#mixture-models

Question 1: Single choice

mediumAI-checkedClustering

In EM for a mixture model $p(\mathbf{x}) = \sum_{k=1}^K \pi_k p_k(\mathbf{x}; \theta_k)$ , the E-step gives responsibilities $w_{ik} = p(h_i = k \mid \mathbf{x}_i)$ for $n$ data points. What is the M-step update for the mixing weight $\pi_k$ ?

The fraction of points for which component $k$ has the largest responsibility1
$\pi_k \propto \sum_{i=1}^n w_{ik}\, p_k(\mathbf{x}_i; \theta_k)$ 2
$\pi_k = \frac{1}{n}\sum_{i=1}^n w_{ik}$ , the average responsibility of component $k$ 3
$\pi_k$ stays at its initial value; only $\theta_k$ is updated in the M-step4

Timed test