KMeans Gaussina Mixture Model (Density Estimation) Consider a task from IOT sensor data : 1D example ALgorithm - warm up EM Algorithm (ML 16.6) Gaussian mixture model (Mixture of Gaussians) we re-format the $p(x)$ $$ p(x) = \sum_{k=1}^{m} \alpha_{k} N(x | \mu_{k}, C_{{k}}) $$ where $k={1, 2, ..., .}$ means $k^{th}$ gaussian dist, $\mu_{k}, C_{k}$ holds mean and std of $k^{th}$ gaussian parameters. parameters : $\Theta = (\alpha_{k}, \mu_{k}, C_{k})$ for $k = {1, 2, ..., \m}$ Expectation steps (guess, instead of single value, you guess the whole universe) maximization : MLE by your guessing, get a modification by bayesian rule. Ref cs229 2018 (ML 16.6) Gaussian mixture model (Mixture of Gaussians) EM_algo from note 最大期望算法
