{ "nbformat": 4, "nbformat_minor": 0, "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": "3.6.7" }, "colab": { "name": "MCMC.ipynb", "provenance": [], "collapsed_sections": [] } }, "cells": [ { "cell_type": "markdown", "metadata": { "id": "IzanQ5HN0xCX", "colab_type": "text" }, "source": [ " $\\quad \\quad \\quad $ *Credit: [Japan Times](https://www.japantimes.co.jp/news/2017/11/10/national/japans-casinos-work-keep-yakuza-deal-problem-drinking-experts/#.W-RJPJMzaUk).*\n" ] }, { "cell_type": "markdown", "metadata": { "id": "25VtwX9J0xCb", "colab_type": "text" }, "source": [ "# **Practical session: MCMC algorithms** (Geneviève Robin, Inria Paris)\n", "\n", "This practical session will consist of three parts. \n", "- In the first part, we experiment two Monte-Carlo Markov-Chain algorithms to sample from probability distributions with unknown normalizing constants: Randow-walk Metropolis-Hastings (RWMH) and the Metropolis adjusted Langevin algorithm (MALA). We will also study the discretization of the overdamped Langevin dynamics.\n", "- In the second part, we experiment how these algorithms can be used to compute empirical averages (empirical mean, etc.), and a Central Limit Theorem (CLT) for such averages. \n", "- Finally in the third part, we experiment the Hamiltonian dynamics and an MCMC algorithm based on it: the Generalized Hamiltonian Monte Carlo (GHMC) algorithm." ] }, { "cell_type": "markdown", "metadata": { "id": "kzjN3Ukr4I9r", "colab_type": "text" }, "source": [ "# 1. MCMC Sampling algorithms" ] }, { "cell_type": "markdown", "metadata": { "id": "-Wj-x3QLDVBT", "colab_type": "text" }, "source": [ "## 1.1. Random walk Metropolis-Hastings algorithm (RWMH)\n" ] }, { "cell_type": "markdown", "metadata": { "id": "A-PRnq88Dtyf", "colab_type": "text" }, "source": [ "The Metropolis–Hastings algorithm is a Markov chain Monte Carlo (MCMC) method for obtaining a sequence of random samples from a probability distribution from which direct sampling is difficult. For instance, when the normalizing constant of the probability distribution is intractable.\n", "\n", "The goal is to generate samples according to a probability measure $\\nu(q)\\propto \\exp(-\\beta V(q))$, where $q$ denotes the position, $\\beta = (k_B T)^{-1}$, and $V$ is a potential function. Recall that the Metropolis-Hastings algorithm produces a Markov Chain $q^1,\\ldots q^n, \\ldots$ iteratively as follows:\n", "\n", "\n", "* Given $q^n$, propose a position $\\tilde{q}^{n+1}$ according to transition probability $T(q^n, \\tilde{q}^{n+1})$\n", "* Accept the proposed position with probability $\\min(1,r(q^n, \\tilde{q}^{n+1}))$, where\n", "$$r(q^n, \\tilde{q}^{n+1}) = \\frac{\\nu(\\tilde{q}^{n+1})T(\\tilde{q}^{n+1}, q^n)}{\\nu({q}^{n})T(q^n,\\tilde{q}^{n+1})}.$$\n", "\n", "In the simplest setting, the proposals are generated through a random walk with Gaussian steps:\n", "$$\\tilde{q}^{n+1} = q^n + \\sigma G_n,$$\n", "where $G_n\\sim\\mathcal{N}(0, Id)$, and $\\sigma$ is the standard deviation of the Gaussian displacements. In this case, $T(\\tilde{q}^{n+1},q^n)=T(q^n,\\tilde{q}^{n+1})$, and thus we simply have $r(q^n, \\tilde{q}^{n+1}) = \\nu(\\tilde{q}^{n+1})/\\nu(q^n)$.\n", "\n", "\n", "Consider the double-well potential function defined by\n", "$$V(q) = (q^2-1)^2 + \\frac{1}{\\sqrt{2\\pi w}}\\exp\\left(-\\frac{(q-c)^2}{2w}\\right),$$\n", "$a\\geq 0$. The energy landscape associated with this potential is represented using the code below.\n" ] }, { "cell_type": "code", "metadata": { "id": "7sgqnIH_GlAd", "colab_type": "code", "outputId": "c2b60368-a332-4ca1-f36d-96711b2b526c", "colab": { "base_uri": "https://localhost:8080/", "height": 283 } }, "source": [ "import matplotlib.pyplot as plt\n", "import numpy as np\n", "import math\n", "\n", "center=0.2\n", "width=0.1\n", "magn=1\n", "\n", "def V(q):\n", " return 0.5*q**2 + magn*math.exp(-(q-center)**2/(2*width))/math.sqrt(2*math.pi*width)\n", "\n", "q=np.linspace(-2, 2,100)\n", "plt.plot(q, list(map(V, q)))\n", "\n" ], "execution_count": 42, "outputs": [ { "output_type": "execute_result", "data": { "text/plain": [ "[]" ] }, "metadata": { "tags": [] }, "execution_count": 42 }, { "output_type": "display_data", "data": { "image/png": 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" ] }, "metadata": { "tags": [] } } ] }, { "cell_type": "markdown", "metadata": { "id": "2wMAlfEiK1u0", "colab_type": "text" }, "source": [ "The corresponding probability distribution is defined as follows:\n", "$$\\nu(q) =\\frac{1}{Z_{\\nu}} \\exp(-\\beta V(q)),$$\n", "where $Z_{\\nu}$ is an **unknown** normalization constant. The shape of the probability distribution is represented using the code below." ] }, { "cell_type": "code", "metadata": { "id": "fsQwWqQMK97w", "colab_type": "code", "outputId": "addd23d5-66ea-452f-d718-4e473844b373", "colab": { "base_uri": "https://localhost:8080/", "height": 283 } }, "source": [ "import scipy.integrate as integrate\n", "\n", "beta=2\n", "\n", "def nu(q):\n", " return math.exp(-beta*V(q))\n", "\n", "Z = integrate.quad(lambda q: nu(q), -10, 10)[0]\n", "\n", "def nu_normed(q):\n", " return math.exp(-beta*V(q))/Z\n", "\n", "q=np.linspace(-2,2,100)\n", "plt.plot(q, list(map(nu_normed, q)))" ], "execution_count": 43, "outputs": [ { "output_type": "execute_result", "data": { "text/plain": [ "[]" ] }, "metadata": { "tags": [] }, "execution_count": 43 }, { "output_type": "display_data", "data": { "image/png": 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" ] }, "metadata": { "tags": [] } } ] }, { "cell_type": "markdown", "metadata": { "id": "gacHlNZ_LlWn", "colab_type": "text" }, "source": [ "Note that, in this 1-D example, we can compute the normalization constant using a quadrature method. However, in general, such procedures are intractable, either because the parameter space (the dimension of $q$) is too large, or because the probability $\\mu$ is defined through the product of a large number of terms (empirical likelihood). Thus, in this lab, we seek to sample $\\mu$ as though $Z_{\\mu}$ was unknown.\n" ] }, { "cell_type": "markdown", "metadata": { "id": "TWuMdbzi7n9D", "colab_type": "text" }, "source": [ "Let us now implement a function which, from the current position $q^n$, returns the new position $q^{n+1}$. Recall that this necessitates two steps: a proposal step and an accept/reject step.\n", "The code is given in the code below, for a given current position $q$ and a given variance of the random walk $\\sigma$." ] }, { "cell_type": "code", "metadata": { "id": "lji0hFjOLxYH", "colab_type": "code", "colab": {} }, "source": [ "def step_mh(q, sigma):\n", " q_tilde = q+sigma*np.random.normal(size=1)\n", " r = min(1, nu(q_tilde)/nu(q))\n", " u = np.random.uniform()\n", " if u" ] }, "metadata": { "tags": [] } } ] }, { "cell_type": "markdown", "metadata": { "id": "YuZlOQ22dZp_", "colab_type": "text" }, "source": [ "## 1.2. Metropolis adjusted Langevin algorithm (MALA)\n", "\n", "In the RWMH algorithm, we proposed moves according to random Gaussian displacements. However, such moves can be inefficient, because they are not informed by the local shape of probability distribution. When information about the potential $V$ are available, they can be used to propose more informed positions: this is the idea behind the MALA algorithm.\n", "\n", "The MALA algorithm corresponds in fact to a Metropolis-Hastings algorithm, where the new steps are proposed using an overdamped Langevin dynamic instead of Gaussian displacements. Intuitievly, the Langevin dynamics drives the random walk towards regions of high probability. The proposal $\\tilde{q}^{n+1}$ writes, given the current position $q^n$:\n", "$$\\tilde{q}^{n+1} = q^n - \\Delta t \\nabla V(q^n) + \\sqrt{\\frac{2\\Delta t}{\\beta}}G^n,$$\n", "where $G_n\\sim\\mathcal{N}(0, Id)$. \n", "\n", "As before, this proposal step is complemented by an acceptance-rejection step, where the proposed position $\\tilde{q}^{n+1}$ is accepted with probability $\\min(1,r(q^n, \\tilde{q}^{n+1}))$, where\n", "$$\n", "r(q^n, \\tilde{q}^{n+1}) = \\frac{\\nu(\\tilde{q}^{n+1})T(\\tilde{q}^{n+1}, q^n)}{\\nu({q}^{n})T(q^n,\\tilde{q}^{n+1})}.\n", "$$\n", "\n", "Recall that, in the RWMH algorithm, $T(\\tilde{q}^{n+1},q^n)=T(q^n,\\tilde{q}^{n+1})$, and thus $r(q^n, \\tilde{q}^{n+1}) = \\nu(\\tilde{q}^{n+1})/\\nu(q^n)$. However, this is no longer the case in MALA:\n", "$$T(q^n,\\tilde{q}^{n+1}) = \\sqrt{\\frac{\\beta}{4\\pi \\Delta t}} \\exp\\left(-\\beta\\frac{|\\tilde{q}^{n+1}-q^n+\\Delta t\\nabla V(q)|^2}{4 \\Delta t}\\right),$$\n", "\n", "$$T(\\tilde{q}^{n+1}, q^n) = \\sqrt{\\frac{\\beta}{4\\pi \\Delta t}} \\exp\\left(-\\beta\\frac{|q^n-\\tilde{q}^{n+1}+\\Delta t\\nabla V(\\tilde{q}^{n+1})|^2}{4 \\Delta t}\\right).$$\n", "\n", "Below, the function step_mala implements one step of the MALA algorithm. From a given position $q$ a given timestep $\\Delta t$, and a given parameter $\\beta$, it outputs the new position according to a Langevin proposal followed by an acceptance-rejection step.\n" ] }, { "cell_type": "code", "metadata": { "id": "vC3dbtrSdgfi", "colab_type": "code", "colab": {} }, "source": [ "def gradV(q):\n", " return q - magn*(q-center)/width*math.exp(-(q-center)**2/(2*width))/math.sqrt(2*math.pi*width)#(4*q*(q**2-1) + a)\n", "\n", "\n", "def step_mala(q, dt, beta):\n", " reject=False\n", " G=np.random.normal(size=1)\n", " q_tilde = q-dt*gradV(q)+math.sqrt(2*dt/beta)*G\n", " log_r = beta*(V(q)-V(q_tilde))\n", " Gtilde2 = beta*(q-q_tilde+dt*gradV(q_tilde))**2/(2*dt)\n", " log_r=log_r + (G**2-Gtilde2)/2\n", " u = math.log(np.random.uniform())\n", " if u<=log_r:\n", " q_next = q_tilde\n", " else:\n", " q_next=q\n", " reject=True\n", " return q_next,reject" ], "execution_count": 0, "outputs": [] }, { "cell_type": "markdown", "metadata": { "id": "NCtUmLcXCPSU", "colab_type": "text" }, "source": [ "Then, applying the MALA algorithm boils down to repeating this step for N iterations, from a given starting point $q^0$. Below is the code to perform N iterations of the MALA algorithm. As before, two plots are output: on the left, the position $q$ in function of the iterations; on the right, the histogram of the sequence $q^0,\\ldots, q^N$, superimposed with the (unknown) target density $\\nu$.\n", "\n", "**Question 3:** Run the code below for increasing values of $\\sigma$. What do you observe ?\n", "\n", "**Question 4:** Run the code below for increasing values of $\\beta$. What happens ?\n", "\n", "**Question 5:** Compute the rejection rate as a function of $\\Delta t$, and check that it scales as a power of $\\Delta t$ for $\\Delta t$ small (which power?). Compare with the rejection rate for RWMH (you first need to implement some rejection count in RWMH, as done below for MALA). \n" ] }, { "cell_type": "code", "metadata": { "id": "HcLVhqqu8mRD", "colab_type": "code", "outputId": "7cbef700-965b-4fbc-f7b3-f69ca6003a49", "colab": { "base_uri": "https://localhost:8080/", "height": 603 } }, "source": [ "q0 = np.random.uniform()\n", "q=q0\n", "dt = 0.1\n", "N = 10000\n", "nb_rejections = 0\n", "qtrace = np.zeros((N,1))\n", "for n in range(N):\n", " q,rejection_flag = step_mala(q, dt, beta)\n", " if rejection_flag: # there was a rejection in MALA\n", " nb_rejections += 1\n", " qtrace[n]=q\n", "\n", "print(\"Average rejection rate\",nb_rejections*1./N) \n", " \n", "fig, axes = plt.subplots(nrows=1, ncols=2, figsize=(16, 8))\n", "axes[0].plot(qtrace)\n", "axes[1].hist(qtrace, bins=100, density=True)\n", "q=np.linspace(-3,3,100)\n", "axes[1].plot(q, list(map(nu_normed, q)))\n", "fig.tight_layout()" ], "execution_count": 31, "outputs": [ { "output_type": "stream", "text": [ "Average rejection rate 0.0073\n" ], "name": "stdout" }, { "output_type": "display_data", "data": { "image/png": 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i5Hp3ZiPeonUAl/wf1aHY6sVkzM5eiX+uWIXJGFAdDhFFiAkeF1Y1HMQ2s4ap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\nml0deGh5cT0wp1mrVN8VrT7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ErNrSHqFGXj5OaxsP5TcQSFzu/UREXuXr76wq8wQPkBum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\n2OlYmH41vLUg7zjqoCzwSJIkSZUiJXjwV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" ] }, "metadata": { "tags": [] } } ] }, { "cell_type": "markdown", "metadata": { "id": "64ooK0IgChQa", "colab_type": "text" }, "source": [ "## 1.3. Overdamped Langevin stochastic differential equation\n", "\n", "The MALA proposal is derived from a Euler-Maruyama discretization of the the following continuous time process:\n", "$$dq_t = -\\nabla V(q_t)\\, dt + \\sqrt{2\\beta^{-1}}dW_t, $$\n", "where $t\\mapsto W_t$ is a standard Wiener process. The process above leaves invariant the probability distribution $\\mu(q)\\propto \\exp(-\\beta V(q))$. In other words, if $q^0\\sim \\mu$, then $q^n\\sim \\mu$, for all $n\\geq 0$. Thus, integrating the overdamped Langevin dynamics should provide a sequence of samples distributed according to $\\mu$. However, the time-discretization introduced to integrate the EDS induces a bias, and the resulting sequence is not distributed exactly according to $\\mu$. This yields the necessity to perform an accept/reject step, in order to correct this bias.\n", "\n", "**Question 6:** Below is the code to perform the integration of the overdamped Langevin dynamics **without** the accept/reject step. Run the code for different values of the step size $\\Delta t$. What do you observe ?\n" ] }, { "cell_type": "code", "metadata": { "id": "WziMTWJyEQ5L", "colab_type": "code", "outputId": "536f253a-d0cd-4d71-f27b-a1386815872c", "colab": { "base_uri": "https://localhost:8080/", "height": 585 } }, "source": [ "def step_ovdLangevin(q, dt):\n", " G=np.random.normal(size=1)\n", " q_tilde = q-dt*gradV(q)+math.sqrt(2*dt/beta)*G\n", " return q_tilde\n", "\n", "q0 = 0\n", "q=q0\n", "dt = 0.1\n", "N = 10000\n", "qtrace = np.zeros((N,1))\n", "for n in range(N):\n", " q = step_ovdLangevin(q, dt)\n", " qtrace[n]=q\n", " \n", " \n", "fig, axes = plt.subplots(nrows=1, ncols=2, figsize=(16, 8))\n", "axes[0].plot(qtrace)\n", "axes[1].hist(qtrace, bins=100, density=True)\n", "q=np.linspace(-3,3,100)\n", "axes[1].plot(q, list(map(nu_normed, q)))\n", "fig.tight_layout()" ], "execution_count": 32, "outputs": [ { "output_type": "display_data", "data": { "image/png": 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74x/n8zOeDJh4oQ8lnScs8i/ncJId1lO0wnTV7Svwb49vdrx9FGK2E4MQiYj8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\nNTkspTDR0iXcsqY35PnR+nUbsskQrRQPKCFEO4NiN7Y78zCG5PegJBm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KMm/gySputpys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\ntsDzr28dxF9OHeY6hkhoaUSZiIhI9oqIc2Xs77yT7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" ] }, "metadata": { "tags": [] } } ] }, { "cell_type": "markdown", "metadata": { "id": "0Cl0yeOIJO-X", "colab_type": "text" }, "source": [ "#2. Empirical averages and Central Limit Theorem (CLT)" ] }, { "cell_type": "markdown", "metadata": { "id": "SCrvV9yEPTku", "colab_type": "text" }, "source": [ "The main purpose of MCMC sampling is to compute empirical averages of quantities of interest, i.e. macroscopic quantities written as averages over thermodynamic ensembles, which are embodied in the target probability measure $\\nu$. Consider an *observable* $\\phi:q\\mapsto \\phi(q)$. MCMC sequences are employed to approximate the average value of $\\phi$, \n", "$$\\mathbb{E}_{\\nu}[\\phi(q)] = \\int_{\\mathbb{R}}\\phi(q)\\nu(dq).$$\n", "\n", "Approximations are computed through empirical averages: let $q^0,\\ldots, q^N$ be a sequence generated by an MCMC algorithm. $\\mathbb{E}_{\\nu}[\\phi(q)]$ is approximated by the following quantity:\n", "$$\\hat{\\phi}_N = \\frac{1}{N}\\sum_{n=1}^N\\phi(q^n).$$" ] }, { "cell_type": "markdown", "metadata": { "id": "hTgqISuqTTJ5", "colab_type": "text" }, "source": [ "**Question 7:** Use the MALA sequence generated above in Section 1.2 to compute the empirical average of the position $q$, given by $\\hat{q}_N = \\frac{1}{N}\\sum_{n=1}^Nq^n$, to approximate $\\mathbb{E}_{\\nu}[q]$. Compute the approximation error $\\hat{q}_N-\\mathbb{E}_{\\nu}[q]$.\n", "\n" ] }, { "cell_type": "code", "metadata": { "id": "LYTm439ZTuO0", "colab_type": "code", "colab": {} }, "source": [ "nb_realizations=100\n", "emp_average = np.zeros((nb_realizations,1))\n", "dt = 0.1\n", "N = 1250\n", "for i in range(nb_realizations):\n", " q0 = np.random.uniform()\n", " q=q0\n", " # generate a new trajectory\n", " traj = np.zeros((N,1))\n", " for n in range(N):\n", " q,flag = step_mala(q, dt, beta)\n", " traj[n]=q\n", " # take empirical average over the trajectory\n", " emp_average[i] = np.sum(traj)/N\n" ], "execution_count": 0, "outputs": [] }, { "cell_type": "code", "metadata": { "id": "nSMQELmeccPj", "colab_type": "code", "outputId": "59237546-623a-4cbb-b3cc-677070468800", "colab": { "base_uri": "https://localhost:8080/", "height": 340 } }, "source": [ "import statistics as stat\n", "\n", "E_q = integrate.quad(lambda q: q*nu_normed(q), -3, 3)[0]\n", "print(\"Theoretical average \",E_q)\n", "Avg_q = np.mean(emp_average)\n", "print(\"Empirical average \",Avg_q)\n", "Var_q = np.var(emp_average,0)[0]\n", "print(\"Variance \",Var_q)\n", "from scipy.stats import norm\n", "plt.hist(emp_average, bins=10, density=True)\n", "q=np.linspace(-1,1,100)\n", "def norm_d(q):\n", " return norm.pdf(q, Avg_q, math.sqrt(Var_q))\n", "plt.plot(q, list(map(norm_d , q)))\n", "plt.axvline(x=E_q, color=\"green\")\n", "plt.axvline(x=Avg_q, color=\"red\")\n" ], "execution_count": 18, "outputs": [ { "output_type": "stream", "text": [ "Theoretical average -0.13941045426849066\n", "Empirical average -0.14795122467462948\n", "Variance 0.06360852797542277\n" ], "name": "stdout" }, { "output_type": "execute_result", "data": { "text/plain": [ "" ] }, "metadata": { "tags": [] }, "execution_count": 18 }, { "output_type": "display_data", "data": { "image/png": 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" ] }, "metadata": { "tags": [] } } ] }, { "cell_type": "markdown", "metadata": { "id": "IUDRufUx4f-u", "colab_type": "text" }, "source": [ "# 3. Hamiltonian dynamics and Generalized Hamiltonian Monte Carlo (GHMC)\n", "\n", "## 3.1 Integration of Hamiltonian dynamics with the Verlet scheme\n", "\n", "In this part, we focus on the Hamiltonian dynamic. Let $M$ be the mass of the particle (in the code we always take $M=1$), and $$H(q(t), p(t)) = V(q(t)) + \\frac{1}{2}p^{\\top}Mp$$ be the Hamiltonian of the system. The Hamiltonian dynamic is given by: \n", "$$\n", "\\begin{aligned}\n", "\\frac{d q(t)}{dt} & = \\nabla_pH(q(t), p(t)) = M^{-1} p(t), \\\\ \n", "\\frac{d p(t)}{dt} & = -\\nabla_qH(q(t), p(t)) = -\\nabla V(q(t)). \n", "\\end{aligned}\n", "$$\n", "To integrate the Hamiltonian dynamic, one may resort to the so-called Verlet scheme. For some time step $\\Delta t$, the Verlet scheme updates the position and momentum variables iteratively in three steps starting from the current point $(q^n, p^n)$:\n", "\n", "\n", "1. $\\displaystyle p^{n+1/2} = p^n - \\frac{\\Delta t}{2}\\nabla V(q^n)$\n", "2. $\\displaystyle q^{n+1} = q^n + \\Delta t M^{-1}p^{n+1/2}$\n", "3. $\\displaystyle p^{n+1} = p^{n+1/2} - \\frac{\\Delta t}{2}\\nabla V(q^{n+1})$\n", "\n", "\n" ] }, { "cell_type": "code", "metadata": { "id": "0qz2mdlqCbbS", "colab_type": "code", "colab": {} }, "source": [ "def step_Verlet(q, p, dt):\n", " p_new = p - 0.5*dt*gradV(q)\n", " q_new = q + dt*p_new\n", " p_new = p_new - 0.5*dt*gradV(q_new)\n", " H = V(q_new) + 0.5*p_new**2\n", " return q_new, p_new, H" ], "execution_count": 0, "outputs": [] }, { "cell_type": "markdown", "metadata": { "id": "OxHg_bJYC-hy", "colab_type": "text" }, "source": [ "One of the fundamental properties of the Hamiltionian dynamics is to preserve the Hamiltonian H. In addition, over a trajectory, the error on the conservation of H induced by the discretization should be of the order of $\\mathcal{O}(\\Delta t^2)$, as emphasized in the plot below.\n", "\n", "**Question 8.** Check numerically these statements." ] }, { "cell_type": "code", "metadata": { "id": "x9dm0Qb9Djgj", "colab_type": "code", "outputId": "d0d7629b-3281-48b8-b58b-d1402b5df1f4", "colab": { "base_uri": "https://localhost:8080/", "height": 301 } }, "source": [ "N = 2000\n", "dt = 0.1 \n", "\n", "q0 = np.random.uniform()\n", "p0 = np.random.uniform()\n", "q=q0\n", "p=p0 \n", "qtrace = np.zeros((N,1))\n", "Htrace = np.zeros((N,1))\n", "for n in range(N):\n", " q, p, H = step_Verlet(q, p, dt)\n", " qtrace[n]=q\n", " Htrace[n]=H\n", "Hmax = np.amax(Htrace)\n", "Hmin = np.amin(Htrace)\n", "print(\"Energy variation \",Hmax-Hmin)\n", "\n", "plt.plot(Htrace)\n" ], "execution_count": 50, "outputs": [ { "output_type": "stream", "text": [ "Energy variation 0.004340379651270432\n" ], "name": "stdout" }, { "output_type": "execute_result", "data": { "text/plain": [ "[]" ] }, "metadata": { "tags": [] }, "execution_count": 50 }, { "output_type": "display_data", "data": { "image/png": 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IAxqTp3dgEPNWbMK8FfNzmv/4wyPoGxjCgtWbGzc08IO/LCo/61+fwPTFz+C0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\nw6xjHTjGkDAQnRinz1ySsv7vjAUIRgBa6wGl1AUAbgXQDeB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" ] }, "metadata": { "tags": [] } } ] }, { "cell_type": "markdown", "metadata": { "id": "hWFxc-U32Oe7", "colab_type": "text" }, "source": [ "## 3.2 Hamiltonian Monte-Carlo \n", "\n", "The Hamiltonian Monte Carlo algorithm corresponds to an instance of the Metropolis–Hastings algorithm, where the proposal is defined through a Hamiltonian dynamics evolution simulated using anumerical integrator (e.g. the leapfrog integrator). As the RWMH and MALA algorithms, it proceeds in two steps. First, from the current state $(q^n, p^n)$, a new state $(\\tilde{q}^{n+1}, \\tilde{p}^{n+1})$ is proposed according to the Hamiltonian dynamics. Then, an acceptance/rejection step is performed, where the proposed state is accepted with probability\n", "$$r = \\min(1, \\exp(-\\beta(H(\\tilde{q}^{n+1}, \\tilde{p}^{n+1})- H(q^n, p^n)))) $$\n", "\n", "**Question 9.** Test the performance of the algorithm for various choices of $\\Delta t$ and $\\gamma$. \n", "\n", "**Question 10.** Check that velocities need to be reversed upon rejection (i.e. if this is not done, then there is some bias in the distribution which is sampled).\n", "\n" ] }, { "cell_type": "code", "metadata": { "id": "0fIRjamZpBvr", "colab_type": "code", "colab": {} }, "source": [ "def step_gHMC(current_q, current_p, dt, gamma, beta):\n", " rejection = False\n", " # update velocities by mixing\n", " alpha = math.exp(-gamma*dt)\n", " p=alpha*current_p+math.sqrt((1-alpha**2)/beta)*np.random.normal(size=1)\n", " # keep configuration before Verlet step\n", " current_p=p\n", " q=current_q\n", " # Verlet step\n", " p=p-dt*gradV(q)/2\n", " q=q+dt* p\n", " p=p-dt*gradV(q)/2 \n", " # compute acceptance rate\n", " current_H=current_p**2/2+V(current_q)\n", " proposed_H=p**2/2+V(q)\n", " r=beta*(current_H- proposed_H)\n", " # perform Metropolis test\n", " u=math.log(np.random.uniform(size=1))\n", " if (u<=r):\n", " q_next=q\n", " p_next=p\n", " else: # reject: beware change of sign for momenta!\n", " q_next=current_q\n", " p_next=-current_p\n", " rejection=True\n", " return q_next, p_next, rejection\n", "\n" ], "execution_count": 0, "outputs": [] }, { "cell_type": "code", "metadata": { "id": "hYcbTqFG0Zz4", "colab_type": "code", "outputId": "04efc0bb-9e2b-408d-ea94-8a00f978427a", "colab": { "base_uri": "https://localhost:8080/", "height": 638 } }, "source": [ "q=np.random.uniform(size=1)\n", "p=np.random.uniform(size=1)\n", "dt = 0.5\n", "gamma = 1\n", "N = 10000\n", "nb_rejections = 0\n", "qtrace = np.zeros((N,1))\n", "ptrace = np.zeros((N,1))\n", "for n in range(N):\n", " q, p, flag = step_gHMC(q, p, dt, gamma, beta)\n", " qtrace[n]=q\n", " if flag:\n", " nb_rejections += 1\n", "\n", "fig, axes = plt.subplots(nrows=1, ncols=2, figsize=(16, 8))\n", "axes[0].plot(qtrace)\n", "axes[1].hist(qtrace, bins=100, normed=True)\n", "q=np.linspace(-3,3,100)\n", "axes[1].plot(q, list(map(nu_normed, q)))\n", "fig.tight_layout()\n", "\n", "print(\"Rejection rate \",nb_rejections*1./N)\n" ], "execution_count": 61, "outputs": [ { "output_type": "stream", "text": [ "/usr/local/lib/python3.6/dist-packages/ipykernel_launcher.py:17: MatplotlibDeprecationWarning: \n", "The 'normed' kwarg was deprecated in Matplotlib 2.1 and will be removed in 3.1. Use 'density' instead.\n" ], "name": "stderr" }, { "output_type": "stream", "text": [ "Rejection rate 0.47671\n" ], "name": "stdout" }, { "output_type": "display_data", "data": { "image/png": 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Yc9eJpZQVt39MknTD/ZsyPk6se0AHGzr1WxfPz/g5mdhaEcvq7+6lsbqqTrz8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\niIiIiIiIiIjkuP8Hu7NKxXwdurEAAAAASUVORK5CYII=\n", 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" ] }, "metadata": { "tags": [] } } ] }, { "cell_type": "markdown", "metadata": { "id": "p_Q0PkVDkcpy", "colab_type": "text" }, "source": [ "**Additional questions** (if you have finished...) \\\\\n", "1 - Implement the discretization of the underdamped Langevin dynamics we have seen during the lectures \\\\\n", "2 - Implement proposal for MALA based on moves with a position-dependent variance, i.e. $\\widetilde{q}^{n+1} = q^n + \\left(- \\sigma^2(q^n) \\nabla V(q^n) + \\sigma(q^n)\\sigma'(q^n) \\right) \\Delta t + \\sigma(q^n) \\sqrt{\\Delta t} \\, G^n $ for a given scalar valued function $\\sigma(q)$ uniformly bounded from below by a positive constant (for instance, $\\sigma(q) = (2+\\cos(q))/3$). \\\\\n", "3 - Implement importance sampling based on a modified potential $$\\widetilde{V}_a(q) = \\frac{a}{\\sqrt{2\\pi w}}\\exp\\left(-\\frac{(q-c)^2}{2w}\\right)$$ for some parameter $a \\geq 0$" ] } ] }