probinet.evaluation.expectation_computation

Functions for computing expectations and related metrics.

Functions

calculate_Q_dense(A, M, pi, mu[, mask, EPS])	Compute the dense Q matrix for the given adjacency tensor and parameters.
calculate_Z(lambda0_aij, eta)	Compute the normalization constant of the Bivariate Bernoulli distribution.
calculate_conditional_expectation(B, u, v, ...)	Calculates the conditional expectation of a given set of parameters.
calculate_conditional_expectation_dyncrep(...)	Calculate the conditional expectation for given dynamic representation.
calculate_expectation(u, v, w, eta)	Compute the expectations for the marginal distribution.
calculate_expectation_acd(U, V, W, Q[, pi])	Calculate the expectation for the adjacency tensor with an additional covariate.
compute_L1loss(X, Xtilde)	Calculate the L1 loss between two matrices.
compute_M_joint(U, V, W, eta)	Return the vectors of joint probabilities of every pair of edges.
compute_expected_adjacency_tensor(U, V, W)	Compute the expected value of the adjacency tensor.
compute_expected_adjacency_tensor_multilayer(u, v, w)	Compute the expected value of the adjacency tensor for multi-covariate data.
compute_lagrange_multiplier(lambda_i, num, den)	Function to calculate the value of the Lagrange multiplier.
compute_marginal_and_conditional_expectation(B, ...)	Return the marginal and conditional expected value.
compute_mean_lambda0(u, v, w)	Compute the mean lambda0 for all entries.
compute_mean_lambda0_dyncrep(u, v, w)	Compute the mean lambda0 for all entries for dynamic reciprocity.
compute_mean_lambda0_nonzero(subs_nz, u, v, w)	Compute the mean lambda0_ij for only non-zero entries.
u_with_lagrange_multiplier(u, x, y)	Function to update the membership matrix 'u' using the Lagrange multiplier.

probinet.evaluation.expectation_computation.calculate_Q_dense(A: ndarray, M: ndarray, pi: float, mu: float, mask: ndarray | None = None, EPS: float = 1e-12) → ndarray

Compute the dense Q matrix for the given adjacency tensor and parameters.

Parameters:

• A (np.ndarray) – Adjacency tensor.

• M (np.ndarray) – Mean adjacency tensor.

• pi (float) – Poisson parameter.

• mu (float) – Mixing parameter.

• mask (Optional[np.ndarray]) – Mask for selecting a subset of the adjacency tensor.

• EPS (float) – Small constant to avoid division by zero.

Returns:

Dense Q matrix.

Return type:

np.ndarray

probinet.evaluation.expectation_computation.calculate_Z(lambda0_aij: ndarray, eta: float) → ndarray

Compute the normalization constant of the Bivariate Bernoulli distribution.

probinet.evaluation.expectation_computation.calculate_conditional_expectation(B: ndarray, u: ndarray, v: ndarray, w: ndarray, eta: float, mean: ndarray | None = None) → ndarray

Calculates the conditional expectation of a given set of parameters.

This function computes the conditional expectation of a multivariate random process based on the provided inputs. It incorporates a scaling parameter (eta) and optionally a mean tensor to compute the result. If the mean tensor is not provided, it defaults to computing a mean based on the input parameters u, v, and w.

Parameters:

• B – A 3-dimensional tensor used in the computation of the weighted mean. The tensor represents the relationship between variables in the multivariate process.

• u – A 1-dimensional array representing the first set of variables contributing to the computation of the mean. Typically corresponds to a principal factor in the model.

• v – A 1-dimensional array representing the second set of variables contributing to the computation of the mean. It complements the u array in forming the joint distribution.

• w – A 1-dimensional array representing the third set of variables interacting with u and v to establish a comprehensive measure of centrality in the model.

• eta – A scaling parameter applied to the tensor factors to adjust their weighted contribution to the overall mean measure of expectations.

• mean – A precomputed 3-dimensional tensor mean to override the default computed mean. If None, the mean will be computed using u, v, and w.

Returns:

A 3-dimensional tensor that represents the computed conditional expectation given the provided parameters. The tensor provides a context-sensitive measure of expectation, calculated as either a default weighted mean or incorporating a provided precomputed mean.

Return type:

np.ndarray

probinet.evaluation.expectation_computation.calculate_conditional_expectation_dyncrep(B_to_T: COO | ndarray, u: ndarray, v: ndarray, w: ndarray, eta: float = 0.0, beta: float = 1.0) → ndarray

Calculate the conditional expectation for given dynamic representation.

This function computes the conditional expectation based on the dynamic representation of the input data, including arrays and graph-based data. It utilizes transformation and normalization techniques such as matrix transposition and scaling.

Parameters:

• B_to_T (GraphDataType) – Graph-based data structure representing relationships or transitions between nodes or states.

• u (np.ndarray) – Input array representing data points or state variables.

• v (np.ndarray) – Input array representing another set of data points or state variables related to u.

• w (np.ndarray) – Auxiliary input array used for reference in the calculation.

• eta (float, optional) – Scaling factor applied to the graph transformation. Default is 0.0.

• beta (float, optional) – Scaling factor applied in the normalization computation. Default is 1.0.

Returns:

Array representing the computed conditional expectation after applying the dynamic representation transformations.

Return type:

np.ndarray

probinet.evaluation.expectation_computation.calculate_expectation(u: ndarray, v: ndarray, w: ndarray, eta: float) → ndarray

Compute the expectations for the marginal distribution.

probinet.evaluation.expectation_computation.calculate_expectation_acd(U: ndarray, V: ndarray, W: ndarray, Q: ndarray, pi: float = 1) → ndarray

Calculate the expectation for the adjacency tensor with an additional covariate.

probinet.evaluation.expectation_computation.compute_L1loss(X: ndarray, Xtilde: ndarray) → float

Calculate the L1 loss between two matrices.

Parameters:

• X (np.ndarray) – The first matrix.

• Xtilde (np.ndarray) – The second matrix to compare against the first matrix.

Returns:

The L1 loss between the two matrices, rounded to three decimal places.

Return type:

float

probinet.evaluation.expectation_computation.compute_M_joint(U: ndarray, V: ndarray, W: ndarray, eta: float) → list

Return the vectors of joint probabilities of every pair of edges.

probinet.evaluation.expectation_computation.compute_expected_adjacency_tensor(U: ndarray, V: ndarray, W: ndarray) → ndarray

Compute the expected value of the adjacency tensor.

probinet.evaluation.expectation_computation.compute_expected_adjacency_tensor_multilayer(u: ndarray, v: ndarray, w: ndarray) → ndarray

Compute the expected value of the adjacency tensor for multi-covariate data.

probinet.evaluation.expectation_computation.compute_lagrange_multiplier(lambda_i: float, num: float, den: float) → float

Function to calculate the value of the Lagrange multiplier.

probinet.evaluation.expectation_computation.compute_marginal_and_conditional_expectation(B: ndarray, U: ndarray, V: ndarray, W: ndarray, eta: float) → tuple

Return the marginal and conditional expected value.

probinet.evaluation.expectation_computation.compute_mean_lambda0(u: ndarray, v: ndarray, w: ndarray) → ndarray

Compute the mean lambda0 for all entries.

probinet.evaluation.expectation_computation.compute_mean_lambda0_dyncrep(u: ndarray, v: ndarray, w: ndarray) → ndarray

Compute the mean lambda0 for all entries for dynamic reciprocity.

probinet.evaluation.expectation_computation.compute_mean_lambda0_nonzero(subs_nz: Tuple[int, int, int], u: ndarray, v: ndarray, w: ndarray, assortative=True) → ndarray

Compute the mean lambda0_ij for only non-zero entries.

probinet.evaluation.expectation_computation.u_with_lagrange_multiplier(u: ndarray, x: ndarray, y: ndarray) → ndarray

Function to update the membership matrix ‘u’ using the Lagrange multiplier.