{ "cells": [ { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "# Probabilistic Programming 2: Bayesian regression and classification\n", "\n", "#### Goal \n", " - Learn how to infer a posterior distribution for a linear regression model using a probabilistic programming language.\n", " - Learn how to infer a posterior distribution for a linear classification model using a probabilistic programming language.\n", " \n", "#### Materials \n", " - Mandatory\n", " - This notebook.\n", " - Lecture notes on [regression](https://nbviewer.jupyter.org/github/bertdv/BMLIP/blob/master/lessons/notebooks/Regression.ipynb).\n", " - Lecture notes on [discriminative classification](https://nbviewer.jupyter.org/github/bertdv/BMLIP/blob/master/lessons/notebooks/Discriminative-Classification.ipynb).\n", " - Optional\n", " - Bayesian linear regression (Section 3.3 [Bishop](https://www.microsoft.com/en-us/research/uploads/prod/2006/01/Bishop-Pattern-Recognition-and-Machine-Learning-2006.pdf))\n", " - Bayesian logistic regression (Section 4.5 [Bishop](https://www.microsoft.com/en-us/research/uploads/prod/2006/01/Bishop-Pattern-Recognition-and-Machine-Learning-2006.pdf))\n", " - [Cheatsheets: how does Julia differ from Matlab / Python](https://docs.julialang.org/en/v1/manual/noteworthy-differences/index.html)." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "slideshow": { "slide_type": "slide" } }, "outputs": [], "source": [ "using Pkg; Pkg.activate(\"../../.\"); Pkg.instantiate();\n", "using IJulia; try IJulia.clear_output(); catch _ end" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Problem: Economic growth\n", "\n", "In 2008, the credit crisis sparked a recession in the US, which spread to other countries in the ensuing years. It took most countries a couple of years to recover. \n", "Now, the year is 2011. The Turkish government is asking you to estimate whether Turkey is out of the recession. You decide to look at the data of the national stock exchange to see if there's a positive trend. " ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "using CSV\n", "using DataFrames\n", "using LinearAlgebra\n", "using Distributions\n", "using StatsFuns\n", "using RxInfer\n", "using Plots\n", "default(label=\"\", margin=10Plots.pt)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Data\n", "\n", "We are going to start with loading in a data set. We have daily measurements from Istanbul, from the 5th of January 2009 until 22nd of February 2011. The dataset comes from an online resource for machine learning data sets: the [UCI ML Repository](https://archive.ics.uci.edu/ml/datasets/ISTANBUL+STOCK+EXCHANGE)." ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
251×2 DataFrame
226 rows omitted
RowdateISE
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15-Jan-093.57537
26-Jan-092.54259
37-Jan-09-2.88617
48-Jan-09-6.22081
59-Jan-090.98599
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713-Jan-091.54453
814-Jan-09-4.11676
915-Jan-090.0661905
1016-Jan-092.20373
1119-Jan-09-2.26925
1220-Jan-09-1.37087
1321-Jan-090.0864697
⋮⋮⋮
24017-Dec-09-1.69489
24118-Dec-090.350124
24221-Dec-092.25302
24322-Dec-090.48947
24423-Dec-09-0.721131
24524-Dec-090.581665
24625-Dec-090.389112
24728-Dec-09-0.0811768
24829-Dec-090.322285
24930-Dec-09-0.227405
25031-Dec-092.21384
2514-Jan-101.02294
" ], "text/latex": [ "\\begin{tabular}{r|cc}\n", "\t& date & ISE\\\\\n", "\t\\hline\n", "\t& String15 & Float64\\\\\n", "\t\\hline\n", "\t1 & 5-Jan-09 & 3.57537 \\\\\n", "\t2 & 6-Jan-09 & 2.54259 \\\\\n", "\t3 & 7-Jan-09 & -2.88617 \\\\\n", "\t4 & 8-Jan-09 & -6.22081 \\\\\n", "\t5 & 9-Jan-09 & 0.98599 \\\\\n", "\t6 & 12-Jan-09 & -2.9191 \\\\\n", "\t7 & 13-Jan-09 & 1.54453 \\\\\n", "\t8 & 14-Jan-09 & -4.11676 \\\\\n", "\t9 & 15-Jan-09 & 0.0661905 \\\\\n", "\t10 & 16-Jan-09 & 2.20373 \\\\\n", "\t11 & 19-Jan-09 & -2.26925 \\\\\n", "\t12 & 20-Jan-09 & -1.37087 \\\\\n", "\t13 & 21-Jan-09 & 0.0864697 \\\\\n", "\t14 & 22-Jan-09 & -0.381506 \\\\\n", "\t15 & 23-Jan-09 & 0.566126 \\\\\n", "\t16 & 26-Jan-09 & 4.68313 \\\\\n", "\t17 & 27-Jan-09 & -0.663498 \\\\\n", "\t18 & 28-Jan-09 & 3.4567 \\\\\n", "\t19 & 29-Jan-09 & -2.05282 \\\\\n", "\t20 & 30-Jan-09 & -0.87767 \\\\\n", "\t21 & 2-Feb-09 & -2.59191 \\\\\n", "\t22 & 3-Feb-09 & 1.52795 \\\\\n", "\t23 & 4-Feb-09 & 1.85778 \\\\\n", "\t24 & 5-Feb-09 & -1.41329 \\\\\n", "\t$\\dots$ & $\\dots$ & $\\dots$ \\\\\n", "\\end{tabular}\n" ], "text/plain": [ "\u001b[1m251×2 DataFrame\u001b[0m\n", "\u001b[1m Row \u001b[0m│\u001b[1m date \u001b[0m\u001b[1m ISE \u001b[0m\n", " │\u001b[90m String15 \u001b[0m\u001b[90m Float64 \u001b[0m\n", "─────┼───────────────────────\n", " 1 │ 5-Jan-09 3.57537\n", " 2 │ 6-Jan-09 2.54259\n", " 3 │ 7-Jan-09 -2.88617\n", " 4 │ 8-Jan-09 -6.22081\n", " 5 │ 9-Jan-09 0.98599\n", " 6 │ 12-Jan-09 -2.9191\n", " 7 │ 13-Jan-09 1.54453\n", " 8 │ 14-Jan-09 -4.11676\n", " ⋮ │ ⋮ ⋮\n", " 245 │ 24-Dec-09 0.581665\n", " 246 │ 25-Dec-09 0.389112\n", " 247 │ 28-Dec-09 -0.0811768\n", " 248 │ 29-Dec-09 0.322285\n", " 249 │ 30-Dec-09 -0.227405\n", " 250 │ 31-Dec-09 2.21384\n", " 251 │ 4-Jan-10 1.02294\n", "\u001b[36m 236 rows omitted\u001b[0m" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Read CSV file\n", "df = DataFrame(CSV.File(\"../datasets/stock_exchange.csv\"))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can plot the evolution of the stock market values over time." ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "image/png": 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levels\n", "scatter(dates_num, \n", " stock_val, \n", " color=\"black\",\n", " label=\"\", \n", " ylabel=\"Stock Market Levels\", \n", " xlabel=\"time (days)\",\n", " xticks=(xtick_points, [dates_str[i] for i in xtick_points]), \n", " size=(800,300))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Model specification\n", "\n", "We have a date $x_i \\in \\mathbb{R}$, referred to as a \"covariate\" or input variable, and the value of the stock exchange at that time point $y_i \\in \\mathbb{R}$, referred to as a \"response\" or output variable. A regression model has parameters $\\theta$, used to predict $y = (y_1, \\dots, y_N)$ from $x = (x_1, \\dots, x_N)$. We are looking for a posterior distribution for the parameters $\\theta$:\n", "\n", "$$\\underbrace{p(\\theta \\mid y, x)}_{\\text{posterior}} \\propto\\ \\underbrace{p(y \\mid x, \\theta)}_{\\text{likelihood}} \\cdot \\underbrace{p(\\theta)}_{\\text{prior}}$$\n", "\n", "We assume each observation $y_i$ is generated via: \n", "\n", "$$ y_i = f_\\theta(x_i) + e_i$$ \n", "\n", "where $e_i$ is white noise, $e_i \\sim \\mathcal{N}(0, \\sigma^2_y)$, and the regression function $f_\\theta$ is linear: $f_\\theta(x) = x \\theta_1 + \\theta_2$. The parameters consist of a slope coefficient $\\theta_1$ and an intercept $\\theta_2$, which are summarized into the vector $\\theta = \\begin{bmatrix}\\theta_1 \\\\ \\theta_2 \\end{bmatrix}$. In practice, we augment the data point $x$ with a 1, i.e., $\\begin{bmatrix}x \\\\ 1 \\end{bmatrix}$, so that we may define $f_\\theta(x) = \\theta^{\\top}x$. \n", "\n", "#### Likelihood\n", "If we integrate out the noise $e$, then we obtain a Gaussian likelihood function centered on $f_\\theta(x)$ with variance $\\sigma^2_Y$:\n", "\n", "$$p(y_i \\mid x_i, \\theta) = \\mathcal{N}(y_i \\mid f_\\theta(x_i),\\sigma^2_y)\\, \\ .$$ \n", "\n", "But this is just for a single sample and we have an entire data set. The likelihood of all $(x,y)$ is:\n", "\n", "$$\\begin{aligned} p(y \\mid x, \\theta) &= \\prod_{i=1}^{N} p(y_i \\mid x_i, \\theta) \\\\ & = \\prod_{i=1}^{N} \\mathcal{N}(y_i \\mid f_{\\theta}(x_i), \\sigma^2_y) \\, . \\end{aligned} $$ \n", "\n", "#### Prior distribution\n", "We know that the weights are real numbers and that they can be negative. That motivates us to use a Gaussian prior:\n", "\n", "$$ p(\\theta) = \\mathcal{N}(\\theta \\mid \\mu_\\theta, \\Sigma_\\theta) \\, .$$\n", "\n", "We can specify these equations almost directly in our PPL." ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [], "source": [ "@model function linear_regression(y, X, μ_θ, Σ_θ, σ2, N)\n", " \"Bayesian linear regression\"\n", " \n", " # Prior distribution of coefficients\n", " θ ~ MvNormalMeanCovariance(μ_θ, Σ_θ)\n", " \n", " for i = 1:N\n", "\n", " # Likelihood of i-th sample\n", " y[i] ~ NormalMeanVariance(dot(θ,X[i]), σ2)\n", " \n", " end\n", "end" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "3.2657337986971937" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Prior parameters\n", "μ_θ, Σ_θ = (zeros(2), diagm(ones(2)))\n", "\n", "# Likelihood variance\n", "σ2_y = var(stock_val)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now that we have our model, it is time to infer parameters." ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Inference results:\n", " Posteriors | available for (θ)\n" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "results = infer(\n", " model = linear_regression(μ_θ=μ_θ, Σ_θ=Σ_θ, σ2=σ2_y, N=num_samples),\n", " data = (y = stock_val, X = [[dates_num[i], 1.0] for i in 1:num_samples]),\n", ")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's visualize the resulting posterior." ] }, { "cell_type": "code", "execution_count": 8, "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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"\n", "We can extract the MAP point estimate to compute and visualize the most probable regression function $f_\\theta$." ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Slope coefficient = 0.000941327449846718\n", "Intercept coefficient = 0.15081258570809555\n" ] } ], "source": [ "# Extract estimated weights\n", "θ_MAP = mode(post_θ)\n", "θ_Σ = cov( post_θ)\n", "\n", "# Report results\n", "println(\"Slope coefficient = \"*string(θ_MAP[1]))\n", "println(\"Intercept coefficient = \"*string(θ_MAP[2]))\n", "\n", "# Make predictions\n", "regression_estimated = zeros(num_samples)\n", "regression_uncertainty = zeros(num_samples) \n", "for (i,date) in enumerate(dates_num)\n", " regression_estimated[i] = date * θ_MAP[1] .+ θ_MAP[2];\n", " regression_uncertainty[i] = [date, 1.]' *θ_Σ * [date, 1.] + σ2_y\n", "end" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ " Let's visualize the estimated regression function." ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "image/png": 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ribbon=regression_uncertainty, color=\"blue\", label=\"regression\", size=(800,300))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The slope coefficient $\\theta_1$ is nearly zero and the plot shows a horizontal line. So the ISE did not experienced a decline, but also did not grow in 2009. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "---\n", "\n", "#### Exercise\n", "\n", "Change the `time period` variable. Re-run the regression and see how the results change." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "---" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Forecasting\n", "\n", "We've answered the Turkish government's question. But before they change their country's economic policy, they want to know what the future looks like if the stock market continues on this trend. In other words, they want us to make predictions for future outputs given our current regression coefficient estimates.\n", "\n", "We can request the toolbox to make predictions for future outputs by providing `missing` data points." ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
251×2 DataFrame
226 rows omitted
RowdateISE
String15Missing
15-Jan-10missing
26-Jan-10missing
37-Jan-10missing
48-Jan-10missing
511-Jan-10missing
612-Jan-10missing
713-Jan-10missing
814-Jan-10missing
915-Jan-10missing
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24831-Dec-10missing
2493-Jan-11missing
2504-Jan-11missing
2515-Jan-11missing
" ], "text/latex": [ "\\begin{tabular}{r|cc}\n", "\t& date & ISE\\\\\n", "\t\\hline\n", "\t& String15 & Missing\\\\\n", "\t\\hline\n", "\t1 & 5-Jan-10 & \\emph{missing} \\\\\n", "\t2 & 6-Jan-10 & \\emph{missing} \\\\\n", "\t3 & 7-Jan-10 & \\emph{missing} \\\\\n", "\t4 & 8-Jan-10 & \\emph{missing} \\\\\n", "\t5 & 11-Jan-10 & \\emph{missing} \\\\\n", "\t6 & 12-Jan-10 & \\emph{missing} \\\\\n", "\t7 & 13-Jan-10 & \\emph{missing} \\\\\n", "\t8 & 14-Jan-10 & \\emph{missing} \\\\\n", "\t9 & 15-Jan-10 & \\emph{missing} \\\\\n", "\t10 & 18-Jan-10 & \\emph{missing} \\\\\n", "\t11 & 19-Jan-10 & \\emph{missing} \\\\\n", "\t12 & 20-Jan-10 & \\emph{missing} \\\\\n", "\t13 & 21-Jan-10 & \\emph{missing} \\\\\n", "\t14 & 22-Jan-10 & \\emph{missing} \\\\\n", "\t15 & 25-Jan-10 & \\emph{missing} \\\\\n", "\t16 & 26-Jan-10 & \\emph{missing} \\\\\n", "\t17 & 27-Jan-10 & \\emph{missing} \\\\\n", "\t18 & 28-Jan-10 & \\emph{missing} \\\\\n", "\t19 & 29-Jan-10 & \\emph{missing} \\\\\n", "\t20 & 1-Feb-10 & \\emph{missing} \\\\\n", "\t21 & 2-Feb-10 & \\emph{missing} \\\\\n", "\t22 & 3-Feb-10 & \\emph{missing} \\\\\n", "\t23 & 4-Feb-10 & \\emph{missing} \\\\\n", "\t24 & 5-Feb-10 & \\emph{missing} \\\\\n", "\t$\\dots$ & $\\dots$ & $\\dots$ \\\\\n", "\\end{tabular}\n" ], "text/plain": [ "\u001b[1m251×2 DataFrame\u001b[0m\n", "\u001b[1m Row \u001b[0m│\u001b[1m date \u001b[0m\u001b[1m ISE \u001b[0m\n", " │\u001b[90m String15 \u001b[0m\u001b[90m Missing \u001b[0m\n", "─────┼────────────────────\n", " 1 │ 5-Jan-10 \u001b[90m missing \u001b[0m\n", " 2 │ 6-Jan-10 \u001b[90m missing \u001b[0m\n", " 3 │ 7-Jan-10 \u001b[90m missing \u001b[0m\n", " 4 │ 8-Jan-10 \u001b[90m missing \u001b[0m\n", " 5 │ 11-Jan-10 \u001b[90m missing \u001b[0m\n", " 6 │ 12-Jan-10 \u001b[90m missing \u001b[0m\n", " 7 │ 13-Jan-10 \u001b[90m missing \u001b[0m\n", " 8 │ 14-Jan-10 \u001b[90m missing \u001b[0m\n", " ⋮ │ ⋮ ⋮\n", " 245 │ 28-Dec-10 \u001b[90m missing \u001b[0m\n", " 246 │ 29-Dec-10 \u001b[90m missing \u001b[0m\n", " 247 │ 30-Dec-10 \u001b[90m missing \u001b[0m\n", " 248 │ 31-Dec-10 \u001b[90m missing \u001b[0m\n", " 249 │ 3-Jan-11 \u001b[90m missing \u001b[0m\n", " 250 │ 4-Jan-11 \u001b[90m missing \u001b[0m\n", " 251 │ 5-Jan-11 \u001b[90m missing \u001b[0m\n", "\u001b[36m 236 rows omitted\u001b[0m" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "future = DataFrame(CSV.File(\"../datasets/stock_futures.csv\"))" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Inference results:\n", " Posteriors | available for (θ)\n", " Predictions | available for (y)\n" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "all_N = num_samples + length(future[!,:date])\n", "all_d = [df[!,:date]; future[!,:date]]\n", "all_y = [stock_val; future[!,:ISE]]\n", "all_X = [[i, 1.0] for i in 1:all_N]\n", "\n", "results = infer(\n", " model = linear_regression(μ_θ=μ_θ, Σ_θ=Σ_θ, σ2=σ2_y, N=all_N),\n", " data = (y = all_y, X = all_X,),\n", " predictvars = (y = KeepLast(),),\n", ")" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Final predicted stock value = 0.6233589655311479 (±3.6142682793047856)\n" ] } ], "source": [ "regression_estimated = mode.(results.predictions[:y])\n", "regression_uncertainty = 2std.(results.predictions[:y]) # 2 standard deviations\n", "\n", "final_prediction = regression_estimated[end]\n", "final_uncertainty = regression_uncertainty[end]\n", "println(\"Final predicted stock value = $final_prediction (±$final_uncertainty)\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Although the prediction itself is positive, its uncertainty tells us that we should not trust this result too much. Let's see what this looks like in a plot." ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "data": { "image/png": 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"scatter!(dates_str, stock_val, color=\"black\", label=\"observations\")\n", "vline!([251], color=\"green\", linewidth=5, linestyle=:dash)\n", "\n", "# Overlay regression function\n", "plot!(1:all_N, regression_estimated, ribbon=regression_uncertainty, color=\"blue\", label=\"regression\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The ribbon is relatively wide. This tells us that the future looks uncertain for the stock market." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Problem: Medical Diagnosis\n", "\n", "A company is trying to develop a measurement device that tells a patient whether they suffer from Chronic Obstructive Pulmonary Disease (COPD). They believe they can detect certain compounds in a saliva sample that indicate the presence of COPD. To test the device, they collect data from both COPD patients and healthy controls. They train a classifier and make predictions on a test sample. If the diagnosis can be accurately predicted, then the new device is deemed an informative tool and will be brought to market." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Data\n", "\n", "The data set comes from the [UCI ML Repository](https://archive.ics.uci.edu/dataset/523/exasens). It contains measurements of 79 participants, split into 40 samples for training and 39 for testing. The columns in the data file marked _:x_ are biometric features (x1,x2 = measured signal, x3 = gender, x4 = age, x5 = smoking) and the final column marked _:y_ is the diagnosis (healthy control =0, COPD =1)." ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [], "source": [ "# Read CSV file\n", "train_data = DataFrame(CSV.File(\"../datasets/diagnosis_train.csv\"))\n", "\n", "# Split dataframe into features and labels\n", "features_train = Matrix(train_data[:,1:5])\n", "labels_train = Vector(train_data[:,6])\n", "\n", "# Store number of features\n", "num_features = size(features_train,2)\n", "\n", "# Number of training samples\n", "num_train = size(features_train,1);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's have a look at measurements from the device." ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "data": { "image/png": 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Are these measurements really informative?" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "---\n", "\n", "#### Exercise\n", "\n", "The plot above shows features 1 and 2. Have a look at the other combinations of features.\n", "\n", "---" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Model specification\n", "\n", "We have features $X$, labels $Y$ and parameters $\\theta$. Same as with regression, we are looking for a posterior distribution of the classification parameters:\n", "\n", "$$\\underbrace{p(\\theta \\mid Y, X)}_{\\text{posterior}} \\propto\\ \\underbrace{p(Y \\mid X, \\theta)}_{\\text{likelihood}} \\cdot \\underbrace{p(\\theta)}_{\\text{prior}}$$\n", "\n", "The likelihood in this case will be of a probit form:\n", "\n", "$$ p(Y \\mid X, \\theta) = \\prod_{i=1}^{N} \\ \\mathcal{B} \\big(Y_i \\mid \\Phi(f_\\theta(X_i) \\big) \\, .$$ \n", "\n", "As you can see it is a Bernoulli distribution with a cumulative normal distribution as transfer (a.k.a. _link_) function: \n", "\n", "$$ \\Phi(x) = \\frac{1}{\\sqrt{2\\pi}} \\int_{-\\infty}^{x} \\exp \\left(-\\frac{t^2}{2} \\right) \\mathrm{d}t \\, .$$ \n", "\n", "The transfer function maps the input ($f_\\theta(X_i)$) to the interval $(0,1)$ so that the result acts as a rate parameter to the Bernoulli. Check Bert's lecture on discriminative classification for more information.\n", "\n", "We will use a Gaussian prior distribution for the classification parameters $\\theta$:\n", "\n", "$$ p(\\theta) = \\mathcal{N}(\\theta \\mid \\mu_\\theta, \\Sigma_\\theta) \\, .$$\n", "\n", "You have probably noticed that this combination of likelihood and prior is not part of the family of conjugate pairings. As such, we don't have an exact posterior. The Laplace approximation is one procedure but under the hood, our toolbox is actually performing a different procedure for obtaining the posterior parameters: [moment matching](https://en.wikipedia.org/wiki/Method_of_moments_(statistics)). The cumulative normal distribution allows for integrating the product of prior and likelihood by hand, with respect to the first (mean) and second (variance) moments. The toolbox is essentially performing a lookup for the analytically derived formula, which computationally cheaper than performing the iterative steps necessary for the Laplace approximation." ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [], "source": [ "# Parameters for priors\n", "μ_θ = zeros(num_features+1,)\n", "Σ_θ = diagm(ones(num_features+1));" ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [], "source": [ "@model function linear_classification(y,X, μ_θ, Σ_θ, N)\n", " \"Bayesian classification model\"\n", " \n", " # Weight prior distribution\n", " θ ~ MvNormalMeanCovariance(μ_θ, Σ_θ)\n", " \n", " # Binary likelihood\n", " for i = 1:N\n", "\n", " y[i] ~ Probit(dot(θ, X[i]))\n", "\n", " end\n", "end" ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Inference results:\n", " Posteriors | available for (θ)\n" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "results = infer(\n", " model = linear_classification(μ_θ=μ_θ, Σ_θ=Σ_θ, N=num_train),\n", " data = (y = labels_train, X = [[features_train[i,:]; 1.0] for i in 1:num_train]),\n", " returnvars = (θ = KeepLast()),\n", " iterations = 10,\n", ")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Unfortunately, we cannot visualize a distribution of more than 2 dimensions. But we can visualize a pair of dimensions:" ] }, { "cell_type": "code", "execution_count": 20, "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", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", " \n", " \n", " \n", "\n", "\n", "\n", "\n", "\n", "\n" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Coefficients to visualize\n", "cix = [1,2]\n", "\n", "# Reduce posterior distribution to chosen dimensions\n", "m_cix = mean(results.posteriors[:θ])[cix]\n", "S_cix = cov( results.posteriors[:θ])[cix,cix]\n", "post_θ = MvNormal(m_cix, S_cix)\n", "\n", "# Reduce prior distribution to chosen dimensions\n", "prior_θ = MvNormal(μ_θ[cix], Σ_θ[cix,cix])\n", "\n", "# Define ranges for plot\n", "x1 = range(-1., length=500, stop=1.)\n", "x2 = range(-1., length=500, stop=1.)\n", "\n", "# Draw contour plots of distributions\n", "p1a = contour(x1, x2, (x1,x2) -> pdf(prior_θ, [x1,x2]), levels=3, xlabel=\"θ1\", ylabel=\"θ2\", title=\"prior\", label=\"\")\n", "p1b = contour(x1, x2, (x1,x2) -> pdf(post_θ, [x1,x2]), levels=3, xlabel=\"θ1\", title=\"posterior\", label=\"\")\n", "plot(p1a, p1b, size=(900,300))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Predict test data\n", "\n", "The device should make accurate predictions for future patients. We can evaluate this with a test data set." ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [], "source": [ "# Read CSV file\n", "test_data = DataFrame(CSV.File(\"../datasets/diagnosis_test.csv\"))\n", "\n", "# Split dataframe into features and labels\n", "features_test = Matrix(test_data[:,1:5])\n", "labels_test = Vector(test_data[:,6])\n", "\n", "# Number of test samples\n", "num_test = size(features_test,1);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can generate the most probable class labels by extracting the most probable classifier weights, calculating the dot product with the test feature vectors, and applying the Probit node's link function. This produces the class label probability and by rounding we get hard assignments to $0$ or $1$. This can be checked against the true test labels." ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Test Accuracy = 92.3076923076923%\n" ] } ], "source": [ "# Extract MAP estimate of classification parameters\n", "θ_MAP = mode(results.posteriors[:θ])\n", "\n", "# Compute dot product between parameters and test data\n", "fθ_pred = [features_test ones(num_test,)] * θ_MAP\n", "\n", "# Predict labels through probit\n", "labels_pred = round.(normcdf.(fθ_pred));\n", "\n", "# Compute classification accuracy of test data\n", "accuracy_test = mean(labels_test .== labels_pred)\n", "\n", "# Report result\n", "println(\"Test Accuracy = \"*string(accuracy_test*100)*\"%\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Those predictions are very accurate. So, is the device informative after all?" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "---\n", "\n", "#### Exercise\n", "\n", "Re-run the classifier on just the saliva measurement features. Does the accuracy drop? And if so, should the device be used?\n", "\n", "---" ] } ], "metadata": { "@webio": { "lastCommId": null, "lastKernelId": null }, "anaconda-cloud": {}, "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 }