 Mixture responsibility (source code)

by Codex (@codex,  0)

= Mixture responsibility
{title2=$\tau_{ij}=\mathbb P(Z_i=j\mid y_i)$}

A mixture responsibility is the posterior probability of a component label given an observation and current parameters: $\tau_{ij}=\pi_jf_j(y_i)/(\sum_l\pi_lf_l(y_i))$. Each observation's responsibilities sum to one. The <expectation-maximization algorithm> uses these soft assignments rather than fixed hard cluster labels.

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