himamo v0.1.0 Himamo.BaumWelch.StepE

Defines components of the E-step of the Baum-Welch algorithm (Expectation).

Calculates required statistics for the given model.

Summary

Computes alpha variable for Baum-Welch

Computes a Matrix where each element is alpha_{t, i} * beta_{t, i}

Computes beta variable for Baum-Welch

Computes gamma variable for Baum-Welch

Computes xi variable for Baum-Welch

compute_alpha(model, obs_seq)

compute_alpha(Himamo.Model.t, Himamo.ObsSeq.t) :: Himamo.Matrix.t

Computes alpha variable for Baum-Welch.

α_t(i) is the probability of being in state S_i at time t after observing the first t symbols.

Returns tuple of tuples (size T×N) where:

compute_alpha_times_beta(alpha, beta)

compute_alpha_times_beta(Himamo.Matrix.t, Himamo.Matrix.t) :: Himamo.Matrix.t

Computes a Matrix where each element is alpha_{t, i} * beta_{t, i}.

This is not matrix multiplication. The result of the above expression is used in multiple places, so the values are computed up front.

compute_beta(model, obs_seq)

compute_beta(Himamo.Model.t, Himamo.ObsSeq.t) :: Himamo.Matrix.t

Computes beta variable for Baum-Welch.

ß_t(i) is the probability of being in state S_i at time t and observing the partial sequence from t+1 to the end.

Returns tuple of tuples (size T×N) where:

compute_gamma(model, obs_seq, list)

compute_gamma(Himamo.Model.t, Himamo.ObsSeq.t, [{:xi, Himamo.Matrix.t}]) :: Himamo.Matrix.t

Computes gamma variable for Baum-Welch.

γ_t(i) is the probability of being in state S_i at time t given the full observation sequence.

Returns tuple of tuples (size T×N) where:

compute_xi(model, obs_seq, list)

compute_xi(Himamo.Model.t, Himamo.ObsSeq.t, alpha: Himamo.Matrix.t, beta: Himamo.Matrix.t) :: Himamo.Matrix.t

Computes xi variable for Baum-Welch.

ξ_t(i,j) is the probability of being in state S_i at time t and in state S_j at time t+1 given the full observation sequence.

Returns tuple of tuples of tuples (size T×N×N) where: