biogeme.expressions.log_sampled_nested module

Arithmetic expressions accepted by Biogeme: sampled nested logit.

class biogeme.expressions.log_sampled_nested.LogSampledNested(utilities, log_probabilities, alternative_ids, mev_utilities, mev_weights, mev_alternative_ids, nests, choice=0)

Bases: Expression

Log probability for a sampled nested logit model.

This expression is designed for the sampling-of-alternatives framework.

It represents the same expression currently generated by GenerateModel.get_nested_logit:

\[\log P(0 \mid S) = K_0 - \log \sum_{i \in S} \exp(K_i),\]

where the corrected kernel is

\[K_i = V_i - \omega_i + M_i,\]

and, if alternative \(i\) belongs to nest \(m\),

\[M_i = (\mu_m - 1) V_i + \left(\frac{1}{\mu_m} - 1\right) \log \sum_{j \in S^{MEV}_m} w_j \exp(\mu_m V_j).\]

Here \(\omega_i\) is the log sampling probability correction and \(w_j\) is the MEV sampling weight.

The expression avoids constructing a large tree of ConditionalSum, ConditionalTermTuple, BelongsTo, exp, and log expressions.

Parameters:

• utilities (dict[int, ExpressionOrNumeric])

• log_probabilities (dict[int, ExpressionOrNumeric])

• alternative_ids (dict[int, ExpressionOrNumeric])

• mev_utilities (dict[int, ExpressionOrNumeric])

• mev_weights (dict[int, ExpressionOrNumeric])

• mev_alternative_ids (dict[int, ExpressionOrNumeric])

• nests (NestsForNestedLogit | OldNestsForNestedLogit)

• choice (ExpressionOrNumeric)

deep_flat_copy()

Deep flat copy.

Return type:

LogSampledNested

get_value()

Evaluate the sampled nested logit log probability using NumPy.

Return type:

float

logit_choice_avail()

Return availability structures appearing in this expression.

Return type:

list[LogitTuple]

recursive_construct_jax_function(numerically_safe)

Generate a compact JAX function for sampled nested logit.

Return type:

Callable[[Array, Array, Array, Array], Array]

Parameters:

numerically_safe (bool)