# pymc.gp.Latent#

class pymc.gp.Latent(*, mean_func=<pymc.gp.mean.Zero object>, cov_func=<pymc.gp.cov.Constant object>)[source]#

Latent Gaussian process.

The gp.Latent class is a direct implementation of a GP. No additive noise is assumed. It is called “Latent” because the underlying function values are treated as latent variables. It has a prior method and a conditional method. Given a mean and covariance function the function $$f(x)$$ is modeled as,

$f(x) \sim \mathcal{GP}\left(\mu(x), k(x, x')\right)$

Use the prior and conditional methods to actually construct random variables representing the unknown, or latent, function whose distribution is the GP prior or GP conditional. This GP implementation can be used to implement regression on data that is not normally distributed. For more information on the prior and conditional methods, see their docstrings.

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.

Examples

# A one dimensional column vector of inputs.
X = np.linspace(0, 1, 10)[:, None]

with pm.Model() as model:
# Specify the covariance function.

# Specify the GP.  The default mean function is Zero.
gp = pm.gp.Latent(cov_func=cov_func)

# Place a GP prior over the function f.
f = gp.prior("f", X=X)

...

# 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

 Latent.__init__(*[, mean_func, cov_func]) Latent.conditional(name, Xnew[, given, jitter]) Returns the conditional distribution evaluated over new input locations Xnew. Latent.marginal_likelihood(name, X, *args, ...) Latent.predict(Xnew[, point, given, diag, model]) Latent.prior(name, X[, reparameterize, jitter]) Returns the GP prior distribution evaluated over the input locations X.

Attributes

 X f