diff --git a/Project.toml b/Project.toml index 7190868c..3046cd7b 100644 --- a/Project.toml +++ b/Project.toml @@ -8,6 +8,7 @@ Documenter = "e30172f5-a6a5-5a46-863b-614d45cd2de4" ForwardDiff = "f6369f11-7733-5829-9624-2563aa707210" InteractiveUtils = "b77e0a4c-d291-57a0-90e8-8db25a27a240" LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e" +MacroTools = "1914dd2f-81c6-5fcd-8719-6d5c9610ff09" Printf = "de0858da-6303-5e67-8744-51eddeeeb8d7" Random = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c" SparseArrays = "2f01184e-e22b-5df5-ae63-d93ebab69eaf" @@ -18,9 +19,9 @@ StatsFuns = "4c63d2b9-4356-54db-8cca-17b64c39e42c" Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40" [compat] -julia = "1" Documenter = "0.25.2" ForwardDiff = "0.10.12" SpecialFunctions = "0.8.0, 0.10.3" StatsBase = "0.32.2, 0.33.1" StatsFuns = "0.9.5" +julia = "1" diff --git a/demo/FFG_nonlinear_kalman_filter.ipynb b/demo/FFG_nonlinear_kalman_filter.ipynb new file mode 100644 index 00000000..853f7ae3 --- /dev/null +++ b/demo/FFG_nonlinear_kalman_filter.ipynb @@ -0,0 +1,1030 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Nonlinear Kalman filtering\n", + "\n", + "In this demo, we will look at dynamical systems with nonlinear state transitions. We will start with a one-dimensional problem; the number of rabbits on an island. This problem seems overly simple, but it is a good way to demonstrate the basic pipeline of working with ForneyLab. The second problem, that of tracking a pendulum, is a bit more realistic in that we translate a differential equation in state-space model form to a probabilistic model. This requires more effort on the part of model specification, but not too much on the part of inference." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## 1. Rabbit population size\n", + "\n", + "We consider a model for the number of rabbits on a particular island. We assume the population size follows a [logistic map](https://en.wikipedia.org/wiki/Logistic_map): initially, it grows exponentially, but as the number of rabbits increases, so does the number of foxes. At some point, population size will drop again. But as the number of rabbits drops, so does the number of foxes, which means the number of rabbits can grow again. We express the change in the population with the following nonlinear state transition:\n", + "\n", + "$$x_{t+1} = r \\cdot x_t(1-x_t)$$\n", + "\n", + "where $r$ is a fertility parameter, reflecting how fast the number of rabbits can grow. $x$ does not reflect the number of rabbits, but rather the proportion of rabbits relative to a maximum population $N$ on the island. This means $x$ is bounded in the interval $[0,1]$.\n", + "\n", + "Every month, we count the number of rabbits $y_t$. We assume that these counts are noisy: sometimes, we count one rabbit twice and sometimes, we miss one. This noise is expressed as a Gaussian distribution centered at $0$, with some measurement noise precision." + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "┌ Info: Precompiling ForneyLab [9fc3f58a-c2cc-5bff-9419-6a294fefdca9]\n", + "└ @ Base loading.jl:1260\n", + "┌ Warning: Package ForneyLab does not have MacroTools in its dependencies:\n", + "│ - If you have ForneyLab checked out for development and have\n", + "│ added MacroTools as a dependency but haven't updated your primary\n", + "│ environment's manifest file, try `Pkg.resolve()`.\n", + "│ - Otherwise you may need to report an issue with ForneyLab\n", + "└ Loading MacroTools into ForneyLab from project dependency, future warnings for ForneyLab are suppressed.\n" + ] + } + ], + "source": [ + "# Import libraries to julia workspace\n", + "using ForneyLab\n", + "using ProgressMeter\n", + "using Plots\n", + "pyplot();" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Generate data\n", + "\n", + "We start by generating a dataset for a rabbit population with a maximum population $N$ and a particular fertility $r$. Note that there are different regimes for different values of $r$ (see [wiki](https://en.wikipedia.org/wiki/Logistic_map)). Here we will look at the simplest cases; when $r$ is between $0$ and $4$." + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [], + "source": [ + "# Length of time-series\n", + "T = 36\n", + "\n", + "# Maximum population size\n", + "N = 100\n", + "\n", + "# Fertility parameter (0 < r < 4)\n", + "fertility = 3.2\n", + "\n", + "# Measurement noise precision\n", + "noise_precision = 0.01\n", + "\n", + "# Initial proportion of rabbits\n", + "x0 = 0.04\n", + "\n", + "# Initialize data array\n", + "states = zeros(T,)\n", + "observations = zeros(T,)\n", + "\n", + "# Initialize previous state variable\n", + "prev_state = x0\n", + "\n", + "for t = 1:T\n", + " \n", + " # State transition\n", + " states[t] = fertility*prev_state*(1-prev_state)\n", + " \n", + " # Observation likelihood\n", + " observations[t] = max(round(N*states[t] .+ sqrt(inv(noise_precision))*randn(1,)[1]), 0.)\n", + " \n", + " # Update \"previous state\"\n", + " prev_state = states[t]\n", + " \n", + "end " + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": "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" + }, + "execution_count": 3, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# Inspect data\n", + "plot(1:T, states.*N, color=\"blue\", xlabel=\"t (months)\", ylabel=\"rabbits\", label=\"true population\")\n", + "scatter!(1:T, observations, ylims=[0, N], color=\"black\", markersize=3, label=\"observed\", legend=:bottomright)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Model specification\n", + "\n", + "We define a state-space model, consisting of a state transition between $x_{t-1}$ and $x_t$ and an observation likelihood between $y_t$ and $x_t$. These are conditional distributions, which we model with certain parametric distributions. In this case, mostly Gaussian distributions.\n", + "\n", + "- The states are the proportion of rabbits relative to a maximum N. To model the rabbit counts, we must multiply the states with the maximum population number $N$. Furthermore, we said that the rabbit counts are noisy (see 'Generate data' section). We assumed that we were counting some rabbits twice and missed others. That justifies using a white noise term: the current rabbit count is Gaussian distributed centered on the current state times the maximum population. For the sake of simplicity in this demo, we assume that we know the size of the noise. It is however straightforward to add a prior for measurement noise and estimate it simultaneously.\n", + "\n", + "- The state transition that we defined above (the [logistic map](https://en.wikipedia.org/wiki/Logistic_map)) is nonlinear in nature (polynomial order 2). To capture this mapping, we have to use a \"Nonlinear\" node. The \"Nonlinear{Unscented}\" node performs an unscented transform to approximate the given function (exact up to polynomial order 3) and approximates the result with a Gaussian distribution.\n", + "\n", + "- We have to specify a prior distribution for the states. Below, we choose a Gaussian distribution, but this is actually not completely valid. In a model using the logistic map, the states are confined to the interval $[0, 1]$. We would therefore have to use a bounded distribution, such as the [Beta](https://en.wikipedia.org/wiki/Beta_distribution). However, a Beta process is much more complicated than a Gaussian process and we will therefore avoid it here.\n", + "\n", + "- We have to specify a prior for the fertility parameter $r$. It is supposed to be a strictly positive number, so ideally we would use something like a [Gamma](https://en.wikipedia.org/wiki/Gamma_distribution) or [log-Normal](https://en.wikipedia.org/wiki/Log-normal_distribution) distribution. However, this, again, complicates inference and we have therefore opted for a Gaussian distribution.\n", + "\n", + "We are going to specify the state-space model in recursive form, i.e. we only specify the previous state, the state transition and the likelihood, and update estimates as observations arrive. We will probably observe that our estimates start out relatively poor but improve over time. " + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "FactorGraph(Dict{Symbol,FactorNode}(:clamp_1 => Clamp{Univariate} with id clamp_1\n", + ",:x_t => Nonlinear{Unscented} with id x_t\n", + ",:placeholder_v_x => Clamp{Univariate} with id placeholder_v_x\n", + ",:y_t => GaussianMeanPrecision with id y_t\n", + ",:placeholder_v_r => Clamp{Univariate} with id placeholder_v_r\n", + ",:placeholder_y_t => Clamp{Univariate} with id placeholder_y_t\n", + ",:clamp_2 => Clamp{Univariate} with id clamp_2\n", + ",:x_tmin1 => GaussianMeanVariance with id x_tmin1\n", + ",:r => GaussianMeanVariance with id r\n", + ",:multiplication_1 => Multiplication with id multiplication_1\n", + "…), Edges:\n", + "Edge belonging to variable m_r: ( placeholder_m_r.i[out] )----( r.i[m] ).\n", + "Edge belonging to variable v_r: ( placeholder_v_r.i[out] )----( r.i[v] ).\n", + "Edge belonging to variable r: ( r.i[out] )----( x_t.i[in2] ).\n", + "Edge belonging to variable m_x: ( placeholder_m_x.i[out] )----( x_tmin1.i[m] ).\n", + "Edge belonging to variable v_x: ( placeholder_v_x.i[out] )----( x_tmin1.i[v] ).\n", + "Edge belonging to variable x_tmin1: ( x_tmin1.i[out] )----( x_t.i[in1] ).\n", + "Edge belonging to variable x_t: ( x_t.i[out] )----( multiplication_1.i[in1] ).\n", + "Edge belonging to variable clamp_1: ( clamp_1.i[out] )----( multiplication_1.i[a] ).\n", + "Edge belonging to variable variable_1: ( multiplication_1.i[out] )----( y_t.i[m] ).\n", + "Edge belonging to variable clamp_2: ( clamp_2.i[out] )----( y_t.i[w] ).\n", + "Edge belonging to variable y_t: ( y_t.i[out] )----( placeholder_y_t.i[out] ).\n", + ", Dict{Symbol,Variable}(:clamp_1 => Variable(:clamp_1, Edges:\n", + "Edge belonging to variable clamp_1: ( clamp_1.i[out] )----( multiplication_1.i[a] ).\n", + "),:x_t => Variable(:x_t, Edges:\n", + "Edge belonging to variable x_t: ( x_t.i[out] )----( multiplication_1.i[in1] ).\n", + "),:v_x => Variable(:v_x, Edges:\n", + "Edge belonging to variable v_x: ( placeholder_v_x.i[out] )----( x_tmin1.i[v] ).\n", + "),:y_t => Variable(:y_t, Edges:\n", + "Edge belonging to variable y_t: ( y_t.i[out] )----( placeholder_y_t.i[out] ).\n", + "),:clamp_2 => Variable(:clamp_2, Edges:\n", + "Edge belonging to variable clamp_2: ( clamp_2.i[out] )----( y_t.i[w] ).\n", + "),:variable_1 => Variable(:variable_1, Edges:\n", + "Edge belonging to variable variable_1: ( multiplication_1.i[out] )----( y_t.i[m] ).\n", + "),:m_x => Variable(:m_x, Edges:\n", + "Edge belonging to variable m_x: ( placeholder_m_x.i[out] )----( x_tmin1.i[m] ).\n", + "),:x_tmin1 => Variable(:x_tmin1, Edges:\n", + "Edge belonging to variable x_tmin1: ( x_tmin1.i[out] )----( x_t.i[in1] ).\n", + "),:r => Variable(:r, Edges:\n", + "Edge belonging to variable r: ( r.i[out] )----( x_t.i[in2] ).\n", + "),:m_r => Variable(:m_r, Edges:\n", + "Edge belonging to variable m_r: ( placeholder_m_r.i[out] )----( r.i[m] ).\n", + ")…), Dict(\"clamp\" => 2,\"multiplication\" => 1,\"variable\" => 1), Dict{Clamp,Tuple{Symbol,Int64}}(Clamp{Univariate} with id placeholder_v_r\n", + " => (:v_r, 0),Clamp{Univariate} with id placeholder_m_r\n", + " => (:m_r, 0),Clamp{Univariate} with id placeholder_m_x\n", + " => (:m_x, 0),Clamp{Univariate} with id placeholder_v_x\n", + " => (:v_x, 0),Clamp{Univariate} with id placeholder_y_t\n", + " => (:y_t, 0)))" + ] + }, + "execution_count": 4, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# Start model specification\n", + "@ffg function nonlinear_kalman(g)\n", + "\n", + " # Prior for fertility parameter\n", + " r ~ GaussianMeanVariance(placeholder(:m_r), placeholder(:v_r), id=:r)\n", + "\n", + " # Define previous state\n", + " x_tmin1 ~ GaussianMeanVariance(placeholder(:m_x), placeholder(:v_x), id=:x_tmin1)\n", + "\n", + " # State transition node\n", + " x_t ~ Nonlinear{Unscented}(x_tmin1, r; g=g, id=:x_t)\n", + "\n", + " # Observation likelihood\n", + " y_t ~ GaussianMeanPrecision(N*x_t, noise_precision, id=:y_t)\n", + "\n", + " # Tell ForneyLab that variable y_t will be observed later on\n", + " placeholder(y_t, :y_t);\n", + "end\n", + "\n", + "# Nonlinear state transition function\n", + "g(x_tmin1, r) = r*x_tmin1*(1-x_tmin1)\n", + "model = nonlinear_kalman(g)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Compile inference algorithm\n", + "\n", + "The message passing algorithm, including a procedure for evaluating the free energy, can be derived automatically." + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [], + "source": [ + "# Define sum-product message passing procedure with state x_t and fertility r as parameters of interest\n", + "algo = messagePassingAlgorithm([:x_t, :r], free_energy=true)\n", + "\n", + "# Compile message passing procedure to an inference algorithm\n", + "code = algorithmSourceCode(algo, free_energy=true);\n", + "\n", + "# Import compiled functions to workspace\n", + "eval(Meta.parse(code));\n", + "\n", + "# Print compiled functions (uncomment if desired)\n", + "# println(code)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Execute inference algorithm\n", + "\n", + "We execute the algorithm in an online fashion: after each timestep the posteriors for the state and fertility parameter are used as priors for the next timestep." + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "\u001b[32mAt time t: 100%|████████████████████████████████████████| Time: 0:00:04\u001b[39m\n" + ] + } + ], + "source": [ + "# Parameters for prior distributions\n", + "m_x_0 = 0.5\n", + "v_x_0 = 2.0\n", + "m_r_0 = 1.0\n", + "v_r_0 = 1.0\n", + "\n", + "# Initialize array to track Free Energy objective\n", + "F = zeros(T,)\n", + "\n", + "# Initialize arrays for storing parameter estimates\n", + "m_x_t = zeros(T,)\n", + "v_x_t = zeros(T,)\n", + "m_r_t = zeros(T,)\n", + "v_r_t = zeros(T,)\n", + "\n", + "# Initialize previous parameter estimates\n", + "m_x_tmin1 = m_x_0\n", + "v_x_tmin1 = v_x_0\n", + "m_r_tmin1 = m_r_0\n", + "v_r_tmin1 = v_r_0\n", + "\n", + "# Start progress bar\n", + "progress_bar = Progress(T, 1, \"At time t: \")\n", + "\n", + "# Recursive estimation procedure (posteriors at t => priors at t+1)\n", + "for t = 1:T\n", + " \n", + " # Update progress bar\n", + " update!(progress_bar, t)\n", + " \n", + " # Store data for current time-step\n", + " data = Dict(:y_t => observations[t],\n", + " :m_x => m_x_tmin1,\n", + " :v_x => v_x_tmin1,\n", + " :m_r => m_r_tmin1,\n", + " :v_r => v_r_tmin1)\n", + "\n", + " # Estimate marginal distributions of interest (x_t and r)\n", + " marginals = step!(data)\n", + " \n", + " # Evaluate free energy\n", + " F[t] = freeEnergy(data, marginals) \n", + " \n", + " # Extract parameters of estimated marginal distributions\n", + " (m_x, v_x) = ForneyLab.unsafeMeanCov(marginals[:x_t])\n", + " (m_r, v_r) = ForneyLab.unsafeMeanCov(marginals[:r])\n", + " \n", + " # Reset parameter estimate arrays for next time-step\n", + " m_x_tmin1 = m_x_t[t] = m_x\n", + " v_x_tmin1 = v_x_t[t] = v_x\n", + " m_r_tmin1 = m_r_t[t] = m_r\n", + " v_r_tmin1 = v_r_t[t] = v_r\n", + " \n", + "end" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Inspect Results" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We will first visualize the estimated states. Since this is a probabilistic model, we can show the uncertainty of the estimates at the same time." + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": "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" + }, + "execution_count": 7, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# Plot true states and overlay estimates\n", + "plot(1:T, states, linewidth=2, ylims=[0., 1.], xlabel=\"time (months)\", ylabel=\"x (proportion rabbits)\", label=\"true\", legend=:bottomright)\n", + "plot!(1:T, m_x_t, linewidth=4, color=\"red\", ribbon=[sqrt.(v_x_t) sqrt.(v_x_t)], alpha=0.6, label=\"estimated\")\n", + "title!(\"Rabbit population size, relative to max\")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Next, we can plot the estimate of the fertility parameter over time. It should vary a bit at the start, but converge towards the end." + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": "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" + }, + "execution_count": 8, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# Plot estimate of fertility parameter r\n", + "plot(1:T, fertility.*ones(T,), color=\"blue\", label=\"true\", legend=:bottomright)\n", + "plot!(1:T, m_r_t, ribbon=[sqrt.(v_r_t) sqrt.(v_r_t)], color=\"red\", linewidth=3, xlabel=\"time (months)\", ylabel=\"r (fertility)\", label=\"estimated\")\n", + "title!(\"Estimate of fertility parameter, over time\")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We tracked free energy for each observation, so we can show how it evolves over time. Note that free energy is a measure of prediction error, weighted by how uncertain the model is about its prediction." + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": "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" + }, + "execution_count": 9, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# Plot free energy objective\n", + "plot(1:T, F, linewidth=3, color=\"red\", xlabel=\"time (months)\", ylabel=\"F (nats)\", label=\"\")\n", + "title!(\"Free energy, over time\")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## 2. Tracking a noisy pendulum\n", + "\n", + "In this problem, we will be tracking a pendulum whose observations are noisy. You can find this example in [Bayesian Filtering & Smoothing](https://www.cambridge.org/core/books/bayesian-filtering-and-smoothing/C372FB31C5D9A100F8476C1B23721A67) by Simon Särkkä (Ex 3.7). Its state transitions are sinusoidal in nature and it hence, qualifies as a nonlinear dynamical system. We can describe the system with the following differential equation:\n", + "\n", + "$$\\begin{align*}\n", + "\\frac{d}{dt} \\begin{bmatrix} x_1 \\\\ x_2 \\end{bmatrix} = \\begin{bmatrix} x_2 \\\\ -g \\sin(x_1) \\end{bmatrix}\n", + "\\end{align*}$$\n", + "\n", + "where $x_1$ represents the angle $\\alpha$ of the pendulum, $x_2$ represents the change in angle $d \\alpha /dt$ and $g$ is gravitational acceleration. We discretise the equation using a forward finite difference: $dx/dt = (x_{t+1} - x_{t})/\\Delta t$. This produces the following discrete state transition:\n", + "\n", + "$$\\begin{align*}\n", + "\\begin{bmatrix} x_{1,t+1} \\\\ x_{2,t+1} \\end{bmatrix} = \\begin{bmatrix} x_{1,t} + x_{2,t}\\Delta t \\\\ x_{2,t} - g \\sin(x_{1,t})\\Delta t \\end{bmatrix}\n", + "\\end{align*}$$\n", + "\n", + "We cannot observe the change in angle directly, only the angle itself (i.e. $x_{1}$). We can select the first element of the state vector by taking the inner product between the vector $[1 \\ 0]$ and the state vector $x_t$. The observation is corrupted by white noise $v_t$:\n", + "\n", + "$$y_t = x_{1,t} + v_t$$\n", + "\n", + "where $v_t \\sim \\mathcal{N}(0, \\tau^{-1})$." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Generate data" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": {}, + "outputs": [], + "source": [ + "# Length of time-series\n", + "T = 500\n", + "Δt = 0.01\n", + "\n", + "# Gravitational acceleration\n", + "G = 9.81\n", + "\n", + "# Measurement noise precision\n", + "noise_precision = 10.\n", + "\n", + "# Initial states\n", + "x0 = [1.0, 0.0]\n", + "\n", + "# Initialize data array\n", + "states = zeros(2,T)\n", + "observations = zeros(T,)\n", + "\n", + "# Initialize previous state variable\n", + "prev_state = x0\n", + "\n", + "for t = 1:T\n", + " \n", + " # State transition\n", + " states[1,t] = prev_state[1] + prev_state[2]*Δt\n", + " states[2,t] = prev_state[2] - G*sin(prev_state[1])*Δt\n", + " \n", + " # Observation likelihood\n", + " observations[t] = states[1,t] + sqrt(inv(noise_precision))*randn(1)[1]\n", + " \n", + " # Update \"previous state\"\n", + " prev_state = states[:,t]\n", + " \n", + "end " + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": "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" + }, + "execution_count": 11, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# Inspect data\n", + "plot((1:T).*Δt, states[1,:], linewidth=3, color=\"blue\", xlabel=\"time (Δt = \"*string(Δt)*\")\", ylabel=\"position pendulum\", label=\"true\", legend=:bottomright)\n", + "scatter!((1:T).*Δt, observations, color=\"black\", markersize=2,label=\"observed\")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Model specification\n", + "\n", + "We will once again define distributions for the state transition and likelihood. This time, we will assume that we don't know the precision parameter $\\tau$ of measurement noise $v_t$. Since $\\tau$ is a strictly positive parameter, we need to use an appropriate distribution. The Gamma distribution is [conjugate](https://en.wikipedia.org/wiki/Conjugate_prior) to the Gaussian likelihood function and will make computation easier." + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "metadata": {}, + "outputs": [], + "source": [ + "# Start model specification\n", + "@ffg function pendulum_model(g)\n", + " # Prior for measurement noise precision\n", + " τ ~ Gamma(placeholder(:a_τ), placeholder(:b_τ))\n", + "\n", + " # Define previous state\n", + " x_tmin1 ~ GaussianMeanVariance(placeholder(:m_x, dims=(2,)), placeholder(:v_x, dims=(2,2)), id=:x_tmin1)\n", + "\n", + " # State transition\n", + " x_t ~ Nonlinear{Unscented}(x_tmin1; g=g, alpha=0.01, id=:x_t)\n", + "\n", + " # Mask the state variable\n", + " x_1 = dot([1., 0.], x_t) ∥ [id=:x_1]\n", + "\n", + " # Observation likelihood\n", + " y_t ~ GaussianMeanPrecision(x_1, τ, id=:y_t)\n", + "\n", + " # Tell ForneyLab that variable y_t will be observed later on\n", + " placeholder(y_t, :y_t);\n", + "end\n", + "\n", + "g(x) = [x[1] + x[2]*Δt, x[2] - G*sin(x[1])*Δt]\n", + "pmodel = pendulum_model(g);" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "G\n", + "\n", + "\n", + "\n", + "9632981053421872971\n", + "\n", + "placeholder_v_x\n", + "\n", + "\n", + "\n", + "2901916651289794450\n", + "\n", + "𝒩\n", + "x_tmin1\n", + "\n", + "\n", + "\n", + "2901916651289794450--9632981053421872971\n", + "\n", + "v_x\n", + "1 out \n", + "3 v \n", + "\n", + "\n", + "\n", + "14291712784273055837\n", + "\n", + "placeholder_m_x\n", + "\n", + "\n", + "\n", + "2901916651289794450--14291712784273055837\n", + "\n", + "m_x\n", + "1 out \n", + "2 m \n", + "\n", + "\n", + "\n", + "12020869735119957912\n", + "\n", + "𝒩\n", + "y_t\n", + "\n", + "\n", + "\n", + "12100042191857196400\n", + "\n", + "Gam\n", + "gamma_1\n", + "\n", + "\n", + "\n", + "12020869735119957912--12100042191857196400\n", + "\n", + "τ\n", + "1 out \n", + "3 w \n", + "\n", + "\n", + "\n", + "18119674305598165182\n", + "\n", + "dot\n", + "dotproduct_1\n", + "\n", + "\n", + "\n", + "12020869735119957912--18119674305598165182\n", + "\n", + "x_1\n", + "1 out \n", + "2 m \n", + "\n", + "\n", + "\n", + "3519077826070577445\n", + "\n", + "clamp_1\n", + "\n", + "\n", + "\n", + "2605895539306962634\n", + "\n", + "placeholder_b_τ\n", + "\n", + "\n", + "\n", + "12100042191857196400--2605895539306962634\n", + "\n", + "b_τ\n", + "1 out \n", + "3 b \n", + "\n", + "\n", + "\n", + "18297010290647028257\n", + "\n", + "placeholder_a_τ\n", + "\n", + "\n", + "\n", + "12100042191857196400--18297010290647028257\n", + "\n", + "a_τ\n", + "1 out \n", + "2 a \n", + "\n", + "\n", + "\n", + "18119674305598165182--3519077826070577445\n", + "\n", + "clamp_1\n", + "1 out \n", + "3 in2 \n", + "\n", + "\n", + "\n", + "7638746435481495184\n", + "\n", + "g{Unscented}\n", + "x_t\n", + "\n", + "\n", + "\n", + "18119674305598165182--7638746435481495184\n", + "\n", + "x_t\n", + "1 out \n", + "2 in1 \n", + "\n", + "\n", + "\n", + "7638746435481495184--2901916651289794450\n", + "\n", + "x_tmin1\n", + "1 out \n", + "2 in1 \n", + "\n", + "\n", + "\n", + "17064125604046218667\n", + "\n", + "placeholder_y_t\n", + "\n", + "\n", + "\n", + "17064125604046218667--12020869735119957912\n", + "\n", + "y_t\n", + "1 out \n", + "1 out \n", + "\n", + "\n", + "\n" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "draw()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Compile inference algorithm\n", + "\n", + "We cannot use exact Bayesian inference here and will therefore switch to an approximate inference scheme: variational message passing." + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": {}, + "outputs": [], + "source": [ + "# Define a factorization for the posterior\n", + "q = PosteriorFactorization(:x_t, :τ, ids=[:x, :τ])\n", + "\n", + "# Define a variational message passing procedure\n", + "algorithm = messagePassingAlgorithm([:x_t, :τ], q, free_energy=true)\n", + "\n", + "# Compile message passing procedure to an inference algorithm\n", + "code = algorithmSourceCode(algorithm, free_energy=true);\n", + "\n", + "# Import compiled functions to workspace\n", + "eval(Meta.parse(code));\n", + "\n", + "# Print compiled functions (uncomment when desired)\n", + "# println(code)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Execute inference algorithm\n", + "\n", + "This piece of code is similar to the previous problem. The only difference is that variational message passing is an optimization problem: we defined a \"recognition\" distribution that approximates the posterior distributions of interest. We have to perform a few iterations of coordinate descent to minimize the KL-divergence between the approximating recognition distribution and the true generative model." + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "\u001b[32mAt time t: 100%|████████████████████████████████████████| Time: 0:00:05\u001b[39m\n" + ] + } + ], + "source": [ + "# Number of iterations\n", + "num_iterations = 3\n", + "\n", + "# Parameters for prior distributions\n", + "m_x_0 = [0., 0.]\n", + "v_x_0 = [0.1 0.;0. 0.1]\n", + "a_τ_0 = 1.0\n", + "b_τ_0 = 0.1\n", + "\n", + "# Initialize array to track Free Energy objective\n", + "F = zeros(T,num_iterations)\n", + "\n", + "# Initialize arrays for storing parameter estimates\n", + "m_x_t = zeros(2,T)\n", + "v_x_t = zeros(2,2,T)\n", + "a_τ_t = zeros(T,)\n", + "b_τ_t = zeros(T,)\n", + "\n", + "# Initialize previous parameter estimates\n", + "m_x_tmin1 = m_x_0\n", + "v_x_tmin1 = v_x_0\n", + "a_τ_tmin1 = a_τ_0\n", + "b_τ_tmin1 = b_τ_0\n", + "\n", + "# Initialize marginal distributions\n", + "marginals = Dict()\n", + "marginals[:x_tmin1] = ProbabilityDistribution(Multivariate, GaussianMeanVariance, m=m_x_0, v=v_x_0)\n", + "marginals[:x_t] = ProbabilityDistribution(Multivariate, GaussianMeanVariance, m=m_x_0, v=v_x_0)\n", + "marginals[:x_1] = ProbabilityDistribution(Univariate, GaussianMeanVariance, m=m_x_0[1], v=v_x_0[1,1])\n", + "marginals[:τ] = ProbabilityDistribution(Univariate, Gamma, a=a_τ_0, b=b_τ_0)\n", + "\n", + "# Start progress bar\n", + "progress_bar = Progress(T, 1, \"At time t: \")\n", + "\n", + "# Recursive estimation procedure (posteriors at t => priors at t+1)\n", + "for t = 1:T\n", + " \n", + " # Update progress bar\n", + " update!(progress_bar, t)\n", + " \n", + " # Store data for current time-step\n", + " data = Dict(:y_t => observations[t],\n", + " :m_x => m_x_tmin1,\n", + " :v_x => v_x_tmin1,\n", + " :a_τ => a_τ_tmin1,\n", + " :b_τ => b_τ_tmin1)\n", + " \n", + " # Iteratively update beliefs\n", + " for tt = 1:num_iterations\n", + " \n", + " # Evaluate free energy\n", + " F[t,tt] = freeEnergy(data, marginals) \n", + " \n", + " # Update recognition distribution for current state\n", + " stepx!(data, marginals)\n", + " \n", + " # Update recognition distribution for measurement noise precision\n", + " stepτ!(data, marginals)\n", + " \n", + " end\n", + " \n", + " # Extract parameters of estimated marginal distributions\n", + " (m_x, v_x) = ForneyLab.unsafeMeanCov(marginals[:x_t])\n", + " (a_τ, b_τ) = values(marginals[:τ].params)\n", + " \n", + " # Reset parameter estimate arrays for next time-step\n", + " m_x_tmin1 = m_x_t[:,t] = m_x\n", + " v_x_tmin1 = v_x_t[:,:,t] = v_x\n", + " a_τ_tmin1 = a_τ_t[t] = a_τ\n", + " b_τ_tmin1 = b_τ_t[t] = b_τ\n", + " \n", + "end" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Inspect results\n", + "\n", + "We can plot the estimates of the angle and the change in the angle, over time, including the uncertainty of the estimates." + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": "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" + }, + "execution_count": 16, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# Plot true states and overlay estimates\n", + "plot((1:T).*Δt, states[1,:], linewidth=2, xlabel=\"time (Δt = \"*string(Δt)*\")\", ylabel=\"angle (α)\", label=\"true\", legend=:bottomright)\n", + "plot!((1:T).*Δt, m_x_t[1,:], linewidth=4, color=\"red\", ribbon=[sqrt.(v_x_t[1,1,:]) sqrt.(v_x_t[1,1,:])], alpha=0.6, label=\"estimated\")\n", + "title!(\"Angle of the pendulum, over time\")" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": "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" + }, + "execution_count": 17, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# Plot true states and overlay estimates\n", + "plot((1:T).*Δt, states[2,:], linewidth=2, xlabel=\"time (Δt = \"*string(Δt)*\")\", ylabel=\"change in angle (dα/dt)\", label=\"true\", legend=:topleft)\n", + "plot!((1:T).*Δt, m_x_t[2,:], linewidth=4, color=\"red\", ribbon=[sqrt.(v_x_t[2,2,:]) sqrt.(v_x_t[2,2,:])], alpha=0.6, label=\"estimated\")\n", + "title!(\"Change in angle of the pendulum, over time\")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We left measurement noise precision as an unknown parameter. The plot shows its estimate over time." + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": "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" + }, + "execution_count": 18, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# Mean and variance of gamma distribution\n", + "m_τ_t = a_τ_t ./ b_τ_t\n", + "v_τ_t = a_τ_t ./ b_τ_t.^2\n", + "\n", + "# Plot estimate of τ\n", + "plot((1:T).*Δt, ones(T,)*noise_precision, label=\"true\", legend=:topleft)\n", + "plot!((1:T).*Δt, m_τ_t, ribbon=[sqrt.(v_τ_t) sqrt.(v_τ_t)], linewidth=3, xlabel=\"time (Δt = \"*string(Δt)*\")\", ylabel=\"precision (τ)\", label=\"estimated\")\n", + "title!(\"Estimate of measurement precision, over time\")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "It is important to look at the evolution of free energy. Remember that free energy is a measure of uncertainty-weighted prediction error. " + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": "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" + }, + "execution_count": 19, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# Plot free energy objective\n", + "plot((1:T).*Δt, F[:,end], linewidth=3, color=\"red\", xlabel=\"time (Δt = \"*string(Δt)*\")\", ylabel=\"F (nats)\", label=\"\")\n", + "title!(\"Free energy at final iteration, over time\")" + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": "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" + }, + "execution_count": 20, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# Plot free energy objective\n", + "plot(1:num_iterations, mean(F, dims=1)', linewidth=3, color=\"red\", xlabel=\"# iterations\", ylabel=\"F (nats)\", label=\"\")\n", + "title!(\"Free energy by iterations, averaged over time\")" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "@webio": { + "lastCommId": null, + "lastKernelId": null + }, + "kernelspec": { + "display_name": "Julia 1.4.0", + "language": "julia", + "name": "julia-1.4" + }, + "language_info": { + "file_extension": ".jl", + "mimetype": "application/julia", + "name": "julia", + "version": "1.4.0" + } + }, + "nbformat": 4, + "nbformat_minor": 4 +} diff --git a/src/ForneyLab.jl b/src/ForneyLab.jl index f763b79e..29f2497d 100644 --- a/src/ForneyLab.jl +++ b/src/ForneyLab.jl @@ -70,6 +70,11 @@ include("factor_graph.jl") # Composite nodes include("factor_nodes/composite.jl") +# Code generation for models +include("codegen/graph.jl") +include("codegen/helpers.jl") +include("codegen/variable.jl") + # Generic methods include("algorithms/cluster.jl") include("message_passing.jl") diff --git a/src/algorithms/inference_algorithm.jl b/src/algorithms/inference_algorithm.jl index fa8ae6c2..581707ae 100644 --- a/src/algorithms/inference_algorithm.jl +++ b/src/algorithms/inference_algorithm.jl @@ -83,6 +83,41 @@ messagePassingAlgorithm(target_variable::Variable, id=Symbol(""), free_energy=false) = messagePassingAlgorithm([target_variable], pfz; id=id, free_energy=free_energy) + +# Shorthands for algorithm compilation by passing only variable ids +function messagePassingAlgorithm(target_variable_ids::Vector{Symbol}, # Quantities of interest + pfz::PosteriorFactorization=currentPosteriorFactorization(); + id=Symbol(""), + free_energy=false) + + target_variables = Vector{Variable}(undef, length(target_variable_ids)) + + for (i, target_variable_id) in enumerate(target_variable_ids) + target_variable = get(currentGraph().variables, target_variable_id, nothing) + if isnothing(target_variable) + error("Variable with id $(target_variable_id) does not exist.") + else + target_variables[i] = target_variable + end + end + + return messagePassingAlgorithm(target_variables, pfz; id=id, free_energy=free_energy) +end + + +function messagePassingAlgorithm(target_variable_id::Symbol, + pfz::PosteriorFactorization=currentPosteriorFactorization(); + id=Symbol(""), + free_energy=false) + + target_variable = get(currentGraph().variables, target_variable_id, nothing) + if isnothing(target_variable) + error("Variable with id $(target_variable_id) does not exist.") + end + + return messagePassingAlgorithm([target_variable], pfz; id=id, free_energy=free_energy) +end + function interfaceToScheduleEntry(algo::InferenceAlgorithm) mapping = Dict{Interface, ScheduleEntry}() for (id, pf) in algo.posterior_factorization diff --git a/src/algorithms/posterior_factor.jl b/src/algorithms/posterior_factor.jl index d397b787..bdbbccb5 100644 --- a/src/algorithms/posterior_factor.jl +++ b/src/algorithms/posterior_factor.jl @@ -43,6 +43,32 @@ end PosteriorFactor(seed_variable::Variable; pfz=currentPosteriorFactorization(), id=generateId(PosteriorFactor)) = PosteriorFactor(Set([seed_variable]), pfz=pfz, id=id) PosteriorFactor(seed_variables::Vector{Variable}; pfz=currentPosteriorFactorization(), id=generateId(PosteriorFactor)) = PosteriorFactor(Set(seed_variables), pfz=pfz, id=id) +function PosteriorFactor(seed_variable_id::Symbol; pfz=currentPosteriorFactorization(), id=generateId(PosteriorFactor)) + + seed_variable = get(currentGraph().variables, seed_variable_id, nothing) + if isnothing(seed_variable) + error("Variable with id $(seed_variable_id) does not exist.") + end + + return PosteriorFactor(Set([seed_variable]), pfz=pfz, id=id) +end + +function PosteriorFactor(seed_variable_ids::Vector{Symbol}; pfz=currentPosteriorFactorization(), id=generateId(PosteriorFactor)) + seed_variables = Vector{Variable}(undef, length(seed_variable_ids)) + + for (i, seed_variable_id) in enumerate(seed_variable_ids) + seed_variable = get(currentGraph().variables, seed_variable_id, nothing) + if isnothing(seed_variable) + error("Variable with id $(seed_variable_id) does not exist.") + else + seed_variables[i] = seed_variable + end + end + + return PosteriorFactor(Set(seed_variables), pfz=pfz, id=id) +end + + """ `messagePassingSchedule()` generates a message passing schedule for the posterior factor """ diff --git a/src/algorithms/posterior_factorization.jl b/src/algorithms/posterior_factorization.jl index 769c5117..1d9c71e9 100644 --- a/src/algorithms/posterior_factorization.jl +++ b/src/algorithms/posterior_factorization.jl @@ -88,6 +88,22 @@ function PosteriorFactorization(args::Vararg{Union{T, Set{T}, Vector{T}} where T return pfz end +""" +Construct a `PosteriorFactorization` consisting of one `PosteriorFactor` for each argument addressed by its id +""" +function PosteriorFactorization(args::Vararg{Union{Symbol, Set{Symbol}, Vector{Symbol}}}; ids=Symbol[]) + pfz = PosteriorFactorization() + isempty(ids) || (length(ids) == length(args)) || error("Length of ids must match length of posterior factor arguments") + for (i, arg) in enumerate(args) + if isempty(ids) + PosteriorFactor(arg, id=generateId(PosteriorFactor)) + else + PosteriorFactor(arg, id=ids[i]) + end + end + return pfz +end + iterate(pfz::PosteriorFactorization) = iterate(pfz.posterior_factors) iterate(pfz::PosteriorFactorization, state) = iterate(pfz.posterior_factors, state) values(pfz::PosteriorFactorization) = values(pfz.posterior_factors) diff --git a/src/codegen/graph.jl b/src/codegen/graph.jl new file mode 100644 index 00000000..96363b3b --- /dev/null +++ b/src/codegen/graph.jl @@ -0,0 +1,26 @@ +export @ffg + +using MacroTools: postwalk, rmlines, prettify, @capture + +macro ffg(expr::Expr) + return esc(postwalk(rmlines, generate_model(expr))) +end + +function generate_model(expr::Expr) + + @capture(expr, (mname_(margs__) = body_) | (function mname_(margs__) body_ end)) || error("Model definition has to be a function.") + + body = postwalk(rewrite_expression, body) + + graph_sym = gensym(:factor_graph) + + result = quote + function $mname($(margs...)) + $(graph_sym) = FactorGraph() + $body + return $(graph_sym) + end + end + + return result +end \ No newline at end of file diff --git a/src/codegen/helpers.jl b/src/codegen/helpers.jl new file mode 100644 index 00000000..9a646998 --- /dev/null +++ b/src/codegen/helpers.jl @@ -0,0 +1,23 @@ +# Extract options dictionary from expression +function get_options(expr::Expr) + options = Dict{Symbol,Any}() + + expr = postwalk(expr) do x + if @capture(x, lhs_ where {exoptions__}) + for option in exoptions + @capture(option, key_ = value_) + options[key] = value + end + return lhs + end + return x + end + + if !isempty(options) + return expr, options + else + return expr, nothing + end +end + +get_options(a::Any) = a, nothing \ No newline at end of file diff --git a/src/codegen/variable.jl b/src/codegen/variable.jl new file mode 100644 index 00000000..3a487e67 --- /dev/null +++ b/src/codegen/variable.jl @@ -0,0 +1,88 @@ +function rewrite_expression(expression::Expr) + expr = if @capture(expression, var_ ~ rhs_) + rewrite_tilde_expression(var, rhs) + elseif @capture(expression, var_ = rhs_) + (rhs, options) = get_options(rhs) + if options === nothing + return expression + end + rewrite_assign_expression(var, rhs, options) + elseif is_for(expression) + rewrite_for_block(expression) + else + expression + end + return expr +end + +rewrite_expression(ex::Any) = ex + +function rewrite_tilde_expression(var, rhs) + + (rhs, options) = get_options(rhs) + @capture(rhs, pdist_(params__)) + + var_id = extract_variable_id(var, options) + + # Build total expression + return :( + begin + # Use existing Variable if it exists, otherwise create a new one + $(var) = try + $(var) + catch _ + Variable(id = $(var_id)) + end + + # Create new variable if: + # - the existing object is not a Variable + # - the existing object is a Variable from another FactorGraph + if (!isa($(var), Variable) + || !haskey(currentGraph().variables, $(var).id) + || currentGraph().variables[$(var).id] !== $(var)) + + $(var) = Variable(id = $(var_id)) + end + + $(pdist)($(var), $(params...)) + $(var) + end + ) +end + +function rewrite_assign_expression(var, rhs, options) + + var_id = extract_variable_id(var, options) + + var_id_sym = gensym() + + return :( + begin + $(var) = $(rhs) + $(var_id_sym) = $(var_id) + if $(var_id_sym) != :auto + # update id of newly created Variable + currentGraph().variables[$(var_id_sym)] = $(var) + delete!(currentGraph().variables, $(var).id) + $(var).id = $(var_id_sym) + end + $(var) + end + ) +end + +# for loop +is_for(expr::Expr) = expr.head === :for +is_for(expr) = false + +function rewrite_for_block(def) + body_block = def.args[2] + + for (i, expr) in enumerate(body_block.args) + body_block.args[i] = rewrite_expression(expr) + end + + return quote + $(def) + end +end \ No newline at end of file diff --git a/src/variable.jl b/src/variable.jl index ccb397a3..e096dc62 100644 --- a/src/variable.jl +++ b/src/variable.jl @@ -184,7 +184,7 @@ end # If variable expression is a symbol # RV x ... function extract_variable_id(expr::Symbol, options) - if haskey(options, :id) + if (options !== nothing) && haskey(options, :id) return check_id_available(options[:id]) else return guard_variable_id(:($(string(expr)))) @@ -194,7 +194,7 @@ end # If variable expression is an indexing expression # RV x[i] ... function extract_variable_id(expr::Expr, options) - if haskey(options, :id) + if (options !== nothing) && haskey(options, :id) return check_id_available(options[:id]) else argstr = map(arg -> :(string($arg)), @view expr.args[2:end])