pymc.gp.MarginalApprox#
- class pymc.gp.MarginalApprox(approx='VFE', *, mean_func=<pymc.gp.mean.Zero object>, cov_func=<pymc.gp.cov.Constant object>)[source]#
Approximate marginal Gaussian process.
The gp.MarginalApprox class is an implementation of the sum of a GP prior and additive noise. It has marginal_likelihood, conditional and predict methods. This GP implementation can be used to implement regression on data that is normally distributed. The available approximations are:
DTC: Deterministic Training Conditional
FITC: Fully independent Training Conditional
VFE: Variational Free Energy
- Parameters
- cov_func: None, 2D array, or instance of Covariance
The covariance function. Defaults to zero.
- mean_func: None, instance of Mean
The mean function. Defaults to zero.
- approx: string
The approximation to use. Must be one of VFE, FITC or DTC. Default is VFE.
References
Quinonero-Candela, J., and Rasmussen, C. (2005). A Unifying View of Sparse Approximate Gaussian Process Regression.
Titsias, M. (2009). Variational Learning of Inducing Variables in Sparse Gaussian Processes.
Bauer, M., van der Wilk, M., and Rasmussen, C. E. (2016). Understanding Probabilistic Sparse Gaussian Process Approximations.
Examples
# A one dimensional column vector of inputs. X = np.linspace(0, 1, 10)[:, None] # A smaller set of inducing inputs Xu = np.linspace(0, 1, 5)[:, None] with pm.Model() as model: # Specify the covariance function. cov_func = pm.gp.cov.ExpQuad(1, ls=0.1) # Specify the GP. The default mean function is `Zero`. gp = pm.gp.MarginalApprox(cov_func=cov_func, approx="FITC") # Place a GP prior over the function f. sigma = pm.HalfCauchy("sigma", beta=3) y_ = gp.marginal_likelihood("y", X=X, Xu=Xu, y=y, sigma=sigma) ... # After fitting or sampling, specify the distribution # at new points with .conditional Xnew = np.linspace(-1, 2, 50)[:, None] with model: fcond = gp.conditional("fcond", Xnew=Xnew)
Methods
MarginalApprox.__init__
([approx, mean_func, ...])MarginalApprox.conditional
(name, Xnew[, ...])Returns the approximate conditional distribution of the GP evaluated over new input locations Xnew.
MarginalApprox.marginal_likelihood
(name, X, ...)Returns the approximate marginal likelihood distribution, given the input locations X, inducing point locations Xu, data y, and white noise standard deviations sigma.
MarginalApprox.predict
(Xnew[, point, diag, ...])Return the mean vector and covariance matrix of the conditional distribution as numpy arrays, given a point, such as the MAP estimate or a sample from a trace.
MarginalApprox.prior
(name, X, *args, **kwargs)Attributes
X
Xu
sigma
y