{ "metadata": { "name": "" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "code", "collapsed": false, "input": [ "from __future__ import division\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "import pymc as pm\n", "\n", "%pylab inline" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Couldn't import dot_parser, loading of dot files will not be possible.\n", "Populating the interactive namespace from numpy and matplotlib\n" ] } ], "prompt_number": 2 }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Learning the Dynamics of a System\n", "\n", "The state of the system is its position and velocity. The velocity is decreased by a damping factor. We want to infer the damping factor of the system." ] }, { "cell_type": "code", "collapsed": false, "input": [ "# The state of the stystem\n", "true_pos = 0.\n", "true_vel = 1.\n", "# Assume linear decrease of the speed of the system\n", "true_damping = -1.5" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 2 }, { "cell_type": "markdown", "metadata": {}, "source": [ "We use simple euler integration to simulate the system." ] }, { "cell_type": "code", "collapsed": false, "input": [ "# timestep\n", "dt = 0.01\n", "\n", "p = true_pos\n", "v = true_vel\n", "positions, velocities = [], []\n", "while True:\n", " # euler integration\n", " p = p + v * dt\n", " v = v + true_damping * dt\n", " \n", " positions.append(p)\n", " velocities.append(v)\n", " \n", " if v <= 0:\n", " break\n", " \n", "fig = plt.figure()\n", "ax = fig.add_subplot(1, 1, 1)\n", "ax.plot(positions, label=\"pos\")\n", "ax.plot(velocities, label=\"vel\")\n", "ax.legend()\n", "ax.grid();" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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"text": [ "" ] } ], "prompt_number": 3 }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Graphical Model\n", "\n", "Let's assume the dynamics of our system (the 1D point mass) are determined by its current state the damping factor $d$. We only observe the position of the object at each time step." ] }, { "cell_type": "code", "collapsed": false, "input": [ "# draf the graphical model with daft\n", "# TODO LaTeX/TikZ is nicer!\n", "from matplotlib import rc\n", "import daft\n", "\n", "model = daft.PGM([5.5, 5.5], origin=[-1., -5])\n", "\n", "model.add_node(daft.Node(\"damping\", r\"$d$\", .5, 0))\n", "\n", "for i in range(3):\n", " model.add_node(daft.Node(\"v\" + str(i), r\"$v_%d$\" % i, i, -2))\n", " model.add_node(daft.Node(\"p\" + str(i), r\"$p_%d$\" % i, i, -3))\n", " model.add_node(daft.Node(\"o\" + str(i), r\"$p_%d$\" % i, i, -4, observed=True))\n", " \n", " model.add_edge(\"damping\", \"v\" + str(i))\n", " model.add_edge(\"v\" + str(i), \"p\" + str(i))\n", " model.add_edge(\"p\" + str(i), \"o\" + str(i))\n", "\n", "for i in range(2):\n", " model.add_edge(\"v\" + str(i), \"v\" + str(i+1))\n", " model.add_edge(\"p\" + str(i), \"p\" + str(i+1))\n", "\n", "\n", "model.render();" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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"text": [ "" ] } ], "prompt_number": 4 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now let's use PyMC to model this." ] }, { "cell_type": "code", "collapsed": false, "input": [ "import pymc as pm\n", "\n", "# let's treat the real positions as observations\n", "observations = positions[:]\n", "\n", "# PRIORS\n", "damping = pm.Normal(\"damping\", mu=0, tau=1/2.**2)\n", "#damping = pm.Uniform(\"damping\", lower=-4, upper=4)\n", "\n", "# we assume little system noise\n", "tau_system_noise = (1 / 0.5**2)\n", "\n", "# the state consist of pos and vel\n", "# vel: we can't judge the initial velocity --> assume it's 0 with big std\n", "vel_states = [pm.Normal(\"v0\", mu=-4, tau=(1 / 2**2))]\n", "# pos: the first pos is just the observation\n", "pos_states = [pm.Normal(\"p0\", mu=observations[0], tau=tau_system_noise)]\n", "\n", "for i in range(1, len(observations)):\n", " new_vel = pm.Normal(\"v\" + str(i),\n", " mu=vel_states[-1] + damping * dt,\n", " tau=tau_system_noise)\n", " new_pos = pm.Normal(\"s\" + str(i),\n", " mu=pos_states[-1] + new_vel * dt,\n", " tau=tau_system_noise)\n", " vel_states.append(new_vel)\n", " pos_states.append(new_pos)\n", "\n", "# some observation noise\n", "tau_observation_noise = (1 / 0.5**2)\n", "obs = pm.Normal(\"obs\", mu=pos_states, tau=tau_observation_noise, value=observations, observed=True)" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Couldn't import dot_parser, loading of dot files will not be possible.\n" ] } ], "prompt_number": 5 }, { "cell_type": "code", "collapsed": false, "input": [ "mcmc = pm.MCMC([damping, vel_states, pos_states])\n", "mcmc.sample(10000, 5000)\n", "pm.Matplot.plot(mcmc.get_node(\"damping\"))\n", "damping_samples = mcmc.trace(\"damping\")[:]\n", "print \"damping -- mean:%f; std:%f\" % (mean(damping_samples), std(damping_samples))\n", "print \"real damping -- %f\" % true_damping" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ " \r", "[****************100%******************] 10000 of 10000 complete" ] }, { "output_type": "stream", "stream": "stdout", "text": [ "Plotting damping\n", " " ] }, { "output_type": "stream", "stream": "stdout", "text": [ "damping -- mean:0.010373; std:2.314968\n", "real damping -- -1.500000\n" ] }, { "metadata": {}, "output_type": "display_data", "png": 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OiMjbuTCIIiLvo4bxjyPvG2OO/UQReTa3zIlKTEzE119/jV9//RXBwcH4y1/+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\nWPfY3OW/OTk5uHbtGgYNGoSePXvi/fffl61wRER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"text": [ "" ] } ], "prompt_number": 10 }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Use pymc.Container\n", "The previous didn't work. Damping is not close to the ture value. vel_states and pos_states is not in the model.\n", "\n", "Let's transform `vel_states` and `pos_states` into a `pymc.Container` and add these states explicitly to the model. The rest stays the same." ] }, { "cell_type": "code", "collapsed": false, "input": [ "# let's treat the real positions as observations\n", "observations = positions[:]\n", "\n", "# PRIORS\n", "damping = pm.Normal(\"damping\", mu=0, tau=1/2.**2)\n", "#damping = pm.Uniform(\"damping\", lower=-4, upper=4)\n", "\n", "# we assume little system noise\n", "tau_system_noise = (1 / 0.5**2)\n", "\n", "# the state consist of pos and vel\n", "# vel: we can't judge the initial velocity --> assume it's 0 with big std\n", "vel_states = [pm.Normal(\"v0\", mu=-4, tau=(1 / 2**2))]\n", "# pos: the first pos is just the observation\n", "pos_states = [pm.Normal(\"p0\", mu=observations[0], tau=tau_system_noise)]\n", "\n", "for i in range(1, len(observations)):\n", " new_vel = pm.Normal(\"v\" + str(i),\n", " mu=vel_states[-1] + damping * dt,\n", " tau=tau_system_noise)\n", " new_pos = pm.Normal(\"s\" + str(i),\n", " mu=pos_states[-1] + new_vel * dt,\n", " tau=tau_system_noise)\n", " vel_states.append(new_vel)\n", " pos_states.append(new_pos)\n", "# use pymc.Container for *_states\n", "vel_states = pm.Container(vel_states)\n", "pos_states = pm.Container(pos_states)\n", "\n", "# some observation noise\n", "tau_observation_noise = (1 / 0.5**2)\n", "obs = pm.Normal(\"obs\", mu=pos_states, tau=tau_observation_noise, value=observations, observed=True)\n", "\n", "# SAMPLE\n", "mcmc = pm.MCMC([damping, obs, vel_states, pos_states])\n", "mcmc.sample(10000, 5000)\n", "pm.Matplot.plot(mcmc.get_node(\"damping\"))\n", "damping_samples = mcmc.trace(\"damping\")[:]\n", "print \"damping -- mean:%f; std:%f\" % (mean(damping_samples), std(damping_samples))\n", "print \"real damping -- %f\" % true_damping" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ " \r", "[****************100%******************] 10000 of 10000 complete" ] }, { "output_type": "stream", "stream": "stdout", "text": [ "Plotting damping\n", " " ] }, { "output_type": "stream", "stream": "stdout", "text": [ "damping -- mean:-0.596854; std:1.894395\n", "real damping -- -1.500000\n" ] }, { "metadata": {}, "output_type": "display_data", "png": 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penqkRCIIgvA3dPeJOn36NLKzs9FdvL0H9pMv4PgwHjMG+OIL+2P79kn3c++9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\n/HGcPXvWu4iJiIiIRolBkyibzYaCggIYjUbU19ejoqIC586d61Nm+vT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"text": [ "" ] } ], "prompt_number": 11 }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Use AdaptiveMetropolis" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# PRIORS\n", "damping = pm.Normal(\"damping\", mu=0, tau=1/2.**2)\n", "damping = pm.Uniform(\"damping\", lower=-4, upper=4)\n", "\n", "# we assume little system noise\n", "tau_system_noise = (1 / 0.5**2)\n", "\n", "# the state consist of pos and vel\n", "# vel: we can't judge the initial velocity --> assume it's 0 with big std\n", "vel_states = [pm.Normal(\"v0\", mu=-4, tau=(1 / 2**2))]\n", "# pos: the first pos is just the observation\n", "pos_states = [pm.Normal(\"p0\", mu=observations[0], tau=tau_system_noise)]\n", "\n", "for i in range(1, len(observations)):\n", " new_vel = pm.Normal(\"v\" + str(i),\n", " mu=vel_states[-1] + damping * dt,\n", " tau=tau_system_noise)\n", " new_pos = pm.Normal(\"s\" + str(i),\n", " mu=pos_states[-1] + new_vel * dt,\n", " tau=tau_system_noise)\n", " vel_states.append(new_vel)\n", " pos_states.append(new_pos)\n", "# use pymc.Container for *_states\n", "vel_states = pm.Container(vel_states)\n", "pos_states = pm.Container(pos_states)\n", "\n", "# some observation noise\n", "tau_observation_noise = (1 / 0.5**2)\n", "\n", "# SAMPLE\n", "mcmc = pm.MCMC([damping, obs, vel_states, pos_states])\n", "mcmc.use_step_method(pm.AdaptiveMetropolis, vel_states)\n", "mcmc.use_step_method(pm.AdaptiveMetropolis, pos_states)\n", "\n", "mcmc.sample(10000, 5000)\n", "pm.Matplot.plot(mcmc.get_node(\"damping\"))\n", "damping_samples = mcmc.trace(\"damping\")[:]\n", "print \"damping -- mean:%f; std:%f\" % (mean(damping_samples), std(damping_samples))\n", "print \"real damping -- %f\" % true_damping" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ " \r", "[****************100%******************] 10000 of 10000 complete" ] }, { "output_type": "stream", "stream": "stdout", "text": [ "Plotting damping\n", " " ] }, { "output_type": "stream", "stream": "stdout", "text": [ "damping -- mean:-0.010985; std:2.332651\n", "real damping -- -1.500000\n" ] }, { "metadata": {}, "output_type": "display_data", "png": 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B/dhPFBERqVCT2oHI+zRyEKUzep4A9rVC5G2yIHdWR0Tk7dwYRBGR90mA6Z8j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\nIiwszGmVJCIiIvI0NoOoupf/FhQUmHRMBwCdOnV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"text": [ "" ] } ], "prompt_number": 12 }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Different approach for adding the states\n", "This was suggested by Delphine Pessoa (https://groups.google.com/forum/#!topic/pymc/u4JB6lCucDY)" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# PRIORS\n", "damping = pm.Normal(\"damping\", mu=0, tau=1/2.**2)\n", "damping = pm.Uniform(\"damping\", lower=-4, upper=4)\n", "\n", "# we assume little system noise\n", "tau_system_noise = (1 / 0.5**2)\n", "mus_vel=[-4]\n", "mus_pos=[observations[0]]\n", "taus=[1 / 2**2]\n", "\n", "for i in range(1, len(observations)):\n", " mus_vel.append(mus_vel[-1] + damping * dt)\n", " mus_pos.append(mus_pos[-1] + mus_vel[-1] * dt)\n", " taus.append(tau_system_noise)\n", "vel_states = pm.Normal(\"vel_states\", mu=mus_vel, tau=taus)\n", "pos_states = pm.Normal(\"pos_states\", mu=mus_pos, tau=taus)\n", "\n", "# SAMPLE\n", "mcmc = pm.MCMC([damping, obs, vel_states, pos_states])\n", "mcmc.use_step_method(pm.AdaptiveMetropolis, vel_states)\n", "mcmc.use_step_method(pm.AdaptiveMetropolis, pos_states)\n", "\n", "mcmc.sample(10000, 5000)\n", "pm.Matplot.plot(mcmc.get_node(\"damping\"))\n", "damping_samples = mcmc.trace(\"damping\")[:]\n", "print \"damping -- mean:%f; std:%f\" % (mean(damping_samples), std(damping_samples))\n", "print \"real damping -- %f\" % true_damping" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ " \r", "[****************100%******************] 10000 of 10000 complete" ] }, { "output_type": "stream", "stream": "stdout", "text": [ "Plotting damping\n", " " ] }, { "output_type": "stream", "stream": "stdout", "text": [ "damping -- mean:-0.012826; std:2.282975\n", "real damping -- -1.500000\n" ] }, { "metadata": {}, "output_type": "display_data", "png": 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iQVRUVBQKCwuNrwsLCxEdHW1nTp3Zc23Vg4gCh77qQUQU+BQJojp37oz8/Hyc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\nuLg4lJaWora2Vu20XFg1HF/N2EOBVcPx1YztH1aiiEjT/Pm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"text": [ "" ] } ], "prompt_number": 13 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Still, the results don't make sense :(" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Rog's approach\n", "See http://stackoverflow.com/questions/20289287/pymc-hierachical-hidden-markov-model?answertab=active#tab-top" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#######################################################################\n", "# Generative Model\n", "\n", "# The initial state of the stystem\n", "true_pos = 0.0\n", "true_vel = 1.0\n", " \n", "# Assume linear decrease of the speed of the system\n", "true_damping = -.5\n", "# Number of steps\n", "N = 167\n", "# Timestep\n", "dt = 0.01\n", " \n", "class PointMass(object):\n", " \"\"\"\n", " Point-mass\n", " \n", " - The state consist of position and velocity.\n", " - The speed is decreased in a linear fashion by a damping factor.\n", " \"\"\" \n", " def __init__(self, damping):\n", " self.damping = damping\n", " \n", " def integrate(self, p0, v0, N, dt):\n", " # The state consist of position and velocity\n", " positions = np.zeros((N,))\n", " velocities = np.zeros((N,))\n", " positions[0] = p0\n", " velocities[0] = v0\n", " for n in range(N - 1):\n", " # Euler integration\n", " positions[n + 1] = positions[n] + velocities[n] * dt\n", " velocities[n + 1] = velocities[n] + self.damping * dt\n", " return (positions, velocities)\n", " \n", "point_mass = PointMass(true_damping)\n", " \n", "positions, velocities = point_mass.integrate(true_pos, true_vel, N, dt)\n", " \n", "# Assume little system noise\n", "std_system_noise = 0.05\n", "tau_system_noise = 1.0/std_system_noise**2\n", " \n", "# Treat the real positions as observations\n", "observations = positions + np.random.randn(N,) * std_system_noise\n", "\n", "#######################################################################\n", "# PyMC MODEL\n", "# Damping is modelled with a Uniform prior\n", "damping = pm.Uniform(\"damping\", lower=-4.0, upper=4.0, value=-0.5)\n", " \n", "# Initial position & velocity unknown -> assume Uniform priors\n", "init_pos = pm.Uniform(\"init_pos\", lower=-1.0, upper=1.0, value=0.5)\n", "init_vel = pm.Uniform(\"init_vel\", lower=0.0, upper=2.0, value=1.5)\n", " \n", "@pm.deterministic\n", "def det_pos(damping=damping, init_pos=init_pos, init_vel=init_vel):\n", " # Apply damping, init_pos and init_vel estimates and integrate\n", " point_mass.damping = damping.item()\n", " pos, vel = point_mass.integrate(init_pos, init_vel, N, dt)\n", " return pos\n", " \n", "# Standard deviation is modelled with a Uniform prior\n", "std_pos = pm.Uniform(\"std\", lower=0.0, upper=1.0, value=0.5)\n", " \n", "@pm.deterministic\n", "def det_prec_pos(std_pos=std_pos):\n", " # Precision, based on standard deviation\n", " return 1.0/std_pos**2\n", " \n", "# The observations are based on the estimated positions and precision\n", "obs_pos = pm.Normal(\"obs\", mu=det_pos, tau=det_prec_pos, value=observations, observed=True)\n", "\n", "#######################################################################\n", "# SAMPLE\n", "mcmc = pm.MCMC([damping, init_pos, init_vel, det_prec_pos, obs_pos])\n", "mcmc.sample(50000, 25000)" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ " \r", "[****************100%******************] 50000 of 50000 complete" ] }, { "output_type": "stream", "stream": "stdout", "text": [ "\n" ] } ], "prompt_number": 4 }, { "cell_type": "code", "collapsed": false, "input": [ "#######################################################################\n", "# ANALYSIS\n", "#mcmc.summary()\n", "pm.Matplot.plot(mcmc.get_node(\"damping\"))\n", "pm.Matplot.plot(mcmc.get_node(\"init_pos\"))\n", "pm.Matplot.plot(mcmc.get_node(\"init_vel\"))\n", " \n", "damping_samples = mcmc.trace(\"damping\")[:]\n", "est_damping = np.mean(damping_samples)\n", "est_std_damping = np.std(damping_samples)\n", " \n", "init_pos_samples = mcmc.trace(\"init_pos\")[:]\n", "est_init_pos = np.mean(init_pos_samples)\n", "est_std_init_pos = np.std(init_pos_samples)\n", " \n", "init_vel_samples = mcmc.trace(\"init_vel\")[:]\n", "est_init_vel = np.mean(init_vel_samples)\n", "est_std_init_vel = np.std(init_vel_samples)\n", " \n", "print \" REAL EST STD\"\n", "print \"damping: %5.2f %5.2f (%4.2f)\" % (true_damping, est_damping, est_std_damping)\n", "print \"position: %5.2f %5.2f (%4.2f)\" % (true_pos, est_init_pos, est_std_init_pos)\n", "print \"velocity: %5.2f %5.2f (%4.2f)\" % (true_vel, est_init_vel, est_std_init_vel)\n", " \n", "# Apply the mean estimates and integrate\n", "pm.damping = est_damping\n", "est_positions, est_velocities = point_mass.integrate(est_init_pos, est_init_vel, N, dt)\n", " \n", "# Plot the system response\n", "fig, (ax1, ax2) = plt.subplots(2, figsize=(12, 9))\n", "\n", "ax1.plot(observations, label=\"true\")\n", "ax1.plot(est_positions, label=\"estimate\")\n", "ax1.legend()\n", "ax1.set_title(\"positions\")\n", "\n", "ax2.plot(velocities, alpha=0.5, label=\"true (unobserved)\")\n", "ax2.plot(est_velocities, label=\"estimate\")\n", "ax2.legend()\n", "ax2.set_title(\"velocities\")\n", "ax2.grid();" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Plotting damping\n", "Plotting" ] }, { "output_type": "stream", "stream": "stdout", "text": [ " init_pos\n", "Plotting" ] }, { "output_type": "stream", "stream": "stdout", "text": [ " init_vel\n", " REAL EST STD" ] }, { "output_type": "stream", "stream": "stdout", "text": [ "\n", "damping: -0.50 -0.45 (0.34)\n", "position: 0.00 0.02 (0.11)\n", "velocity: 1.00 0.95 (0.29)\n" ] }, { "metadata": {}, "output_type": "display_data", "png": 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ZuND8vdL9KhaKoaGWn/PvAV99SxBK0ADtO1BfaseL3JKV+fe/TcEh1Yicigrl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ugxK5lCDWrnCp2FmKl9SOUzkc9U9qSVt4nVrfRWF/nbU5Q46ysjIkJyejuroa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\nyO1tIes4uV7qt64n18uBvee9w58WhYWFIjQ0VAQHB4ucnBwhhBDr168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nu2YN8O674vLMmc5t0VqcWe0zEAT7ckzBwTaP6fbt2s7vDb7/3tcWEARBBB5+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PHJh/j+SmTU25yZo1ecPvzp2m60afPvD11zm/i7Q0+Ogjs+L+xhtw8805g6/F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\nQ/0WkjznOc95znOe8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