{ "cells": [ { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "# Generative Classification" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "### Preliminaries\n", "\n", "- Goal \n", " - Introduction to linear generative classification with a Gaussian-categorical generative model\n", " \n", "- Materials \n", " - Mandatory\n", " - These lecture notes\n", " - Optional\n", " - Bishop pp. 196-202 (section 4.2 focusses on binary classification, whereas in these lecture notes we describe generative classification for multiple classes). " ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "### Challenge: an apple or a peach?\n", "\n", "- **Problem**: You're given numerical values for the skin features roughness and color for 200 pieces of fruit, where for each piece of fruit you also know if it is an apple or a peach. Now you receive the roughness and color values for a new piece of fruit but you don't get its class label (apple or peach). What is the probability that the new piece is an apple?" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "- **Solution**: To be solved later in this lesson.\n", "\n", "- Let's first generate a data set (see next slide)." ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "\u001b[32m\u001b[1m Activating\u001b[22m\u001b[39m project at `~/github/bertdv/BMLIP/lessons`\n" ] } ], "source": [ "using Pkg; Pkg.activate(\"../.\"); Pkg.instantiate();\n", "using IJulia; try IJulia.clear_output(); catch _ end" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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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", "\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", "\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": [ "using Plots, Distributions\n", "\n", "N = 250; p_apple = 0.7; Σ = [0.2 0.1; 0.1 0.3]\n", "p_given_apple = MvNormal([1.0, 1.0], Σ) # p(X|y=apple)\n", "p_given_peach = MvNormal([1.7, 2.5], Σ) # p(X|y=peach)\n", "X = Matrix{Float64}(undef,2,N); y = Vector{Bool}(undef,N) # true corresponds to apple\n", "for n=1:N\n", " y[n] = (rand() < p_apple) # Apple or peach?\n", " X[:,n] = y[n] ? rand(p_given_apple) : rand(p_given_peach) # Sample features\n", "end\n", "X_apples = X[:,findall(y)]'; X_peaches = X[:,findall(.!y)]' # Sort features on class\n", "x_test = [2.3; 1.5] # Features of 'new' data point\n", "\n", "scatter(X_apples[:,1], X_apples[:,2], label=\"apples\", marker=:x, markerstrokewidth=3) # apples\n", "scatter!(X_peaches[:,1], X_peaches[:,2], label=\"peaches\", marker=:+, markerstrokewidth=3) # peaches\n", "scatter!([x_test[1]], [x_test[2]], label=\"unknown\") # 'new' unlabelled data point\n" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "### Generative Classification Problem Statement\n", "\n", "- Given is a data set $D = \\{(x_1,y_1),\\dotsc,(x_N,y_N)\\}$\n", " - inputs $x_n \\in \\mathbb{R}^M$ are called **features**.\n", " - outputs $y_n \\in \\mathcal{C}_k$, with $k=1,\\ldots,K$; The **discrete** targets $\\mathcal{C}_k$ are called **classes**." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "- We will again use the 1-of-$K$ notation for the discrete classes. Define the binary **class selection variable**\n", "$$\n", "y_{nk} = \\begin{cases} 1 & \\text{if } \\, y_n \\in \\mathcal{C}_k\\\\\n", "0 & \\text{otherwise} \\end{cases}\n", "$$\n", " - (Hence, the notations $y_{nk}=1$ and $y_n \\in \\mathcal{C}_k$ mean the same thing.)" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "- The plan for generative classification: build a model for the joint pdf $p(x,y)= p(x|y)p(y)$ and use Bayes to infer the posterior class probabilities \n", "\n", "$$\n", "p(y|x) = \\frac{p(x|y) p(y)}{\\sum_{y^\\prime} p(x|y^\\prime) p(y^\\prime)} \\propto p(x|y)\\,p(y)\n", "$$" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "### 1 - Model specification \n", "\n", "##### Likelihood\n", "\n", "- Assume Gaussian **class-conditional distributions** with **equal covariance matrix** across the classes,\n", " $$\n", " p(x_n|\\mathcal{C}_{k}) = \\mathcal{N}(x_n|\\mu_k,\\Sigma)\n", " $$\n", "with notational shorthand: $\\mathcal{C}_{k} \\triangleq (y_n \\in \\mathcal{C}_{k})$." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "##### Prior\n", "\n", "- We use a categorical distribution for the class labels $y_{nk}$: \n", "$$p(\\mathcal{C}_{k}) = \\pi_k$$\n", "\n" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "- Hence, using the one-hot coding formulation for $y_{nk}$, the generative model $p(x_n,y_n)$ can be written as\n", "\n", "$$\\begin{align*}\n", " p(x_n,y_n) &= \\prod_{k=1}^K p(x_n,y_{nk}=1)^{y_{nk}} \\\\\n", " &= \\prod_{k=1}^K \\left( \\pi_k \\cdot\\mathcal{N}(x_n|\\mu_k,\\Sigma)\\right)^{y_{nk}}\n", "\\end{align*}$$\n" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "- We will refer to this model as the **Gaussian-Categorical Model** (GCM). \n", " - N.B. In the literature, this model (with possibly unequal $\\Sigma_k$ across classes) is often called the Gaussian Discriminant Analysis model and the special case with equal covariance matrices $\\Sigma_k=\\Sigma$ is also called Linear Discriminant Analysis. We think these names are a bit unfortunate as it may lead to confusion with the [discriminative method for classification](https://nbviewer.org/github/bertdv/BMLIP/blob/master/lessons/notebooks/Discriminative-Classification.ipynb)." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "- As usual, once the model has been specified, the rest (inference for parameters and model prediction) through straight probability theory." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "### Computing the log-likelihood\n", "\n", "- The log-likelihood given the full data set $D=\\{(x_n,y_n), n=1,2,\\ldots,N\\}$ is then\n", "$$\\begin{align*}\n", "\\log\\, p(D|\\theta) &\\stackrel{\\text{IID}}{=} \\sum_n \\log \\prod_k p(x_n,y_{nk}=1\\,|\\,\\theta)^{y_{nk}} \\\\\n", " &= \\sum_{n,k} y_{nk} \\log p(x_n,y_{nk}=1\\,|\\,\\theta) \\\\\n", " &= \\sum_{n,k} y_{nk} \\log p(x_n|y_{nk}=1) + \\sum_{n,k} y_{nk} \\log p(y_{nk}=1) \\\\\n", " &= \\sum_{n,k} y_{nk} \\log\\mathcal{N}(x_n|\\mu_k,\\Sigma) + \\sum_{n,k} y_{nk} \\log \\pi_k \\\\\n", " &= \\sum_{n,k} y_{nk} \\underbrace{ \\log\\mathcal{N}(x_n|\\mu_k,\\Sigma) }_{ \\text{see Gaussian lecture} } + \\underbrace{ \\sum_k m_k \\log \\pi_k }_{ \\text{see multinomial lecture} } \n", "\\end{align*}$$\n", "where we used $m_k \\triangleq \\sum_n y_{nk}$." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "### 2 - Parameter Inference for Classification\n", "\n", "- We'll do Maximum Likelihood estimation for $\\theta = \\{ \\pi_k, \\mu_k, \\Sigma \\}$ from data $D$." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "- Recall (from the previous slide) the log-likelihood (LLH)\n", "\n", "$$\n", "\\log\\, p(D|\\theta) = \\sum_{n,k} y_{nk} \\underbrace{ \\log\\mathcal{N}(x_n|\\mu_k,\\Sigma) }_{ \\text{Gaussian} } + \\underbrace{ \\sum_k m_k \\log \\pi_k }_{ \\text{multinomial} } \n", "$$" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "- Maximization of the LLH for the GDA model breaks down into\n", " - **Gaussian density estimation** for parameters $\\mu_k, \\Sigma$, since the first term contains exactly the log-likelihood for MVG density estimation. We've already done this, see the [Gaussian distribution lesson](https://nbviewer.jupyter.org/github/bertdv/BMLIP/blob/master/lessons/notebooks/The-Gaussian-Distribution.ipynb#ML-for-Gaussian).\n", " - **Multinomial density estimation** for class priors $\\pi_k$, since the second term holds exactly the log-likelihood for multinomial density estimation, see the [Multinomial distribution lesson](https://nbviewer.jupyter.org/github/bertdv/BMLIP/blob/master/lessons/notebooks/The-Multinomial-Distribution.ipynb#ML-for-multinomial). \n", " " ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ " - The ML for multinomial class prior (we've done this before!)\n", "$$\\begin{align*} \n", "\\hat \\pi_k = \\frac{m_k}{N} \n", "\\end{align*}$$" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "- Now group the data into separate classes and do MVG ML estimation for class-conditional parameters (we've done this before as well):\n", "$$\\begin{align*}\n", " \\hat \\mu_k &= \\frac{ \\sum_n y_{nk} x_n} { \\sum_n y_{nk} } = \\frac{1}{m_k} \\sum_n y_{nk} x_n \\\\\n", " \\hat \\Sigma &= \\frac{1}{N} \\sum_{n,k} y_{nk} (x_n-\\hat \\mu_k)(x_n-\\hat \\mu_k)^T \\\\\n", " &= \\sum_k \\hat \\pi_k \\cdot \\underbrace{ \\left( \\frac{1}{m_k} \\sum_{n} y_{nk} (x_n-\\hat \\mu_k)(x_n-\\hat \\mu_k)^T \\right) }_{ \\text{class-cond. variance} } \\\\\n", " &= \\sum_k \\hat \\pi_k \\cdot \\hat \\Sigma_k\n", "\\end{align*}$$\n", "where $\\hat \\pi_k$, $\\hat{\\mu}_k$ and $\\hat{\\Sigma}_k$ are the sample proportion, sample mean and sample variance for the $k$th class, respectively." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "- Note that the binary class selection variable $y_{nk}$ groups data from the same class." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "### 3 - Application: Class prediction for new Data\n", "\n", "- Let's apply the trained model to predict the class for given a 'new' input $x_\\bullet$:\n", "$$\\begin{align*}\n", "p(\\mathcal{C}_k|x_\\bullet,D ) &= \\int p(\\mathcal{C}_k|x_\\bullet,\\theta ) \\underbrace{p(\\theta|D)}_{\\text{ML: }\\delta(\\theta - \\hat{\\theta})} \\mathrm{d}\\theta \\\\\n", "&= p(\\mathcal{C}_k|x_\\bullet,\\hat{\\theta} ) \\\\\n", "&\\propto p(\\mathcal{C}_k)\\,p(x_\\bullet|\\mathcal{C}_k) \\\\\n", "&= \\hat{\\pi}_k \\cdot \\mathcal{N}(x_\\bullet | \\hat{\\mu}_k, \\hat{\\Sigma}) \\\\\n", " &\\propto \\hat{\\pi}_k \\exp \\left\\{ { - {\\frac{1}{2}}(x_\\bullet - \\hat{\\mu}_k )^T \\hat{\\Sigma}^{ - 1} (x_\\bullet - \\hat{\\mu}_k )} \\right\\}\\\\\n", " &=\\exp \\Big\\{ \\underbrace{-\\frac{1}{2}x_\\bullet^T \\hat{\\Sigma}^{ - 1} x_\\bullet}_{\\text{not a function of }k} + \\underbrace{\\hat{\\mu}_k^T \\hat{\\Sigma}^{-1}}_{\\beta_k^T} x_\\bullet \\underbrace{- {\\frac{1}{2}}\\hat{\\mu}_k^T \\hat{\\Sigma}^{ - 1} \\hat{\\mu}_k + \\log \\hat{\\pi}_k }_{\\gamma_k} \\Big\\} \\\\\n", " &\\propto \\frac{1}{Z}\\exp\\{\\beta_k^T x_\\bullet + \\gamma_k\\} \\\\\n", " &\\triangleq \\sigma\\left( \\beta_k^T x_\\bullet + \\gamma_k\\right)\n", "\\end{align*}$$\n", "where \n", "$\\sigma(a_k) \\triangleq \\frac{\\exp(a_k)}{\\sum_{k^\\prime}\\exp(a_{k^\\prime})}$ is called a [**softmax**](https://en.wikipedia.org/wiki/Softmax_function) (a.k.a. **normalized exponential**) function, and\n", "$$\\begin{align*}\n", "\\beta_k &= \\hat{\\Sigma}^{-1} \\hat{\\mu}_k \\\\\n", "\\gamma_k &= - \\frac{1}{2} \\hat{\\mu}_k^T \\hat{\\Sigma}^{-1} \\hat{\\mu}_k + \\log \\hat{\\pi}_k \\\\\n", "Z &= \\sum_{k^\\prime}\\exp\\{\\beta_{k^\\prime}^T x_\\bullet + \\gamma_{k^\\prime}\\}\\,. \\quad \\text{(normalization constant)} \n", "\\end{align*}$$" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "- The softmax function is a smooth approximation to the max-function. Note that we did not a priori specify a softmax posterior, but rather it followed from applying Bayes rule to the prior and likelihood assumptions. " ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "- Note the following properties of the softmax function $\\sigma(a_k)$:\n", " - $\\sigma(a_k)$ is monotonicaly ascending function and hence it preserves the order of $a_k$. That is, if $a_j>a_k$ then $\\sigma(a_j)>\\sigma(a_k)$. \n", " - $\\sigma(a_k)$ is always a proper probability distribution, since $\\sigma(a_k)>0$ and $\\sum_k \\sigma(a_k) = 1$. \n", " " ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "### Discrimination Boundaries\n", "\n", "- The class log-posterior $\\log p(\\mathcal{C}_k|x) \\propto \\beta_k^T x + \\gamma_k$ is a linear function of the input features." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "- Thus, the contours of equal probability (**discriminant functions**) are lines (hyperplanes) in the feature space\n", "$$\n", "\\log \\frac{{p(\\mathcal{C}_k|x,\\theta )}}{{p(\\mathcal{C}_j|x,\\theta )}} = \\beta_{kj}^T x + \\gamma_{kj} = 0\n", "$$\n", "where we defined $\\beta_{kj} \\triangleq \\beta_k - \\beta_j$ and similarly for $\\gamma_{kj}$." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "- How to classify a new input $x_\\bullet$? The Bayesian answer is a posterior distribution $ p(\\mathcal{C}_k|x_\\bullet)$. If you must choose, then the class with maximum posterior class probability\n", "$$\\begin{align*}\n", "k^* &= \\arg\\max_k p(\\mathcal{C}_k|x_\\bullet) \\\\\n", " &= \\arg\\max_k \\left( \\beta _k^T x_\\bullet + \\gamma_k \\right)\n", "\\end{align*}$$\n", "is an appealing decision. " ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "### Code Example: Working out the \"apple or peach\" example problem\n", "\n", "We'll apply the above results to solve the \"apple or peach\" example problem." ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "p(apple|x=x∙) = 0.758239422055906\n" ] }, { "data": { "image/png": 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Distributions, Plots\n", "# Multinomial (in this case binomial) density estimation\n", "p_apple_est = sum(y.==true) / length(y)\n", "π_hat = [p_apple_est; 1-p_apple_est]\n", "\n", "# Estimate class-conditional multivariate Gaussian densities\n", "d1 = fit_mle(FullNormal, X_apples') # MLE density estimation d1 = N(μ₁, Σ₁)\n", "d2 = fit_mle(FullNormal, X_peaches') # MLE density estimation d2 = N(μ₂, Σ₂)\n", "Σ = π_hat[1]*cov(d1) + π_hat[2]*cov(d2) # Combine Σ₁ and Σ₂ into Σ\n", "conditionals = [MvNormal(mean(d1), Σ); MvNormal(mean(d2), Σ)] # p(x|C)\n", "\n", "# Calculate posterior class probability of x∙ (prediction)\n", "function predict_class(k, X) # calculate p(Ck|X)\n", " norm = π_hat[1]*pdf(conditionals[1],X) + π_hat[2]*pdf(conditionals[2],X)\n", " return π_hat[k]*pdf(conditionals[k], X) ./ norm\n", "end\n", "println(\"p(apple|x=x∙) = $(predict_class(1,x_test))\")\n", "\n", "# Discrimination boundary of the posterior (p(apple|x;D) = p(peach|x;D) = 0.5)\n", "β(k) = inv(Σ)*mean(conditionals[k])\n", "γ(k) = -0.5 * mean(conditionals[k])' * inv(Σ) * mean(conditionals[k]) + log(π_hat[k])\n", "function discriminant_x2(x1)\n", " # Solve discriminant equation for x2\n", " β12 = β(1) .- β(2)\n", " γ12 = (γ(1) .- γ(2))[1,1]\n", " return -1*(β12[1]*x1 .+ γ12) ./ β12[2]\n", "end\n", "\n", "scatter(X_apples[:,1], X_apples[:,2], label=\"apples\", marker=:x, markerstrokewidth=3) # apples\n", "scatter!(X_peaches[:,1], X_peaches[:,2], label=\"peaches\", marker=:+, markerstrokewidth=3) # peaches\n", "scatter!([x_test[1]], [x_test[2]], label=\"unknown\") # 'new' unlabelled data point\n", "\n", "x1 = range(-1,length=10,stop=3)\n", "plot!(x1, discriminant_x2(x1), color=\"black\", label=\"\") # Plot discrimination boundary\n", "plot!(x1, discriminant_x2(x1), fillrange=-10, alpha=0.2, color=:blue, label=\"\")\n", "plot!(x1, discriminant_x2(x1), fillrange=10, alpha=0.2, color=:red, xlims=(-0.5, 3), ylims=(-1, 4), label=\"\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Why Be Bayesian?\n", "\n", "- A student in one of the previous years posed the following question at Piazza: \n", " \n", " > \" After re-reading topics regarding generative classification, this question popped into my mind: Besides the sole purpose of the lecture, which is getting to know the concepts of generative classification and how to implement them, are there any advantages of using this instead of using deep neural nets? DNNs seem simpler and more powerful.\"\n", "\n", "- The following answer was provided: \n", "\n", " - If you are only are interested in approximating a function, say $y=f_\\theta(x)$, and you have lots of examples $\\{(x_i,y_i)\\}$ of desired behavior, then often a non-probabilistic DNN is a fine approach.\n", "\n", " - However, if you are willing to formulate your models in a probabilistic framework, you can improve on the deterministic approach in many ways, eg,\n", "\n", " > 1. Bayesian evidence for model performance assessment. This means you can use the whole data set for training without an ad-hoc split into testing and training data sets.\n", "\n", " > 2. Uncertainty about parameters in the model is a measure that allows you to do _active learning_, ie, choose data that is most informative (see also the [lesson on intelligent agents](https://nbviewer.org/github/bertdv/BMLIP/blob/master/lessons/notebooks/Intelligent-Agents-and-Active-Inference.ipynb)). This will allow you to train on small data sets, whereas the deterministic DNNs generally require much larger data sets.\n", " \n", " > 3. Prediction with uncertainty/confidence bounds.\n", " \n", " > 4. Explicit specification and separation of your assumptions.\n", " \n", " > 5. A framework that supports scoring both accuracy and model complexity in the same currency (probability). How are you going to penalize the size of your network in a deterministic framework?\n", " \n", " > 6. Automatic learning rates, no tuning parameters. For instance, the Kalman gain is a data-dependent, optimal learning rate. How will _you_ choose your learning rates in a deterministic framework? Trial and error?\n", " \n", " > 7. Principled absorption of different sources of knowledge. Eg, outcome of one set of experiments can be captured by a posterior distribution that serves as a prior distribution for the next set of experiments.\n", " \n", " > Admittedly, it's not easy to understand the probabilistic approach, but it is worth the effort.\n", "\n", "\n", "\n", "\n" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "### Recap Generative Classification\n", "\n", "- Gaussian-Categorical Model specification: \n", "\n", "$$p(x,\\mathcal{C}_k|\\,\\theta) = \\pi_k \\cdot \\mathcal{N}(x|\\mu_k,\\Sigma)$$" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "- If the class-conditional distributions are Gaussian with equal covariance matrices across classes ($\\Sigma_k = \\Sigma$), then\n", " the discriminant functions are hyperplanes in feature space." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "- ML estimation for $\\{\\pi_k,\\mu_k,\\Sigma\\}$ in the GCM model breaks down to simple density estimation for Gaussian and multinomial/categorical distributions." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "- Posterior class probability is a softmax function\n", "$$ p(\\mathcal{C}_k|x,\\theta ) \\propto \\exp\\{\\beta_k^T x + \\gamma_k\\}$$\n", "where $\\beta _k= \\Sigma^{-1} \\mu_k$ and $\\gamma_k=- \\frac{1}{2} \\mu_k^T \\Sigma^{-1} \\mu_k + \\log \\pi_k$." ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "slideshow": { "slide_type": "skip" } }, "outputs": [ { "data": { "text/html": [ "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "open(\"../../styles/aipstyle.html\") do f\n", " display(\"text/html\", read(f,String))\n", "end" ] } ], "metadata": { "@webio": { "lastCommId": null, "lastKernelId": null }, "anaconda-cloud": {}, "celltoolbar": "Slideshow", "kernelspec": { "display_name": "Julia 1.9.3", "language": "julia", "name": "julia-1.9" }, "language_info": { "file_extension": ".jl", "mimetype": "application/julia", "name": "julia", "version": "1.9.3" } }, "nbformat": 4, "nbformat_minor": 4 }