKvTHkYgSnBprg/bKEUWdBpRhhtLB\nymR+12dTMUJ+8/dQFJlbxaMLDIa3sJh7aMMHATCm4sCRlGkDHp1EOo4z6cgVAN4cIe6xt1BzxLyi\nS+A7v5IvoCOLUQz6hzzPdA3XVyI2KJtngzn3fjkEHvssSddmy6x3KJFPbXw6pAOvLMTbCzuh9Dnc\nQar5kH5HLYfkPrd7heMNyEqHRTqojPB9OqhikDFa1ckN0qGGUEqh2/Vk8LfMRnw6ClUAV98RSStR\n5kTxtT9xr7deC3z3F8mNcHJVNgy6T7FtwG5CN0/EvBL3rSKTrXVaFD7T5v1MyPORD5HhfTr+5m9y\nzCsp1jqdNsuRVHi32kxoFeMcn458cpAOqXrpzE9dzXKQjpo5g3RIgR5v/nXgwEWN0jGSaS3SIAWk\nY3Zim5HVZ+XdEBd3DZ1EOo4zaa2b1VWH00LbNCKTNop0pDph5DntKE9+O5JFR54ZGQON21/htFE6\n+FC9NXHmlYzO4K9slAJw3wfDdMI3cs0rsk+HdnavUEpEJA1eoeLTsYGLHK3Dg12tPGt259V1gJQb\nnw7/1VtsmVVQwJ4rgD3PCZ5lk5a+J4Cdz29+b3o78NingRmKlGjgjjeBvkSHC/nJlpvzQAOr94Qp\nLLAZW1CYNu3qrTzyEFBKh/SdOcV4PU15E0S5DBC5iFPkmyfJaV1aRaIk2zTB1q7Qp0Oqew/RLFlH\n0og5QCJT+Mxig85Kfd7x6XCUjgyfjjorSevvXhHMRdlIB+ssav5wkWXrxMfaLwAAIABJREFULey+\nCa4aM3K7S1O8jHSsyIwxd7xp+SkdAAr71Tu9sE20UdT9AZjbCy5q/hnGcTpgPPJnwGOfyRDS7+SW\nF6dgUWVlFKRDINZRMl2x/sCiFMI4Eje+S0Y6uN0rionTQZEOZxXPMJ65p+YenMi67tnAxPrmBExN\n+GnBp6PoI8u8YoKQTU4BUKpyJNX8AWRxVIAxr9Tns2Q29lgcGIdPYkT88CPA33/C4ZeldLTZvbJ6\nb5jCJjkyARz8LnD/74l8OKWjKIBzvICjuOGV1dkqhlauhkyxGBFChGRq/WyDdMzSM9C0cso+58Ab\nmBw5SIdAHtIBDumImVfE9lLdv/GxG9NJqdIRM6/MPA3Y/oNCcbRuzd9A+XDvF95O9VEU+LWb3g18\n02uLHX5sKI1GpQBs2kSfkHJ7axC0JUYui3ScVDqOE2mQFXGXmRxZ7TV3cOYcSdOrGpGcwaWszCwp\nXoESZaFi/13HQDpint0Ab17JmOD8/s0OfP/yPpyx4mk8Aye9jHQMhmSCiZ298p03Ane/i6T1ynvO\nB4HLP0J2YFB+vtJhqLuYV9frm0GmAq6NIynbbCLmFeqQaGHkEbcxj5SFG5jJvcAxjs0Y6SuHzvVu\nhALWYMZQAZt/AzhETEy2rXK7DIhyGsZ66TVlJcHMMRAlcI6kktKhaxSvSuciHZdtvZbJ4o8DVR/I\nONIGvpn1kQ0fQiqi5qgkDh8S0hFyAL72AeEZh3TUN0I+oEhH6v3YVULFabASuP4/AZtjpy5W/Euz\nq0UVChddRFmZ8ufXV7/9imKQDqt0TPkHd54gtLyVjqUyr9TMRzGvRCh5am0oQlCcHaBSOyZaOTcm\nKIWqCPeH3nhVfSbfztDFugk+tkSueaU/4O8HWs/8zjr2Qb1l1qeVT3Nh1hr1smhCzbz6MzGHLJ8O\nXzQMIB21nhscLICoc5EOztGO6yasbN4k6FETdTIiS2zSpvZ4oV5jcZ4wMNGWOivxK8//Vc+s0Eww\nnU5EBo0xfDpA2kzDo6Qn8QZIh2xe0T4qRc5pefvbORn9MUxDqZamA/Nn2Mlo21kKWJgmy6djT8TM\nGCuHRTqELBLSMQ59YydTjsu8VGb3CgR/G219o9Jm7BsNgDTnufmN04SXkpaf0qE11k2tqy62/ysG\nGWBzuZd2oMrZgy4uGTJabGRFkzGHGx7mE/qKgL90b4V0JEiH20rxsv+fKd8lf6BjlQ5dRBxJnYQA\nqq23IdJB00eQjkBAvlc6waJMRMFCT3oRSe3IPJFX1zdWipUy/9dh0FsjHSQmhm9e8ev2yIPAZxOn\npcaardP+mYRM9EbZvJI5ojsxFjS4CqrdabhXq5WO1fjT13zEM69Uf1ikoyq8lag8afYAt3hwMPk0\na+UoHQo48pT68qUv4can0KcDaOrs93/fKxsA7rfmRM7vIQ3vS0lr2vs1OY9PFOn4GgnXyZYrycIg\nHXX9p5COFG+GTBl19WUoeFbpEGOoWJQ9A+m4/PLq77597v0TJTz6slI6bp6ZwTcOHcK6qbU4+5Oz\nwJaXh4lYZzNy8y/PAb77/5oL7+uX3RGQjsjzob+tlaRNTT41WUjdKAJPCAd8jYR05Go+eTz+8R/d\nJ9GBniU64Fbf7PQzGaVjwNjvgejSpYpIyjzQZTP4aNTwsqpXo54p45Z3Iqt+vEHThkEX1J7mZ+D9\nzphXJOfeO/4D8LnIwVjAeBMsY17pFCpj9avkcsWoUaRYk3eSO6h0aPwy5qqDNJw2MWwmmGgESg3o\n6DIxAkd+/q+AAxcG6c45x0M6nOwSAqqjyBLbeoKFUyWbbdP8ROSb56jSmwqDnjE57/lKWKKUzW6Z\nXdwHdGfJgxZKgIOWec9s41ncDyzsdZCOrN0rbLv18uRESzWbFUIn3wTSwcj3Ez9R/e1569CTSscx\noKvurGJLlAC6Wgiaw3ZM0pE+e054sJIlFplIjdKxlUDMvMJA3jF+9h12zfHpRkE6cvDFEc4kqFMo\nvgytAVx7M/AtFz2RJgZ/wBqSFWzUp8PhIUyOeuiKKCEdlpgIgTGyaM/+lTeFvGoio8Waxz35pHZS\n8QUyPqPUvoJ8jHxfJ2Eb6zmKIh1jmlfoRxecMqPmlbIH3PVrwN9VYwPnSKpUCulItWUN3PIOnL/v\nbeGjB1/L5li3liiLQTuNjRny9+bjXvj3qj5gTZ15E1FE6ciNSHr/j+cUxBQt9Fm2r/qymL/slllP\nsfr264BbXw+KdKT7jTSmekhHP9+js1DKa4uq+ZuJdFhfDl/pOFHOZFlWSod9mYWyHOlAo+on5zRo\nqJwQVw7B75HITBKcl7ibhLn2ViVBoKgxzCttwrL791PoAkNlCWDn9wP3/rRzv2CwcW1s1FzRAWyd\nkOXp5/FKhxOJ2a5I9IRTVhSCTpFBL8rJQ3xtbvyh5ncQXKjJoa2pre3uFUrhmW1xmqcn8IaP87bM\nRtI4SEfJntKZ7HaHNuHQx/88vE92r8RRN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V7pXicuTmQlUQ5s7qYsTsexx8oq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\nQRB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BEARRFEjoIAiCIAiiKPx/YqDdj5gXhR0AAAAASUVORK5CYII=\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.figure(figsize=(9, 9))\n", "plt.hold(True)\n", "plt.plot(samples['x'],'b-', label='x')\n", "plt.plot(samples['y'], 'g-', label='y')\n", "plt.plot(samples['z'], 'c-', label='z')\n", "plt.plot([50, 50], [-5, 9], 'k-', label='Warm-up period', linewidth=4)\n", "plt.legend()\n", "plt.title(\"Trace plot of Markov Chain\")\n", "plt.hold(False)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### No-U-Turn Sampler with dual averaging\n", "Like HMCda in No-U-Turn sampler with dual averaging (NUTSda) we adapt the stepsize during the course of sampling thus completely eliminates the need of specifying stepsize. Thus we can use NUTSda without any hand tuning at all." ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " x y z\n", "0 0.457420 0.500307 0.211056\n", "1 0.457420 0.500307 0.211056\n", "2 0.457420 0.500307 0.211056\n", "3 0.457420 0.500307 0.211056\n", "4 1.822813 0.537422 0.005842\n", "5 -0.195423 1.578560 1.047900\n", "6 0.522322 0.176574 1.763822\n", "7 0.124225 0.655759 4.003954\n", "8 0.124225 0.655759 4.003954\n", "9 0.337818 1.170382 4.146218\n" ] } ], "source": [ "from pgmpy.sampling import NoUTurnSamplerDA as NUTSda\n", "NUTSda_sampler = NUTSda(model=model, grad_log_pdf=GradLogPDFGaussian)\n", "samples = NUTSda_sampler.sample(initial_pos=[0.457420, 0.500307, 0.211056], num_adapt=10, num_samples=10)\n", "print(samples)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Apart from the sample method all the four algorithms (HMC, HMCda, NUTS, NUTSda) provides another method to sample from model named generate_sample method. generate_sample method returns a generator type object whose each iteration yields a sample. The sample returned is a simple numpy.array object. The arguments for generate_sample method and sample method for all algorithms are same" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "scrolled": true }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[[ 1.23158312e+00 2.08966925e+00 5.47064070e+00]\n", " [ 1.23158312e+00 2.08966925e+00 5.47064070e+00]\n", " [ 1.23158312e+00 2.08966925e+00 5.47064070e+00]\n", " [ 2.42754370e-04 -9.07581018e-01 2.22786641e+00]\n", " [ 3.80037176e+00 4.20666799e+00 2.93898094e+00]\n", " [ 1.84557224e+00 3.03691158e+00 5.05047756e+00]\n", " [ 1.84557224e+00 3.03691158e+00 5.05047756e+00]\n", " [ 1.90819711e+00 3.83294495e+00 4.98059422e+00]\n", " [ 9.22139874e-01 4.11755511e+00 4.50041160e+00]\n", " [ 9.22139874e-01 4.11755511e+00 4.50041160e+00]]\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "/home/utgup/anaconda3/lib/python3.5/site-packages/pgmpy-0.1.6-py3.5.egg/pgmpy/sampling/NUTS.py:412: RuntimeWarning: invalid value encountered in true_divide\n", " if np.random.rand() < candidate_set_size2 / (candidate_set_size2 + candidate_set_size):\n" ] } ], "source": [ "generate_samples = NUTSda_sampler.generate_sample(initial_pos=[0.4574, 0.503, 0.211], num_adapt=10, num_samples=10)\n", "samples = np.array([sample for sample in generate_samples])\n", "print(samples)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Support for coustom Models\n", "One can also use HMC, HMCda, NUTS and NUTSda to sample from a user defined model, all one has to do is create class for finding log of probability density function and gradient log of probability density function using base class provided by pgmpy, and give this class as a parameter to grad_log_pdf argument in all of these algorithms (HMC[da], NUTS[da]).\n", "\n", "In this example we will define our own logisitcs distribution and use NUTSda to sample from it.\n", "\n", "The probability density of logistic distribution is given by:\n", "\n", "$$P(x; \\mu, s) = \\frac{e^{-\\frac{x- \\mu}{s}}}{s(1 + e^{-\\frac{x - \\mu}{s}})^2}$$\n", "\n", "Thus the log of this probability density function (potential energy function) can be written as:\n", "\n", "$$log(P(x; \\mu, s)) = -\\frac{x - \\mu}{s} - log(s) - 2 log(1 + e^{-\\frac{x - \\mu}{s}})$$\n", "\n", "And the gradient of potential energy :\n", "\n", "$$\\frac{\\partial log(P(x; \\mu, s))}{\\partial x} = - \\frac{1}{s} + \\frac{2e^{-\\frac{x - \\mu}{s}}}{s(1 + e^{-\\frac{x - \\mu}{s}})}$$" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/home/utgup/anaconda3/lib/python3.5/site-packages/pgmpy-0.1.6-py3.5.egg/pgmpy/sampling/NUTS.py:412: RuntimeWarning: invalid value encountered in true_divide\n", " if np.random.rand() < candidate_set_size2 / (candidate_set_size2 + candidate_set_size):\n", "/home/utgup/anaconda3/lib/python3.5/site-packages/ipykernel/__main__.py:45: MatplotlibDeprecationWarning: pyplot.hold is deprecated.\n", " Future behavior will be consistent with the long-time default:\n", " plot commands add elements without first clearing the\n", " Axes and/or Figure.\n", "/home/utgup/anaconda3/lib/python3.5/site-packages/matplotlib/__init__.py:917: UserWarning: axes.hold is deprecated. Please remove it from your matplotlibrc and/or style files.\n", " warnings.warn(self.msg_depr_set % key)\n", "/home/utgup/anaconda3/lib/python3.5/site-packages/matplotlib/rcsetup.py:152: UserWarning: axes.hold is deprecated, will be removed in 3.0\n", " warnings.warn(\"axes.hold is deprecated, will be removed in 3.0\")\n", "/home/utgup/anaconda3/lib/python3.5/site-packages/ipykernel/__main__.py:49: MatplotlibDeprecationWarning: pyplot.hold is deprecated.\n", " Future behavior will be consistent with the long-time default:\n", " plot commands add elements without first clearing the\n", " Axes and/or Figure.\n" ] }, { "data": { "image/png": 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ygixa9/fSk5mGM+uyiUSPQltEIqahvYeTZk6AL47cCo6F0BKqjbaQCseqEIkO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\nhbXW6VJEDkuhLSIjqtnXlbS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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Importing th base class structure for log and gradient log of probability density function\n", "from pgmpy.sampling import BaseGradLogPDF\n", "\n", "# Base class for user defined continuous factor\n", "from pgmpy.factors.distributions import CustomDistribution\n", "\n", "\n", "# Defining pdf of a Logistic distribution with mu = 5, s = 2\n", "def logistic_pdf(x):\n", " power = - (x - 5.0) / 2.0\n", " return np.exp(power) / (2 * (1 + np.exp(power))**2)\n", "\n", "# Calculating log of logistic pdf\n", "def log_logistic(x):\n", " power = - (x - 5.0) / 2.0\n", " return power - np.log(2.0) - 2 * np.log(1 + np.exp(power))\n", "\n", "# Calculating gradient log of logistic pdf\n", "def grad_log_logistic(x):\n", " power = - (x - 5.0) / 2.0\n", " return - 0.5 - (2 / (1 + np.exp(power))) * np.exp(power) * (-0.5)\n", "\n", "# Creating a logistic model\n", "logistic_model = CustomDistribution(['x'], logistic_pdf)\n", "\n", "# Creating a class using base class for gradient log and log probability density function\n", "class GradLogLogistic(BaseGradLogPDF):\n", "\n", " def __init__(self, variable_assignments, model):\n", " BaseGradLogPDF.__init__(self, variable_assignments, model)\n", " self.grad_log, self.log_pdf = self._get_gradient_log_pdf()\n", "\n", " def _get_gradient_log_pdf(self):\n", " return (grad_log_logistic(self.variable_assignments),\n", " log_logistic(self.variable_assignments))\n", "\n", "# Generating samples using NUTS\n", "sampler = NUTSda(model=logistic_model, grad_log_pdf=GradLogLogistic)\n", "samples = sampler.sample(initial_pos=np.array([0.0]), num_adapt=10000,\n", " num_samples=10000)\n", "\n", "x = np.linspace(-30, 30, 10000)\n", "y = [logistic_pdf(i) for i in x]\n", "plt.figure(figsize=(8, 8))\n", "plt.hold(1)\n", "plt.plot(x, y, label='real logistic pdf')\n", "plt.hist(samples.values, normed=True, histtype='step', bins=200, label='Samples NUTSda')\n", "plt.legend()\n", "plt.hold(0)\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "anaconda-cloud": {}, "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": "3.8.10" } }, "nbformat": 4, "nbformat_minor": 1 }