pymc.gp.TP

class pymc.gp.TP(*, mean_func=<pymc.gp.mean.Zero object>, scale_func=<pymc.gp.cov.Constant object>, cov_func=None, nu=None, parameterization=None)

Student’s T process prior.

The usage is nearly identical to that of gp.Latent. The differences are that it must be initialized with a degrees of freedom parameter, and TP is not additive. Given a mean and a kernel function, and a degrees of freedom parameter, the function \(f(x)\) is modeled as,

\[f(X) \sim \mathcal{TP}\left( \mu(X), k(X, X'), \nu \right)\]

How the kernel \(k\) is interpreted is controlled by the parameterization argument. The default ("scale") treats \(k\) as the scale matrix of an underlying MvStudentT, which makes the actual prior covariance equal to \(\nu / (\nu - 2) \, k\). The "covariance" option treats \(k\) as the actual covariance, matching the convention in Shah, Wilson, and Ghahramani (2014). The default will change to "covariance" in a future release; see the parameterization parameter below for migration guidance.

Parameters:

mean_funcMean, default Zero

The mean function.

scale_func2D array_like, or Covariance, default Constant

The kernel function. Interpreted as the scale matrix or the actual covariance depending on the parameterization argument.

cov_func2D array_like, or Covariance, default None

Deprecated, previous version of “scale_func”

nufloat

The degrees of freedom. For parameterization="covariance" the kernel only equals the prior covariance when \(\nu > 2\).

parameterization{“scale”, “covariance”}, optional

Whether the kernel returned by scale_func is treated as the scale matrix of the underlying multivariate Student-t ("scale", the current default) or as the actual covariance of the prior ("covariance", matching Shah, Wilson, and Ghahramani 2014). When left unspecified, "scale" is used and a FutureWarning is emitted because the default will change in a future release. Pass the value explicitly to silence the warning.

References

• Shah, A., Wilson, A. G., and Ghahramani, Z. (2014). Student-t Processes as Alternatives to Gaussian Processes. arXiv preprint arXiv:1402.4306.

Methods

TP.__init__(*[, mean_func, scale_func, ...])
TP.conditional(name, Xnew[, jitter])	Return the conditional distribution evaluated over new input locations Xnew.
TP.marginal_likelihood(name, X, *args, **kwargs)
TP.predict(Xnew[, point, given, diag, model])
TP.prior(name, X[, reparameterize, jitter])	Return the TP prior distribution evaluated over the input locations X.

Attributes

X
f
nu