Lecture 10 : Expectation - Maximization Algorithm ( LaTeX prepared by Shaobo Fang
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چکیده
Consider a set of data points with their classes labeled, and assume that each class is a Gaussian as shown in Figure 1(a). Given this set of data points, finding the means of two Gaussian can be done easily by estimating the sample mean, as the class labels are known. Now imagine that the classes are not labeled as shown in Figure 1(b). How should we determine the mean for each of the classes then? In order to solve this problem, we could use an iterative approach: first make a guess of the class label for each data point, then compute the means and update the guess of the class labels again. We repeat until the means converge. The problem of estimating parameters in the absence of labels is known as unsupervised learning. There are many unsupervised learning methods. We will focus on the Expectation Maximization (EM) algorithm.
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