Module risk

operalib.risk implements risk model and their gradients.

class operalib.risk.ORFFHingeLoss

Define Hinge loss for ORFF models and its gradient.

Methods

__call__(coefs, ground_truth, phix, ker)

Compute the hinge loss value for ORFF models.

functional_grad
functional_grad_val

__call__(coefs, ground_truth, phix, ker)

Compute the hinge loss value for ORFF models.

Parameters:

coefs : {vector-like}, shape = [n_samples1 * n_targets]

Coefficient to optimise

ground_truth : {vector-like}

Targets samples

phix : {LinearOperator}

X ORFF mapping operator acting on the coefs

Returns:

float : Empirical ORFF hinge loss

__init__()

Initialize Hhnge ORFF loss.

__weakref__

list of weak references to the object (if defined)

class operalib.risk.ORFFLSLoss

Define Least squares loss for ORFF models and its gradient.

Methods

__call__(coefs, ground_truth, phix, ker)	Compute the Least squares loss value for ORFF models.
functional_grad(coefs, ground_truth, phix, ker)	Compute the Least squares loss gradient for ORFF models.
functional_grad_val(coefs, ground_truth, …)	Compute the Least squares loss gradient and value for ORFF models.

__call__(coefs, ground_truth, phix, ker)

Compute the Least squares loss value for ORFF models.

Parameters:

coefs : {vector-like}, shape = [n_samples1 * n_targets]

Coefficient to optimise

ground_truth : {vector-like}

Targets samples

phix : {LinearOperator}

X ORFF mapping operator acting on the coefs

Returns:

float : Empirical ORFF least square loss

__init__()

Initialize Least squares ORFF loss.

__weakref__

list of weak references to the object (if defined)

functional_grad(coefs, ground_truth, phix, ker)

Compute the Least squares loss gradient for ORFF models.

Parameters:

coefs : {vector-like}, shape = [n_samples1 * n_targets]

Coefficient to optimise

ground_truth : {vector-like}

Targets samples

phix : {LinearOperator}

X ORFF mapping operator acting on the coefs

Returns:

float : Empirical ORFF least square loss gradient

functional_grad_val(coefs, ground_truth, phix, ker)

Compute the Least squares loss gradient and value for ORFF models.

Parameters:

coefs : {vector-like}, shape = [n_samples1 * n_targets]

Coefficient to optimise

ground_truth : {vector-like}

Targets samples

phix : {LinearOperator}

X ORFF mapping operator acting on the coefs

Returns:

tuple : Empirical ORFF least square loss value and gradient

class operalib.risk.ORFFRidgeRisk(lbda, loss='LS')

Define Ridge risk for ORFF models and its gradient.

Methods

__call__(coefs, ground_truth, phix, ker)	Compute the Empirical ORFF ridge risk.
functional_grad(coefs, ground_truth, phix, ker)	Compute the gradient of the Empirical ORFF ridge risk.
functional_grad_val(coefs, ground_truth, …)	Compute the gradient and value of the Empirical ORFF ridge risk.

__call__(coefs, ground_truth, phix, ker)

Compute the Empirical ORFF ridge risk.

Parameters:

coefs : {vector-like}, shape = [n_samples1 * n_targets]

Coefficient to optimise

ground_truth : {vector-like}

Targets samples

phix : {LinearOperator}

X ORFF mapping operator acting on the coefs

Returns:

float : Empirical ORFF ridge risk

__init__(lbda, loss='LS')

Initialize Empirical ORFF ridge risk.

Parameters:

lbda : {float}

Small positive values of lbda improve the conditioning of the problem and reduce the variance of the estimates. Lbda corresponds to (2*C)^-1 in other linear models such as LogisticRegression or LinearSVC.

__weakref__

list of weak references to the object (if defined)

functional_grad(coefs, ground_truth, phix, ker)

Compute the gradient of the Empirical ORFF ridge risk.

Parameters:

coefs : {vector-like}, shape = [n_samples1 * n_targets]

Coefficient to optimise

ground_truth : {vector-like}

Targets samples

phix : {LinearOperator}

X ORFF mapping operator acting on the coefs

Returns:

{vector-like} : gradient of the Empirical ORFF ridge risk

functional_grad_val(coefs, ground_truth, phix, ker)

Compute the gradient and value of the Empirical ORFF ridge risk.

Parameters:

coefs : {vector-like}, shape = [n_samples1 * n_targets]

Coefficient to optimise

ground_truth : {vector-like}

Targets samples

phix : {LinearOperator}

X ORFF mapping operator acting on the coefs

Returns:

Tuple{float, vector-like} : Empirical ORFF ridge risk and its gradient

returned as a tuple.

class operalib.risk.ORFFSCSVMLoss

Define the Simplex Cone Support Vector Machine loss and its gradient.

Methods

__call__
functional_grad
functional_grad_val

__call__(...) <==> x(...)

__init__()

x.__init__(…) initializes x; see help(type(x)) for signature

__weakref__

list of weak references to the object (if defined)

class operalib.risk.OVKRidgeRisk(lbda)

Define Kernel ridge risk and its gradient.

Methods

__call__(coefs, ground_truth, Gram[, …])	Compute the Empirical OVK ridge risk.
functional_grad(coefs, ground_truth, Gram[, …])	Compute the gradient of the Empirical OVK ridge risk.
functional_grad_val(coefs, ground_truth, Gram)	Compute the gradient and value of the Empirical OVK ridge risk.

__call__(coefs, ground_truth, Gram, weight=None, zeronan=None)

Compute the Empirical OVK ridge risk.

Parameters:

coefs : {vector-like}, shape = [n_samples1 * n_targets]

Coefficient to optimise

ground_truth : {vector-like}

Targets samples

Gram : {LinearOperator}

Gram matrix acting on the coefs

weight: {LinearOperator}

zeronan: {LinearOperator}

Returns:

float : Empirical OVK ridge risk

__init__(lbda)

Initialize Empirical kernel ridge risk.

Parameters:

lbda : {float}

Small positive values of lbda improve the conditioning of the problem and reduce the variance of the estimates. Lbda corresponds to (2*C)^-1 in other linear models such as LogisticRegression or LinearSVC.

__weakref__

list of weak references to the object (if defined)

functional_grad(coefs, ground_truth, Gram, weight=None, zeronan=None)

Compute the gradient of the Empirical OVK ridge risk.

Parameters:

coefs : {vector-like}, shape = [n_samples1 * n_targets]

Coefficient to optimise

ground_truth : {vector-like}

Targets samples

Gram : {LinearOperator}

Gram matrix acting on the coefs

weight: {LinearOperator}

zeronan: {LinearOperator}

Returns:

{vector-like} : gradient of the Empirical OVK ridge risk

functional_grad_val(coefs, ground_truth, Gram, weight=None, zeronan=None)

Compute the gradient and value of the Empirical OVK ridge risk.

Parameters:

coefs : {vector-like}, shape = [n_samples1 * n_targets]

Coefficient to optimise

ground_truth : {vector-like}

Targets samples

Gram : {LinearOperator}

Gram matrix acting on the coefs

L : array, shape = [n_samples_miss, n_samples_miss]

Graph Laplacian of data with missing targets (semi-supervised learning).

Returns:

Tuple{float, vector-like} : Empirical OVK ridge risk and its gradient

returned as a tuple.