Responsibilities in Mixture Models
The responsibility gamma(z_nk) = pi_k N(x_n | mu_k, Sigma_k) / sum_j pi_j N(x_n | mu_j, Sigma_j) is the posterior probability, via Bayes' theorem, that component k generated point x_n; each point gets a soft, fractional membership across all components.
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The responsibility gamma(z_nk) = pi_k N(x_n | mu_k, Sigma_k) / sum_j pi_j N(x_n | mu_j, Sigma_j) is the posterior probability, via Bayes' theorem, that component k generated point x_n; each point gets a soft, fractional membership across all components.
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