Gaussian Linear Model

Routine for polynomial regression (Gaussian Linear Model)

class gaussianlinear.GLM(theta: numpy.ndarray, y: numpy.ndarray, order: int = 2, var: float = 1e-05, x_trans: bool = False, y_trans: bool = False, use_mean: bool = True)

Bases: object

Gaussian Linear Model (GLM) class for polynomial regression

compute_basis(test_point: numpy.ndarray = None) → numpy.ndarray

Compute the input basis functions

Param

test_point (np.ndarray: optional) : if a test point is provided, phi_star is calculated

Returns

phi or phi_star (np.ndarray) : the basis functions

do_transformation() → None

Perform all transformations

evidence() → numpy.ndarray

Calculates the log-evidence of the model

Returns

log_evidence (np.ndarray) : the log evidence of the model

inv_noise_cov() → numpy.ndarray

Calculate the inverse of the noise covariance matrix

Returns

mat_inv (np.ndarray) : inverse of the noise covariance

inv_prior_cov() → numpy.ndarray

Calculate the inverse of the prior covariance matrix

mat_inv (np.ndarray) : inverse of the prior covariance matrix (parametric part)

noise_covariance() → None

Build the noise covariance matrix

posterior_coefficients() → Tuple[numpy.ndarray, numpy.ndarray]

Calculate the posterior coefficients

beta_bar (np.ndarray) : mean posterior

lambda_cap (np.ndarray) : covariance of the regression coefficients

prediction(test_point: numpy.ndarray) → Tuple[numpy.ndarray, numpy.ndarray]

Given a test point, the prediction (mean and variance) will be computed

Param

test_point (np.ndarray) : vector of test point in parameter space

Returns

post_mean (np.ndarray) : mean of the posterior

Returns

post_var (np.ndarray) : variance of the posterior

regression_prior(mean: numpy.ndarray = None, cov: numpy.ndarray = None, lambda_cap: float = 1) → None

Specify the regression prior (mean and covariance)

Param

mean (np.ndarray) : default zeros

Param

cov (np.ndarray) : default identity matrix

Param

lambda_cap (float) : width of the prior covariance matrix (default 1)