{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Probabilistic Programming 4: Bayesian filtering & smoothing\n", "\n", "#### Goal \n", " - Learn how to setup problems for dynamical systems.\n", " - Learn how to infer states and noise in linear Gaussian state-space model using variational inference.\n", "\n", "#### Materials \n", " - Mandatory\n", " - This notebook\n", " - Lecture notes on dynamical models\n", " - Optional\n", " - [Review of latent variable models](https://doi.org/10.1146/annurev-statistics-022513-115657)\n", " - [Bayesian Filtering & Smoothing](https://www.cambridge.org/core/books/bayesian-filtering-and-smoothing/C372FB31C5D9A100F8476C1B23721A67)\n", " - [Differences between Julia and Matlab / Python](https://docs.julialang.org/en/v1/manual/noteworthy-differences/index.html)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Note that none of the material below is new. The point of the Probabilistic Programming sessions is to solve practical problems so that the concepts from Bert's lectures become less abstract." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "using Pkg; Pkg.activate(\"../../.\"); Pkg.instantiate();\n", "using IJulia; try IJulia.clear_output(); catch _ end" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "using JLD\n", "using Statistics\n", "using LinearAlgebra\n", "using Distributions\n", "using RxInfer\n", "using ColorSchemes\n", "using LaTeXStrings\n", "using Plots\n", "default(label=\"\", grid=false, linewidth=3, margin=10Plots.pt)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Problem: shaking buildings\n", "\n", "Suppose you are contacted to estimate how resistant a building is to shaking caused by minor earthquakes. You decide to model the building as a [mass-spring-damper](https://en.wikipedia.org/wiki/Mass-spring-damper_model) system, described by:\n", "\n", "$$m \\ddot{x} + c\\dot{x} + kx = w \\, ,$$\n", "\n", "where $m$ corresponds to the mass of the building, $c$ is friction and $k$ the stiffness of the building's main supports. You don't know the external force acting upon the building and decide to model it as white noise $w$. In essence, this means you think the building will be pushed to the left as strongly on average as it will be pushed to the right. A simple discretization scheme with substituted variable $z = [x \\ \\dot{x}]$ and time-step $\\Delta t$ yields:\n", "\n", "$$z_{k} = \\underbrace{\\begin{bmatrix} 1 & \\Delta t \\\\ \\frac{-k}{m}\\Delta t & \\frac{-c}{m}\\Delta t + 1 \\end{bmatrix}}_{A} z_{k-1} + q_k \\, ,$$\n", "\n", "where $q_k \\sim \\mathcal{N}(0, Q)$ with covariance matrix $Q$. \n", "\n", "You place a series of sensors on the building that measure the displacement:\n", "\n", "$$ y_k = \\underbrace{\\begin{bmatrix} 1 & 0 \\end{bmatrix}}_{C} z_k + r_k \\, $$\n", "\n", "where the measurement noise is white as well: $r_k \\sim \\mathcal{N}(0, \\sigma^2)$. You have a good estimate of the variance $\\sigma^2$ from previous sensor calibrations and decide to consider it a known variable." ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "image/png": 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[lecture on Dynamic Systems](https://nbviewer.org/github/bertdv/BMLIP/blob/master/lessons/notebooks/Dynamic-Models.ipynb), we can derive the following probabilistic state-space model:\n", "\n", "$$\\begin{aligned} p(z_k \\mid z_{k-1}) =&\\ \\mathcal{N}(z_k \\mid A z_{k-1}, Q)\\\\ p(y_k \\mid z_k) =&\\ \\mathcal{N}(y_k \\mid C z_k, \\sigma^2) \\, . \\end{aligned}$$\n", "\n", "For now, we will use a simple structure for the process noise covariance matrix, e.g. $Q = I$. If we consider a Gaussian prior distribution for the initial state\n", "\n", "$$ p(z_0) = \\mathcal{N}(m_0, S_0) \\, ,$$\n", "\n", "we obtain a complete generative model:\n", "\n", "$$\\begin{aligned} \\underbrace{p(y_{1:T}, z_{0:T})}_{\\text{generative model}} = \\underbrace{p(z_0)}_{\\text{prior}} \\, \\prod_{k=1}^T \\, \\underbrace{p(y_k \\mid z_k)}_{\\text{likelihood}} \\, \\underbrace{p(z_k \\mid z_{k-1})}_{\\text{state transition}} \\end{aligned}$$\n", "\n", "To define this model in RxInfer, we must start with the process matrices:" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "2×2 Matrix{Float64}:\n", " 1.0 0.0\n", " 0.0 1.0" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Transition matrix\n", "A = [1 Δt; -stiffness/mass*Δt -friction/mass*Δt+1]\n", "\n", "# Emission matrix\n", "C = [1.0, 0.0]\n", "\n", "# Set process noise covariance matrix\n", "Q = diagm(ones(2))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Next, we define a linear Gaussian dynamical system with only the states as unknown variables:" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Inference results:\n", " Posteriors | available for (z_0, z)\n", " Free Energy: | Real[444.922]\n" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "@model function LGDS(y, A,C,Q, σ, T)\n", " \"State estimation in linear Gaussian dynamical system\"\n", " \n", " # Prior state\n", " z_0 ~ MvNormalMeanCovariance(zeros(2), diageye(2))\n", " \n", " z_kmin1 = z_0\n", " for k in 1:T\n", " \n", " # State transition\n", " z[k] ~ MvNormalMeanCovariance(A * z_kmin1, Q)\n", " \n", " # Likelihood\n", " y[k] ~ NormalMeanVariance(dot(C, z[k]), σ)\n", " \n", " # Update recursive aux\n", " z_kmin1 = z[k]\n", " \n", " end\n", "end\n", "\n", "results = infer(\n", " model = LGDS(A=A,C=C,Q=Q, σ=σ, T=T),\n", " data = (y = [observations[k] for k in 1:T],),\n", " free_energy = true,\n", ")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's extract the inferred states and visualize them." ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "WARNING: both ExponentialFamily and ReactiveMP export \"MvNormalMeanScalePrecision\"; uses of it in module RxInfer must be qualified\n" ] }, { "data": { "image/png": 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This is most likely due to our process noise covariance matrix not being calibrated. So can we improve? \n", "\n", "---\n", "\n", "Of course, as Bayesians, we can just treat $Q$ as an unknown random variable and infer its posterior distribution. Adjusting the model is straightforward. The probabilistic state-space model becomes:\n", "\n", "$$\\begin{aligned} p(z_k \\mid z_{k-1},Q) =&\\ \\mathcal{N}(z_k \\mid A z_{k-1}, Q)\\\\ p(y_k \\mid z_k) =&\\ \\mathcal{N}(y_k \\mid C z_k, \\sigma^2) \\, , \\end{aligned}$$\n", "\n", "with priors\n", "\n", "$$\\begin{aligned} p(Q) =&\\ \\mathcal{W}^{-1}(\\nu, \\Lambda) \\\\ p(z_0) =&\\ \\mathcal{N}(m_0, S_0) \\, . \\end{aligned}$$\n", "\n", "The $\\mathcal{W}^{-1}$ represents an inverse-Wishart distribution with degrees-of-freedom $\\nu$ and scale matrix $\\Lambda$. This will give the following generative model:\n", "\n", "$$\\begin{aligned} \\underbrace{p(y_{1:T}, z_{0:T}, Q)}_{\\text{generative model}} = \\underbrace{p(z_0)p(Q)}_{\\text{priors}} \\, \\prod_{k=1}^T \\, \\underbrace{p(y_k \\mid z_k)}_{\\text{likelihood}} \\, \\underbrace{p(z_k \\mid z_{k-1},Q)}_{\\text{state transition}}\n", "\\end{aligned}$$\n", "\n", "Our model definition in ReactiveMP is only slightly larger:" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [], "source": [ "@model function LGDS_Q(y, A,C,σ,T)\n", " \"State estimation in a linear Gaussian dynamical system with unknown process noise\"\n", " \n", " # Prior state\n", " z_0 ~ MvNormalMeanCovariance(zeros(2), diageye(2))\n", " \n", " # Process noise covariance matrix\n", " Q ~ InverseWishart(10, diageye(2))\n", " \n", " z_kmin1 = z_0\n", " for k in 1:T\n", " \n", " # State transition\n", " z[k] ~ MvNormalMeanCovariance(A * z_kmin1, Q)\n", " \n", " # Likelihood\n", " y[k] ~ NormalMeanVariance(dot(C, z[k]), σ^2)\n", " \n", " # Update recursive aux\n", " z_kmin1 = z[k]\n", " \n", " end\n", "end" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "---\n", "\n", "#### Exercise\n", "\n", "Think of what might be appropriate prior parameters for the Inverse-Wishart distribution. Should its mean be high or low here?\n", "\n", "---" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The variational inference procedure for estimating states and the process noise covariance matrix simultaneously requires a bit more thought, but is still very straightforward:" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "\u001b[32mProgress: 100%|█████████████████████████████████████████| Time: 0:00:04\u001b[39m\u001b[K\n" ] }, { "data": { "text/plain": [ "Inference results:\n", " Posteriors | available for (z_0, Q, z)\n", " Free Energy: | Real[363.876, 362.371, 361.232, 360.361, 359.69, 359.169, 358.761, 358.44, 358.185, 357.983 … 357.083, 357.083, 357.083, 357.083, 357.083, 357.084, 357.084, 357.084, 357.084, 357.084]\n" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Iterations of variational inference\n", "num_iters = 100\n", "\n", "# Initialize variational marginal distributions\n", "init = @initialization begin\n", " q(z) = MvNormalMeanCovariance(zeros(2), diageye(2))\n", " q(Q) = InverseWishart(10, diageye(2))\n", "end\n", "\n", "# Define variational distribution factorization\n", "constraints = @constraints begin\n", " q(z_0,z,Q) = q(z_0, z)q(Q)\n", "end\n", "\n", "# Variational inference procedure\n", "results = infer(\n", " model = LGDS_Q(A=A,C=C, σ=σ, T=T),\n", " data = (y = [observations[k] for k in 1:T],),\n", " constraints = constraints,\n", " iterations = num_iters,\n", " options = (limit_stack_depth = 100,),\n", " initialization = init,\n", " free_energy = true,\n", " showprogress = true,\n", ")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Again, let's inspect the free energy to see if we have converged." ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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That looks good. Let's extract the inferred states and visualize." ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "image/png": 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"\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "m_z = cat(mean.(last(results.posteriors[:z]))...,dims=2)\n", "v_z = cat(var.(last(results.posteriors[:z]))...,dims=2)\n", "\n", "plot(time, states[1,:], color=\"red\", label=\"states\", xlabel=\"time (sec)\", ylabel=\"train position\")\n", "plot!(time, m_z[1,:], color=\"blue\", ribbon=v_z[1,:], label=\"inferred\")\n", "scatter!(time, observations, color=\"black\", alpha=0.2, label=\"observations\", legend=:topleft, size=(800,300))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "That's much smoother. The free energy of this model ($\\mathcal{F} = 357.08$) is smaller than that of the earlier model with $Q$ set to an identity matrix ($\\mathcal{F} = 434.10$). That means that the added cost of inferring the matrix $Q$ is offset by the increase in performance it provides. \n", "\n", "The error with respect to the true states seems smaller as well, but in practice we of course can't check this.\n", "\n", "Let's inspect the inferred process noise covariance matrix:" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "2×2 Matrix{Float64}:\n", " 0.0600162 0.00526415\n", " 0.00526415 0.146396" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "Q_MAP = mean(last(results.posteriors[:Q]))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We do not have enough data to recover the true process noise covariance matrix exactly, but the result is definitely closer to the truth." ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "2×2 Matrix{Float64}:\n", " 0.00173611 0.0240885\n", " 0.0240885 0.549072" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# True data\n", "Q_true = data[\"Q\"]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's visualize that for a closer look:" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "data": { "image/png": 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heatmap(Q_true, axis=([], false), yflip=true, title=\"True\", clims=clims)\n", "plot(p401,p402, layout=(1,2), size=(900,300))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "---\n", "\n", "#### Exercise\n", "\n", "Can you come up with a way to improve the model even further?\n", "\n", "---" ] } ], "metadata": { "@webio": { "lastCommId": null, "lastKernelId": null }, "kernelspec": { "display_name": "Julia 1.10.5", "language": "julia", "name": "julia-1.10" }, "language_info": { "file_extension": ".jl", "mimetype": "application/julia", "name": "julia", "version": "1.10.5" } }, "nbformat": 4, "nbformat_minor": 4 }