{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Probabilistic Programming 4: Latent Variable & Dynamic Models\n", "\n", "#### Goal \n", " - Understand how to estimate latent variables in models.\n", " - Understand how to estimate states in dynamical models.\n", "\n", "#### Materials \n", " - Mandatory\n", " - This notebook\n", " - Lecture notes on latent variable models\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\n", "Pkg.activate(\"./workspace\")\n", "Pkg.instantiate();" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "using JLD\n", "using Statistics\n", "using StatsBase\n", "using LinearAlgebra\n", "using ProgressMeter\n", "using ColorSchemes\n", "using LaTeXStrings\n", "using ForneyLab\n", "using Plots\n", "pyplot();\n", "\n", "import LinearAlgebra: I\n", "import ForneyLab: unsafeMean\n", "include(\"../scripts/clusters.jl\");\n", "include(\"../scripts/filters.jl\");" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Problem: Stone Tools\n", "\n", "Archeologists have asked for your help in analyzing data on stone tools. It is believed that primitive humans created tools by striking stones with others. During this process, the stone loses flakes, which have been preserved. The archeologists have recovered these flakes from various locations and time periods and want to know whether this stone tool shaping process has improved over the centuries." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Data\n", "\n", "The data is available from the [UCI Machine Learning Repository](https://archive.ics.uci.edu/ml/datasets/StoneFlakes). Each instance represents summary information of the stone flakes for a particular site. We will be using the attributes _flaking angle_ (FLA) and the _proportion of the dorsal surface worked_ (PROZD) for now." ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "dataset = load(\"../datasets/stoneflakes.jld\");" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "I've done some pre-processing on the data set, namely [z-scoring](https://nl.wikipedia.org/wiki/Z-score) and removing two outliers. This reduces the scale of the attributes which helps numerical stability during optimization. \n", "\n", "Now let's visualize the data with a scatterplot." ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "image/png": 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" }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "scatter(dataset[\"data\"][:,1], \n", " dataset[\"data\"][:,2], \n", " label=\"\", \n", " xlabel=\"Proportion of worked dorsal surface (PROZD)\",\n", " ylabel=\"Flaking angle (FLA)\",\n", " size=(800,300))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Model specification\n", "\n", "We will be clustering this data with a Gaussian mixture model, to see if we can identify clear types of stone tools. The generative model for a Gaussian mixture consists of:\n", "\n", "$$p(X, z, \\phi, \\mu, \\Lambda) =\\ \\underbrace{p(X \\mid z, \\mu, \\Lambda)}_{\\text{likelihood}}\\ \\times \\ \\underbrace{p(z \\mid \\phi)}_{\\text{prior latent variables}} \\ \\times \\ \\underbrace{p(\\mu \\mid \\Lambda)\\ p(\\Lambda)\\ p(\\phi)}_{\\text{prior parameters}}$$\n", "\n", "with the likelihood of observation $X_i$ being a Gaussian raised to the power of the latent assignment variables $z$\n", "\n", "$$p(X_i \\mid z, \\mu, \\Lambda) = \\prod_{k=1}^{K} \\mathcal{N}(X_i \\mid \\mu_k, \\Lambda_k^{-1})^{z_i = k}$$\n", "\n", "the prior for each latent variable $z_i$ being a Categorical distribution\n", "\n", "$$p(z_i \\mid \\phi) = \\text{Categorical}(z_i \\mid \\phi)$$\n", "\n", "and priors for the parameters being\n", "\n", "\\begin{align*}\n", "p(\\mu_k \\mid \\Lambda_k) =&\\ \\mathcal{N}(\\mu_k \\mid m_0, l_0^{-1}\\Lambda_k^{-1}) \\qquad &\\text{for all}\\ k \\\\\n", "p(\\Lambda_k) =&\\ \\text{Wishart}(\\Lambda_k \\mid V_0, n_0) \\qquad &\\text{for all}\\ k \\\\\n", "p(\\phi) =&\\ \\text{Dirichlet}(\\phi \\mid a_0) \\, ,\n", "\\end{align*}\n", "\n", "We will be implementing this model directly in ForneyLab. If you're unfamiliar with these distributions or with the Gaussian mixture model, have another look at Bert's lectures.\n", "\n", "---\n", "\n", "First, we will do a bit of bookkeeping." ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [], "source": [ "# Data dimensionality\n", "num_features = size(dataset[\"data\"],2)\n", "\n", "# Sample size\n", "num_samples = size(dataset[\"data\"],1)\n", "\n", "# Number of mixture components\n", "num_components = 3;\n", "\n", "# Identity matrix (convenience variable)\n", "Id = Matrix{Float64}(I, num_features, num_features);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Mixture models can be sensitive to initialization, so we are going to specify the prior parameters explicitly." ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [], "source": [ "# Prior means\n", "m0 = [ 1.0 0.0 -1.0;\n", " -1.0 0.0 1.0];\n", "\n", "# Prior scale matrices\n", "V0 = cat(Id, Id, Id, dims=3)\n", "\n", "# Prior degrees of freedom \n", "n0 = num_features\n", "\n", "# Prior concentration parameters\n", "a0 = ones(num_components);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now to start the factor graph. " ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [], "source": [ "# Start a graph\n", "graph1 = FactorGraph()\n", "\n", "# Initialize vector variables\n", "z = Vector{Variable}(undef, num_samples)\n", "X = Vector{Variable}(undef, num_samples)\n", "Λ = Vector{Variable}(undef, num_components)\n", "μ = Vector{Variable}(undef, num_components)\n", "\n", "# Mixture weights are drawn from a Dirichlet distribution\n", "@RV ϕ ~ Dirichlet(a0)\n", "\n", "θ = []\n", "for k = 1:num_components\n", " \n", " # Parameters of k-th component\n", " @RV Λ[k] ~ Wishart(V0[:,:,k], n0)\n", " @RV μ[k] ~ GaussianMeanPrecision(m0[:,k], Λ[k])\n", " \n", " push!(θ, μ[k], Λ[k])\n", "end\n", "\n", "for i = 1:num_samples\n", " \n", " # Assignment variable\n", " @RV z[i] ~ Categorical(ϕ)\n", " \n", " # Gaussian mixture component\n", " @RV X[i] ~ GaussianMixture(z[i], θ...)\n", " \n", " # Add data \n", " placeholder(X[i], :X, dims=(num_features,), index=i)\n", "end" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This is another _iid_ setting, which means the graph will be too large to visualize.\n", "\n", "The next step is to compile an inference algorithm." ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [], "source": [ "# Specify recognition factorization (mean-field)\n", "q = PosteriorFactorization(ϕ, μ[1], Λ[1], μ[2], Λ[2], μ[3], Λ[3], z, \n", " ids=[:ϕ, :μ_1, :Λ_1, :μ_2, :Λ_2, :μ_3, :Λ_3, :z])\n", "\n", "# Generate the algorithm\n", "algorithm = messagePassingAlgorithm(free_energy=true)\n", "source_code = algorithmSourceCode(algorithm, free_energy=true);\n", "eval(Meta.parse(source_code));" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "After that, we feed in data, initialize recognition factors and run the inference procedure." ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "\u001b[32mProgress: 100%|█████████████████████████████████████████| Time: 0:00:51\u001b[39m\n" ] } ], "source": [ "# Convert data to a format suited to ForneyLab\n", "observations = [dataset[\"data\"][i,:] for i in 1:num_samples]\n", "\n", "# Add to data dictionary\n", "data = Dict(:X => observations)\n", "\n", "# Prepare recognition distributions\n", "marginals = Dict()\n", "marginals[:ϕ] = ProbabilityDistribution(Dirichlet, a=ones(num_components,))\n", "for k = 1:num_components\n", " marginals[:μ_*k] = ProbabilityDistribution(Multivariate, GaussianMeanPrecision, m=m0[:,k], w=Id)\n", " marginals[:Λ_*k] = ProbabilityDistribution(Wishart, v=Id, nu=num_features)\n", "end\n", "for i = 1:num_samples\n", " marginals[:z_*i] = ProbabilityDistribution(Categorical, p=ones(num_components,)./num_components)\n", "end\n", "\n", "# Number of iterations\n", "num_iterations = 20\n", "\n", "# Preallocate free energy tracking array\n", "F = Float64[]\n", "\n", "# Execute algorithm\n", "@showprogress for i = 1:num_iterations\n", " \n", " # Update assignments\n", " stepz!(data, marginals)\n", " \n", " # Update parameters\n", " stepϕ!(data, marginals)\n", " stepμ_1!(data, marginals)\n", " stepΛ_1!(data, marginals)\n", " stepμ_2!(data, marginals)\n", " stepΛ_2!(data, marginals)\n", " stepμ_3!(data, marginals)\n", " stepΛ_3!(data, marginals)\n", " \n", " # Store variational free energy for visualization\n", " push!(F, freeEnergy(data, marginals))\n", "end" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Alright, we're done. Let's track the evolution of free energy." ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "image/png": 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" }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Plot free energy to check for convergence\n", "plot(1:num_iterations, F, color=\"black\", label=\"\", xlabel=\"Number of iterations\", ylabel=\"Free Energy\", size=(800,300))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "That looks like it is nicely decreasing. We might want to increase the number of iterations a bit more.\n", "\n", "Let's now visualize the cluster on top of the observations." ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "scrolled": true }, "outputs": [ { "data": { "image/png": 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" }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" }, { "name": "stderr", "output_type": "stream", "text": [ "sys:1: UserWarning: The following kwargs were not used by contour: 'label'\r\n" ] } ], "source": [ "# Estimated means (unsafeMean retrieves parameters directly)\n", "μ1_estimated = unsafeMean(marginals[:μ_1])\n", "μ2_estimated = unsafeMean(marginals[:μ_2])\n", "μ3_estimated = unsafeMean(marginals[:μ_3])\n", "\n", "# Estimated precisions\n", "Λ1_estimated = unsafeMean(marginals[:Λ_1])\n", "Λ2_estimated = unsafeMean(marginals[:Λ_2])\n", "Λ3_estimated = unsafeMean(marginals[:Λ_3])\n", "\n", "# Invert to covariances\n", "Σ1_estimated = inv(Λ1_estimated)\n", "Σ2_estimated = inv(Λ2_estimated)\n", "Σ3_estimated = inv(Λ3_estimated)\n", "\n", "# Select dimensions to plot\n", "dims_plot = [1, 2]\n", "dim_limsx = [minimum(dataset[\"data\"][:,dims_plot[1]])-1, maximum(dataset[\"data\"][:,dims_plot[1]])+1]\n", "dim_limsy = [minimum(dataset[\"data\"][:,dims_plot[2]])-1, maximum(dataset[\"data\"][:,dims_plot[2]])+1]\n", "\n", "# Plot data and overlay estimated posterior probabilities\n", "plot_clusters(dataset[\"data\"][:, dims_plot], \n", " μ=[μ1_estimated[dims_plot], μ2_estimated[dims_plot], μ3_estimated[dims_plot]], \n", " Σ=[Σ1_estimated[dims_plot,dims_plot], Σ2_estimated[dims_plot,dims_plot], Σ3_estimated[dims_plot,dims_plot]], \n", " x1=range(dim_limsx[1], step=0.01, stop=dim_limsx[2]), \n", " x2=range(dim_limsy[1], step=0.01, stop=dim_limsy[2]),\n", " colorlist=[:reds, :blues, :greens],\n", " size=(600,400))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "That doesn't look bad. The three Gaussians nicely cover all samples." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "---\n", "\n", "#### $\\ast$ **Try for yourself**\n", "\n", "Play around with the number of components. Can you get an equally good coverage with just 2 components? What if you had 4?\n", "\n", "---" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Problem: Alpine Railways\n", "\n", "The Swiss Federal Railways company operates a series of [mountain railways](https://en.wikipedia.org/wiki/List_of_mountain_railways_in_Switzerland) bringing hikers (in the summer) and skiers (in the winter) up the Alps. They are setting up a new fallback security system where they intend to track trains through cameras and remote sensors. They want you to design a system to keep track of the trains' positions. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Data\n", "\n", "A train going uphill updates its position according to: new position = old position + velocity x length of time-step + noise. The noise represents the train randomly slipping and sliding back down. We observe the train through a remote sensor, producing noisy observations of its position. \n", "\n", "You receive a data set with past recordings. Your job is to set up an online filtering system, which can be deployed later on to process the incoming signal in real-time." ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "data": { "image/png": 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" }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" } ], "source": [ "signal = load(\"../datasets/alpinerails_filtering.jld\");\n", "\n", "# Unpack data\n", "states = signal[\"X\"]\n", "observations = signal[\"Y\"]\n", "transition = signal[\"A\"]\n", "emission = signal[\"C\"]\n", "process_noise = signal[\"Q\"]\n", "measurement_noise = signal[\"R\"]\n", "T = signal[\"T\"]\n", "Δt = signal[\"Δt\"];\n", "\n", "# Size\n", "M = size(states,1)\n", "N = size(observations,1)\n", "\n", "# Visualize\n", "plot(1:T, states[1,:], color=\"red\", label=\"states\", grid=false, xlabel=\"time (t)\", ylabel=\"train position\")\n", "scatter!(1:T, observations[1,:], markersize=2, color=\"black\", label=\"observations\", size=(800,300))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Model specification\n", "\n", "We define noisy observations $y_k \\in \\mathbb{R}^{1}$ with latent states $x_k \\in \\mathbb{R}^{2}$. Observations $y_k$ are generated through a Gaussian likelihood centered on an emission matrix $C$ times the current state $x_k$ perturbed by measurement noise with covariance matrix $R$. State transitions follow a Gaussian distribution centered on a transition matrix $A$ times the previous state perturbed by process noise with covariance matrix $Q$. In equation form, these are:\n", "\n", "\\begin{align}\n", "p(x_k \\mid x_{k-1}) =&\\ \\mathcal{N}(x_k \\mid A x_{k-1}, Q)\\\\\n", "p(y_k \\mid x_k) =&\\ \\mathcal{N}(y_k \\mid C x_k, R) \\, .\n", "\\end{align}\n", "\n", "We have a prior for the previous state $x_{k-1} \\sim \\mathcal{N}(m_{k-1}, V_{k-1})$. In filtering problems, we feed the estimates of the current states as the parameters for the previous state in the next time-step." ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\r\n", "\r\n", "\r\n", "\r\n", "\r\n" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Initialize a graph\n", "graph2 = FactorGraph()\n", "\n", "# Define initial state prior\n", "@RV x_kmin1 ~ GaussianMeanVariance(placeholder(:m_kmin1, dims=(M,)), \n", " placeholder(:V_kmin1, dims=(M,M)))\n", " \n", "# State transition\n", "@RV x_k ~ GaussianMeanVariance(transition * x_kmin1, process_noise)\n", " \n", "# Observation likelihood\n", "@RV y_k ~ GaussianMeanVariance(dot(emission, x_k), measurement_noise)\n", " \n", "# Tell FL that y is observed\n", "placeholder(y_k, :y_k);\n", "\n", "# Visualize subgraph\n", "ForneyLab.draw(graph2)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We'll now construct the algorithm and infer results. " ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [], "source": [ "# Generate inference algorithm\n", "algorithm = messagePassingAlgorithm(x_k)\n", "source_code = algorithmSourceCode(algorithm)\n", "eval(Meta.parse(source_code));" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "For filtering, we use the same graph in each time-step." ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "\u001b[32mProgress: 100%|█████████████████████████████████████████| Time: 0:00:01\u001b[39m\n" ] } ], "source": [ "# Initialize recognition distribution marginals\n", "marginals = Dict(:x_k => vague(GaussianMeanVariance, M))\n", "\n", "# Initialize message array\n", "messages = Array{Message}(undef, 5)\n", "\n", "# Keep track of estimates\n", "m_x = 10*ones(M,T+1)\n", "V_x = repeat(10*Matrix{Float64}(I,M,M), outer=(1,1,T+1))\n", "\n", "@showprogress for k = 1:T\n", " \n", " # Initialize data\n", " data = Dict(:y_k => observations[k],\n", " :m_kmin1 => m_x[:,k],\n", " :V_kmin1 => V_x[:,:,k])\n", " \n", " # Update states\n", " step!(data, marginals, messages)\n", " \n", " # Store estimates\n", " m_x[:,k+1] = mean(marginals[:x_k])\n", " V_x[:,:,k+1] = cov(marginals[:x_k])\n", " \n", "end" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's check whether everything went ok. We'll visualize the state estimations." ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "data": { "image/png": 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" }, "execution_count": 16, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Visualization\n", "plot(1:T, states[1,:], color=\"red\", label=\"states\", grid=false)\n", "plot!(1:T, m_x[1,2:end], ribbon=[sqrt.(V_x[1,1,2:end]), sqrt.(V_x[1,1,2:end])], fillalpha=0.2, color=\"blue\", label=\"inferred\")\n", "scatter!(1:T, observations[1,:], markersize=2, color=\"black\", label=\"observations\", size=(800,300))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We're going to inspect some messages. Let's open up the algorithm and look up the marginal computation for the final $x_k$. It will be the multiplication of two messages, one consisting of the state transition prediction and the other consisting of the measurement likelihood. " ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "begin\n", "\n", "function step!(data::Dict, marginals::Dict=Dict(), messages::Vector{Message}=Array{Message}(undef, 5))\n", "\n", "messages[1] = ruleSPGaussianMeanVarianceOutNPP(nothing, Message(Multivariate, PointMass, m=data[:m_kmin1]), Message(MatrixVariate, PointMass, m=data[:V_kmin1]))\n", "messages[2] = ruleSPMultiplicationOutNGP(nothing, messages[1], Message(MatrixVariate, PointMass, m=[1.0 0.1; 0.0 1.0]))\n", "messages[3] = ruleSPGaussianMeanVarianceOutNGP(nothing, messages[2], Message(MatrixVariate, PointMass, m=[0.01 0.0; 0.0 0.1]))\n", "messages[4] = ruleSPGaussianMeanVarianceMPNP(Message(Univariate, PointMass, m=data[:y_k]), nothing, Message(Univariate, PointMass, m=0.1))\n", "messages[5] = ruleSPDotProductIn1GNP(messages[4], nothing, Message(Multivariate, PointMass, m=[1.0, 0.0]))\n", "\n", "marginals[:x_k] = messages[3].dist * messages[5].dist\n", "\n", "return marginals\n", "\n", "end\n", "\n", "end # block\n" ] } ], "source": [ "println(source_code)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Alright, we need messages 3 and 5. Let's visualize them along with the state marginal." ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [ { "data": { "image/png": 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" }, "execution_count": 18, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Collect state transition prediction\n", "m_statepred = convert(ProbabilityDistribution{Multivariate, GaussianMeanVariance}, messages[3].dist)\n", "\n", "# Collect observation likelihood\n", "m_likelihood = convert(ProbabilityDistribution{Multivariate, GaussianMeanVariance}, messages[5].dist)\n", "\n", "# Collect corrected prediction\n", "state_marginal = convert(ProbabilityDistribution{Multivariate, GaussianMeanVariance}, marginals[:x_k])\n", "\n", "# # Extract x-coordinates\n", "m_statepred_x = ProbabilityDistribution(Univariate, GaussianMeanVariance, m=m_statepred.params[:m][1], v=m_statepred.params[:v][1,1])\n", "m_likelihood_x = ProbabilityDistribution(Univariate, GaussianMeanVariance, m=m_likelihood.params[:m][1], v=m_likelihood.params[:v][1,1])\n", "state_marginal_x = ProbabilityDistribution(Univariate, GaussianMeanVariance, m=state_marginal.params[:m][1], v=state_marginal.params[:v][1,1])\n", "\n", "# Plot of the prediction, noisy measurement, and corrected prediction for x-coordinate\n", "plot_messages(m_statepred_x, m_likelihood_x, state_marginal_x, size=(800,300))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As you can see, the state estimate is a combination of the state prediction, produced by the message from the state transition node, and the observation likelihood, produced by the message from the likelihood. " ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "---\n", "\n", "#### $\\ast$ **Try for yourself**\n", "\n", "Re-run the inference procedure and stop at an earlier time-step, for example $k$=2. How does the balance between the state prediction and the observation likelihood differ?\n", "\n", "---" ] } ], "metadata": { "@webio": { "lastCommId": null, "lastKernelId": null }, "kernelspec": { "display_name": "Julia 1.6.3", "language": "julia", "name": "julia-1.6" }, "language_info": { "file_extension": ".jl", "mimetype": "application/julia", "name": "julia", "version": "1.6.3" } }, "nbformat": 4, "nbformat_minor": 4 }