gammy.models.bayespy.GAM

GAM

class GAM(formula, tau=None, theta=None)[source]

Bases: object

Generalized additive model with BayesPy backend

Currently tau is fixed to Gamma distribution, i.e., it is not possible to manually define the noise level. Note though that one can set tight values for α, β in Gamma(α, β), recalling that mean = α / β and variance = α / β ** 2. The upside is that by estimating the noise level, one gets a nice prediction uncertainty estimate.

Currently Gaussian requirement deeply built in. Tau being Gamma implies, by conjugacy, that theta must be Gaussian.

Does not support scalar valued Gaussian r.v.. Could be implemented using GaussianARD but this would require a lot of refactoring for such a small feature – after all one can define an auxiliary bias term with a very tight prior.

TODO: Statistics for basis function evaluations at grid points.

FIXME: BayesPy fit fails with the following example:

gammy.bayespy.GAM(
    gammy.Scalar()
).fit(np.array([0]), np.array([1]))
Parameters
formulagammy.formulae.Formula

Formula object containing the terms and prior

thetabp.nodes.Gaussian

Model parameters vector

taubp.nodes.Gamma

Observation noise precision (inverse variance)

__len__() → int[source]

Number of model parameters

property covariance_theta

Covariance estimate of model parameters

fit(input_data, y, repeat=1000, verbose=False, **kwargs) → gammy.models.bayespy.GAM[source]

Update BayesPy nodes and construct a GAM predictor

WARNING: Currently mutates the original object’s theta and tau.

An option to “reset” the original object to prior is to use the method initialize_from_prior() of BayesPy nodes.

Parameters
input_datanp.ndarray

Input data

ynp.ndarray

Observations

repeatint

BayesPy allowed repetitions in variational Bayes learning

verbosebool

BayesPy logging

formula

Model formula

property inv_mean_tau

Additive observation noise variance estimate

load(filepath: str, **kwargs) → gammy.models.bayespy.GAM[source]

Load model from a file on disk

marginal_residual(input_data, y, i: int) → numpy.ndarray[source]

Calculate marginal residual for a given term

Parameters
input_datanp.ndarray
marginal_residuals(input_data, y) → List[numpy.ndarray][source]

Marginal (partial) residuals

Parameters
input_datanp.ndarray

Input data

ynp.ndarray

Observations

property mean_theta

Mean estimate of model parameters

Posterior if model is fitted, otherwise prior.

predict(input_data) → numpy.ndarray[source]

Calculate mean of posterior predictive at inputs

Parameters
input_datanp.ndarray
predict_marginal(input_data, i: int) → numpy.ndarray[source]

Predict a term separately

Parameters
input_datanp.ndarray
predict_marginals(input_data) → List[numpy.ndarray][source]

Predict all terms separately

Parameters
input_datanp.ndarray
predict_variance(input_data) → Tuple[numpy.ndarray][source]

Predict mean and variance

Parameters
input_datanp.ndarray
predict_variance_marginal(input_data, i: int) → Tuple[numpy.ndarray][source]

Predict marginal distributions means and variances

Parameters
input_datanp.ndarray
predict_variance_marginals(input_data) → List[Tuple[numpy.ndarray]][source]

Predict variance (theta) for marginal parameter distributions

NOTE: Analogous to self.predict_variance_theta but for marginal distributions. Adding observation noise does not make sense as we don’t know how it is splitted among the model terms.

Parameters
input_datanp.ndarray
predict_variance_theta(input_data) → Tuple[numpy.ndarray][source]

Predict observations with variance from model parameters

Parameters
input_datanp.ndarray
save(filepath: str) → None[source]

Save the model to disk

Supported file formats: JSON and HDF5

tau

Node for additive noise precision

theta

Node for model parameters

theta_marginal(i: int) → bayespy.inference.vmp.nodes.gaussian.Gaussian[source]

Extract marginal distribution for a specific term

property theta_marginals

Nodes for the basis specific marginal distributions