splisosm.likelihood

Likelihood functions and pvalue-approximation utilities.

Functions

liu_sf(t, lambs[, dofs, deltas, kurtosis])	Compute p-values for weighted sums of chi-squared variables using the Liu approximation.
log_prob_fastdm(concentration, counts[, mask])	Compute optimized Dirichlet-multinomial log-likelihood.
log_prob_fastmult(probs, counts[, mask])	Compute optimized multinomial log-likelihood.
log_prob_fastmult_batched(probs, counts[, mask])	Compute batched optimized multinomial log-likelihood.
log_prob_fastmvn(locs, cov_eigvals, cov_eigvecs, data)	Compute multivariate normal log-likelihood with eigendecomposition.
log_prob_fastmvn_batched(locs, cov_eigvals, ...[, ...])	Compute batched multivariate normal log-likelihood with eigendecomposition.

Module Contents

splisosm.likelihood.liu_sf(t, lambs, dofs=None, deltas=None, kurtosis=False)

Compute p-values for weighted sums of chi-squared variables using the Liu approximation.

Let \(X = \sum_{i=1}^{d} \lambda_i * \chi^2(h_i, \delta_i)\) be a linear combination of d chi-squared random variables, each with degree of freedom \(h_i\) and noncentrality \(\delta_i\), this function approximates :math:Pr(X > t) using the Liu moment-matching approach [LTZ09].

Parameters:

• t (numpy.typing.ArrayLike) – Shape (n,), observed test statistic.

• lambs (numpy.typing.ArrayLike) – Shape (d,), weights of each chi-squared component.

• dofs (Optional[numpy.typing.ArrayLike]) – Shape (d,), degrees of freedom for each component. Defaults to all ones.

• deltas (Optional[numpy.typing.ArrayLike]) – Shape (d,), noncentrality parameters for each component. Defaults to all zeros.

• kurtosis (bool) – If True, uses kurtosis matching proposed in [LWL12]; otherwise uses the original skewness matching [LTZ09].

Returns:

P-values of shape (n,) computed as Pr(X > t).

Return type:

ndarray

Notes

From limix/chiscore

splisosm.likelihood.log_prob_fastdm(concentration, counts, mask=None)

Compute optimized Dirichlet-multinomial log-likelihood.

Parameters:

• concentration (Tensor) – Isoform concentration tensor of shape (n_isos, n_spots).

• counts (Tensor) – Isoform count tensor of shape (n_isos, n_spots).

• mask (Optional[Tensor]) – Spot mask of shape (n_spots,). Entries with value 1 are treated as masked and are ignored when computing likelihood.

Returns:

Scalar log-likelihood.

Return type:

Tensor

splisosm.likelihood.log_prob_fastmult(probs, counts, mask=None)

Compute optimized multinomial log-likelihood.

Parameters:

• probs (Tensor) – Isoform ratio tensor of shape (n_isos, n_spots).

• counts (Tensor) – Isoform count tensor of shape (n_isos, n_spots).

• mask (Optional[Tensor]) – Spot mask of shape (n_spots,). Entries with value 1 are treated as masked and are ignored when computing likelihood.

Returns:

Scalar log-likelihood.

Return type:

Tensor

splisosm.likelihood.log_prob_fastmult_batched(probs, counts, mask=None)

Compute batched optimized multinomial log-likelihood.

Parameters:

• probs (Tensor) – Batched isoform ratio tensor of shape (batch_size, n_isos, n_spots).

• counts (Tensor) – Batched isoform count tensor of shape (batch_size, n_isos, n_spots).

• mask (Optional[Tensor]) – Mask tensor of shape (batch_size, n_spots). Entries with value 1 are treated as masked and are ignored when computing likelihood.

Returns:

Log-likelihood values of shape (batch_size,).

Return type:

Tensor

splisosm.likelihood.log_prob_fastmvn(locs, cov_eigvals, cov_eigvecs, data, mask=None)

Compute multivariate normal log-likelihood with eigendecomposition.

Classes along the first axis are treated as independent, and the log-likelihood is computed as the sum of log-likelihoods for each class.

Parameters:

• locs (Tensor) – Mean tensor of shape (n_classes, n_spots).

• cov_eigvals (Tensor) – Covariance eigenvalues of shape (n_classes, n_spots) or (1, n_spots).

• cov_eigvecs (Tensor) – Covariance eigenvectors of shape (n_classes, n_spots, n_spots) or (1, n_spots, n_spots).

• data (Tensor) – Observation tensor of shape (n_classes, n_spots).

• mask (Optional[Tensor]) – Spot mask of shape (n_spots,). Entries with value 1 are treated as masked and are ignored when computing likelihood.

Returns:

Scalar log-likelihood.

Return type:

Tensor

Raises:

ValueError – If covariance eigendecomposition shapes are incompatible with data.

splisosm.likelihood.log_prob_fastmvn_batched(locs, cov_eigvals, cov_eigvecs, data, mask=None, residual_eigval=None)

Compute batched multivariate normal log-likelihood with eigendecomposition.

Classes along the second axis are treated as independent, and the log-likelihood is computed as the sum of log-likelihoods for each class.

Supports both full-rank and low-rank covariance approximations. In the full-rank case (residual_eigval=None) the covariance is C = V diag(c) V^T and both cov_eigvals and cov_eigvecs have n_spots entries in their last dimension.

In the low-rank case (residual_eigval provided) the covariance is approximated as

\[C \approx V_k \operatorname{diag}(c_k) V_k^T + d\,(I - V_k V_k^T)\]

where V_k (n_spots × k) contains the top-k eigenvectors, c_k (k) the corresponding eigenvalues, and d is the scalar residual eigenvalue (the noise-only contribution for the uncaptured modes). The log-likelihood is then computed via the Woodbury identity.

Parameters:

• locs (Tensor) – Batched mean tensor of shape (batch_size, n_classes, n_spots).

• cov_eigvals (Tensor) – Full-rank: shape (batch_size, n_classes, n_spots). Low-rank: shape (batch_size, n_classes, k) with k ≤ n_spots.

• cov_eigvecs (Tensor) – Full-rank: shape (batch_size, n_classes, n_spots, n_spots). Low-rank: shape (batch_size, n_classes, n_spots, k).

• data (Tensor) – Batched observation of shape (batch_size, n_classes, n_spots).

• mask (Tensor, optional) – Batched mask tensor of shape (batch_size, n_spots). Entries with value 1 are treated as masked and are ignored when computing likelihood.

• residual_eigval (Tensor, optional) – Low-rank residual eigenvalue d of shape (batch_size, n_classes, 1). When None (default), full-rank computation is used.

Returns:

Log-likelihood values of shape (batch_size,).

Return type:

Tensor

Raises:

ValueError – If covariance decomposition shapes are incompatible with input sizes.