sparsesurv.gradients module

Summary

Functions:

aft_gradient

Calculates the negative gradient of the AFT model wrt eta.

aft_gradient_beta

Calculates the negative gradient of the AFT model wrt beta.

eh_gradient

Calculates the negative gradient of the EH model wrt eta.

eh_gradient_beta

Calculates the negative gradient of the EH model wrt beta.

Reference

aft_gradient(linear_predictor, time, event, bandwidth=None)[source]

Calculates the negative gradient of the AFT model wrt eta.

Parameters:

  • linear_predictor (npt.NDArray[np.float64]) – Linear predictor of the training data of dimension n.

  • time (npt.NDArray[np.float64]) – Time of the training data of dimension n. Assumed to be sorted.

  • event (npt.NDArray[np.int64]) – Event indicator of the training data of dimension n.

  • bandwidth (Optional[float], optional) – Bandwidth to kernel-smooth the profile likelihood. Will be estimated if not specified. Defaults to None.

Returns:

Negative gradient of the AFT model wrt eta. Of dimensionality n.

Return type:

npt.NDArray[np.float64]

aft_gradient_beta(beta, X, time, event, bandwidth=None)[source]

Calculates the negative gradient of the AFT model wrt beta.

Note

Utility function to be used with off-the-shelf optimisers (e.g., scipy). Since the main gradient function calculates the gradient wrt eta (see aft_gradient), we recover the gradient wrt beta through a matrix multiplication.

Parameters:

  • beta (npt.NDArray[np.float64]) – Coefficient vector of length p.

  • X (npt.NDArray[np.float64]) – Design matrix of the training data. N rows and p columns.

  • time (npt.NDArray[np.float64]) – Time of the training data of length n. Assumed to be sorted.

  • event (npt.NDArray[np.int64]) – Event indicator of the training data of length n.

  • bandwidth (Optional[float], optional) – Bandwidth to kernel-smooth the profile likelihood. Will be estimated empirically if not specified. Defaults to None.

Returns:

Negative gradient of the AFT model wrt beta of length p.

Return type:

npt.NDArray[np.float64]

eh_gradient(linear_predictor, time, event, bandwidth=None)[source]

Calculates the negative gradient of the EH model wrt eta.

Parameters:

  • linear_predictor (npt.NDArray[np.float64]) – Linear predictor of the training data. N rows and 2 columns.

  • time (npt.NDArray[np.float64]) – Time of the training data of length n. Assumed to be sorted.

  • event (npt.NDArray[np.int64]) – Event indicator of the training data of length n.

  • bandwidth (Optional[float], optional) – Bandwidth to kernel-smooth the profile likelihood. Will be estimated if not specified. Defaults to None.

Returns:

Negative gradient of the EH model wrt eta of length 2n.

Return type:

np.array

eh_gradient_beta(beta, X, time, event, bandwidth=None)[source]

Calculates the negative gradient of the EH model wrt beta.

Note

Utility function to be used with off-the-shelf optimisers (e.g., scipy). Since the main gradient function calculates the gradient wrt eta (see eh_gradient), we recover the gradient wrt beta through a matrix multiplication.

Parameters:

  • beta (npt.NDArray[np.float64]) – Coefficient vector. Length 2p to account for the two coefficients that were stacked into one vector (see pcsurv.eh.EH for details).

  • X (npt.NDArray[np.float64]) – Design matrix of the training data. N rows and 2p columns.

  • time (npt.NDArray[np.float64]) – Time of the training data of length n. Assumed to be sorted.

  • event (npt.NDArray[np.int64]) – Event indicator of the training data of length n.

  • bandwidth (Optional[float], optional) – Bandwidth to kernel-smooth the profile likelihood. Will be estimated if not specified. Defaults to None. Defaults to None.

Returns:

Negative gradient of the AFT model wrt beta of length 2p.

Return type:

npt.NDArray[np.float64]