skgpuppy.Covariance module

class skgpuppy.Covariance.Covariance

Bases: object

Superclass for all covariance functions

cov_matrix(x, theta)
Parameters:
  • x – list of d-dimensional vectors of size N
  • theta – hyperparameters
Returns:

NxN covariance matrix
cov_matrix_ij(xi, xj, theta)
Parameters:
  • xi – list of d-dimensional vectors of size N1
  • xj – list of d-dimensional vectors of size N2
  • theta – hyperparameters
Returns:

N1xN2 covariance matrix between xi and xj
get_Hessian(u, xi, theta)

Get the Hessian of the covariance function with respect to u

Parameters:
  • u – d-dimensional vector
  • xi – d-dimensional vector
  • theta – hyperparameters
Returns:

Hessian
get_Jacobian(u, xi, theta)

Get the Jacobian of the covariance function with respect to u

Parameters:
  • u – d-dimensional vector
  • xi – d-dimensional vector
  • theta – hyperparameters
Returns:

Jacobian
get_theta(x, t)

Guesses the initial theta vector for the hyperparameter optimization step

Returns:initial theta vector
inv_cov_matrix(x, theta, cov_matrix=None)
Parameters:
  • x – list of d-dimensional vectors
  • theta – hyperparameters
  • cov_matrix – invert this precalculated cov matrix for x and theta
Returns:

inverse of the covariance matrix
ml_estimate(x, t)
Parameters:
  • x – list of d-dimensional vectors
  • t – list of responses
Returns:

maximum likelihood estimate for theta
class skgpuppy.Covariance.Dot

Bases: object

A class to inspect the matrix multiplication complexity

reset()

Reset the gathered statistics

class skgpuppy.Covariance.GaussianCovariance

Bases: skgpuppy.Covariance.Covariance

The classic Gaussian squared exponential covariance function. Suitable to approximate smooth functions.

cov_matrix(x, theta)
cov_matrix_ij(xi, xj, theta)
get_Hessian(u, xi, theta)
get_Jacobian(u, xi, theta)
get_theta(x, t)
inv_cov_matrix(x, theta, cov_matrix=None)
Parameters:
  • x – list of d-dimensional vectors
  • theta – hyperparameters
  • cov_matrix – invert this precalculated cov matrix for x and theta
Returns:

inverse of the covariance matrix
ml_estimate(x, t)
Parameters:
  • x – list of d-dimensional vectors
  • t – list of responses
Returns:

maximum likelihood estimate for theta
class skgpuppy.Covariance.PeriodicCovariance

Bases: skgpuppy.Covariance.Covariance

A class to represent a mixed Gaussian and periodic covariance.

Warning

No derivatives for uncertainty propagation and faster hyperparameter optimization implemented yet.

cov_matrix(x, theta)
Parameters:
  • x – list of d-dimensional vectors of size N
  • theta – hyperparameters
Returns:

NxN covariance matrix
cov_matrix_ij(xi, xj, theta)
Parameters:
  • xi – list of d-dimensional vectors of size N1
  • xj – list of d-dimensional vectors of size N2
  • theta – hyperparameters
Returns:

N1xN2 covariance matrix between xi and xj
get_Hessian(u, xi, theta)

Get the Hessian of the covariance function with respect to u

Parameters:
  • u – d-dimensional vector
  • xi – d-dimensional vector
  • theta – hyperparameters
Returns:

Hessian
get_Jacobian(u, xi, theta)

Get the Jacobian of the covariance function with respect to u

Parameters:
  • u – d-dimensional vector
  • xi – d-dimensional vector
  • theta – hyperparameters
Returns:

Jacobian
get_theta(x, t)
inv_cov_matrix(x, theta, cov_matrix=None)
Parameters:
  • x – list of d-dimensional vectors
  • theta – hyperparameters
  • cov_matrix – invert this precalculated cov matrix for x and theta
Returns:

inverse of the covariance matrix
ml_estimate(x, t)
Parameters:
  • x – list of d-dimensional vectors
  • t – list of responses
Returns:

maximum likelihood estimate for theta
class skgpuppy.Covariance.SPGPCovariance(m)

Bases: skgpuppy.Covariance.Covariance

A covariance function for fast matrix inversion on large datasets based on Snelsons thesis.

Snelson, E. L. Flexible and efficient Gaussian process models for machine learning, Gatsby Computational Neuroscience Unit, University College London, 2007

Warning

No derivatives for uncertainty propagation implemented yet.

Warning

Not as efficient as it should be.

cov_matrix(x, theta)
cov_matrix_ij(xi, xj, theta)
get_Hessian(u, xi, theta)

Get the Hessian of the covariance function with respect to u

Parameters:
  • u – d-dimensional vector
  • xi – d-dimensional vector
  • theta – hyperparameters
Returns:

Hessian
get_Jacobian(u, xi, theta)

Get the Jacobian of the covariance function with respect to u

Parameters:
  • u – d-dimensional vector
  • xi – d-dimensional vector
  • theta – hyperparameters
Returns:

Jacobian
get_theta(x, t)
inv_cov_matrix(x, theta, cov_matrix=None)
ml_estimate(x, t)
Parameters:
  • x – list of d-dimensional vectors
  • t – list of responses
Returns:

maximum likelihood estimate for theta
skgpuppy.Covariance.dldot(a, B)
Parameters:
  • a – diagonal of a diagonal matrix
  • B – Matrix
skgpuppy.Covariance.drdot(A, b)
Parameters:
  • A – Matrix
  • b – diagonal of a diagonal matrix
skgpuppy.Covariance.tracedot(A, B)
Parameters:
  • A – Matrix
  • B – Matrix
Returns:

trace(dot(A,B))