STATS 306B Methods for Applied Statistics: Unsupervised Learning

Abstract

(a) Implement the EM algorithm for an HMM with hidden states zt ∈ {1, . . . , k} (for any k > 1) and isotropic Gaussian emission probabilities, p(xt|zt), for xt ∈ Rd (d ≥ 1). That is, xt|zt = j ∼ N (μj , σ2 j I) for unknown parameters (μj , σ2 j ). Do not use a pre-existing implementation. Note: The α and β recursions involve the repeated multiplication of small numbers and hence are susceptible to numerical underflow. Section 12.7 of the assigned HMM chapter presents an effective normalization strategy for countering this numerical underflow.