Machine Learning Methods for Behaviour Analysis and Anomaly Detection in Video by Olga Isupova

Author:Olga Isupova
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

(3.23)

(3.24)

(3.25)

(3.26)

where is the digamma function.

Using these additional notations, the E-like step is formulated in the same way as the E-step of the EM-algorithm, replacing everywhere the estimates of parameters with the corresponding tilde introduced notation and true posterior distributions of the hidden variables with the corresponding approximated ones in (3.10)–(3.16). The full details of the VB-algorithm derivation are presented in Appendix B.

The point estimates of parameters can be obtained by expected values of the posterior approximated distributions. An expected value for a Dirichlet distribution (a posterior distribution for all the parameters) is a normalised vector of hyperparameters. Using the expressions for the hyperparameters from (3.19)–(3.22), the final parameter estimates can be obtained by:

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