Grouped transition matrices

GroupedTransitions stores transition probabilities for models whose states can be partitioned into equally sized groups. Entries on the diagonal blocks stay fully parameterised while every off-diagonal block shares a single probability per pair of groups. This reduces the number of learnable parameters and keeps the transition matrix stochastic after each Baum–Welch update.

julia> trans = HMMRBM.GroupedTransitions(3, 2);  # 3 groups, 2 states each

julia> size(trans)
(6, 6)

julia> trans[1, 4]
0.16666666666666666

Grouped transitions can be passed directly to the transitions field of MultiSeqHMM and will be kept consistent during the EM loop via HMMRBM.baum_welch_transition_update!.

Constructors

HMMRBM.GroupedTransitions — Type

struct GroupedTransitions{T, W<:AbstractArray{T,3}, B<:AbstractMatrix{T}} <: AbstractMatrix{T}

GroupedTransitions(within, between)
GroupedTransitions(::Type{<:AbstractArray}, ::Type{<:AbstractMatrix}, group_count, states_per_group)
GroupedTransitions(::Type{<:Real}, group_count, states_per_group)
GroupedTransitions(group_count, states_per_group)

A transition matrix with grouped structure. The states are divided into group_count groups, each containing states_per_group states. Transitions within the same group are free, while transitions between different groups share the same probability.

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Accessors

HMMRBM.group_count — Function

group_count(A::GroupedTransitions)

Get the number of groups represented by the grouped transition matrix.

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HMMRBM.states_per_group — Function

states_per_group(A::GroupedTransitions)

Get the number of states per group represented by the grouped transition matrix.

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HMMRBM.state_count — Method

state_count(A::GroupedTransitions)

Get the total number of states represented by the grouped transition matrix.

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Training support

HMMRBM.baum_welch_transition_update! — Method

baum_welch_transition_update!(trans, logtrans, expected)

Update the transition matrix trans and logtrans in place using the expected transition counts expected.

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