discrete_transition_decode_marginal(marginal_name::String, marginal::Contingency{T, <:AbstractArray{T, N}}) where {T, N}

Decode the marginal distribution into a tuple of dimensions and a probability vector.

Arguments

• marginal_name: The name of the marginal distribution.
• marginal: The marginal distribution.

For example, if the marginal distribution is "int1t5", we know that "in" corresponds to dimension 2, and "t1" and "t5" correspond to dimensions 3 and 7 of the contingency tensor. Therefore, the function will return (2, 3, 7) and the contingency tensor marginal.p.

discrete_transition_marginal_rule(message_names, messages, marginals_names, marginals, q_a)

Compute the marginal for one of the Categorical interfaces of the DiscreteTransition node. This function is similar to discrete_transition_structured_message_rule but uses multiply_dimensions instead of sum_out_dimensions for the messages.

Arguments

• message_names: The names of the incoming messages. These are the variables in the same factorization cluster as the variable over which we are computing the message.
• messages: The incoming messages. These are guaranteed to be either Categorical, Bernoulli or PointMass distributions.
• marginals_names: The names of the other marginal distributions attached to the DiscreteTransition node. These marginal distributions are not in the same factorization cluster as the variable over which we are computing the message.
• marginals: The incoming marginals. These are guaranteed to be either Contingency, Categorical, Bernoulli or PointMass distributions.
• q_a: The marginal distribution over the transition tensor.

discrete_transition_process_marginals(e_log_a, marginals_names, marginals)

Process the marginals to update the expected log transition matrix. This is a common operation used by both discrete_transition_structured_message_rule and discrete_transition_marginal_rule.

Arguments

• e_log_a: The expected log of the transition matrix.
• marginals_names: The names of the marginal distributions.
• marginals: The marginal distributions.

Returns

• The updated expected log transition matrix.

multiply_dimensions(tensor::AbstractArray{T, M}, dims::NTuple{N, Int}, values::AbstractArray{T, N}) where {T, M, N}

Multiply the tensor with the values along the specified dimensions. This is similar to sum_out_dimensions but doesn't sum the result, only performs the elementwise multiplication.

sum_out_dimensions(tensor::AbstractArray{T, M}, dims::NTuple{N, Int}, values::AbstractArray{T, N}) where {T, M, N}

Sum out the dimensions of the tensor that are not part of the marginal distribution. This is a generalization of an inner product, where we also figure out which dimensions of the tensor align with the dimensions of values.

discrete_transition_process_messages(e_log_a, message_names, messages, callback)

Process the messages to update the expected log transition matrix. This is a common operation used by both discrete_transition_structured_message_rule and discrete_transition_marginal_rule. The callback function is used to update the expected log transition matrix. This argument toggles between marginalising out a variable (for messages) and computing a joint marginal distribution.

discrete_transition_structured_message_rule(message_names, messages, marginals_names, marginals, q_a)

Compute the message for one of the Categorical interfaces of the DiscreteTransition node. This function 1. Computes the expected log of the transition matrix e_log_a 2. For every incoming marginal distribution, it determines which dimension of the contingency tensor it corresponds to. 3. It then uses sum_out_dimensions to to compute the inner product of e_log_a with the marginal distribution along the specified dimension. 4. The result of this is the VMP message, which we have to exponentiate and multiply with the incoming messages. 5. The result is then normalized to sum to 1.

Arguments

• message_names: The names of the incoming messages. These are the variables in the same factorization cluster as the variable over which we are computing the message.
• messages: The incoming messages. These are guaranteed to be either Categorical, Bernoulli or PointMass distributions.
• marginals_names: The names of the other marginal distributions attached to the DiscreteTransition node. These marginal distributions are not in the same factorization cluster as the variable over which we are computing the message.
• marginals: The incoming marginals. These are guaranteed to be either Contingency, Categorical, Bernoulli or PointMass distributions.
• q_a: The marginal distribution over the transition tensor.