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‎docs/source/notebooks/GP-Latent.ipynb

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"If `gp` is part of a sum of GP objects, it can be conditioned on different components of that sum using the optional keyword argument `given`,\n",
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"\n",
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"```python\n",
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" f_star_diff = gp.conditional(\"f_star_diff\", n_points=100, X_star, given=a_different_gp)\n",
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" f_star_diff = gp.conditional(\"f_star_diff\", n_points=100, X_star, \n",
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" gp=a_different_gp)\n",
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"```"
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]
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},
@@ -125,7 +126,8 @@
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{
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‎docs/source/notebooks/GP-Marginal.ipynb

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‎pymc3/gp/gp.py

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Original file line numberDiff line numberDiff line change
@@ -53,8 +53,47 @@ def predict(self, Xnew, point=None, given=None, diag=False):
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@conditioned_vars(["X", "f"])
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class Latent(Base):
56-
""" Where the GP f isnt integrated out, and is sampled explicitly
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R"""
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The `gp.Latent` class is a direct implementation of a GP. No addiive
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noise is assumed. It is called "Latent" because the underlying function
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values are treated as latent variables. It has a `prior` method, and a
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`conditional` method. Given a mean and covariance function, the
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function $f(x)$ is modeled as,
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.. math::
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f(x) \sim \mathcal{GP}\left(\mu(x), k(x, x')\right)
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Use the `prior` and `conditional` methods to construct random
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variables representing the unknown, or latent, function whose
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distribution is the GP prior or GP conditional. This GP implementation
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can be used to implement regression with non-normal likelihoods or
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classification.
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Parameters
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----------
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cov_func : None, 2D array, or instance of Covariance
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The covariance function. Defaults to matrix of zeros.
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mean_func : None, instance of Mean
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The mean function. Defaults to a vector of ones.
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Notes
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-----
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- After initializing the GP object with a mean and covariance
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function, it can be added to other `Latent` GP objects.
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- For more information on the `prior` and `conditional` methods,
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see their docstrings.
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Examples
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--------
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.. code:: python
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with pm.Model() as model:
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"""
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def __init__(self, mean_func=None, cov_func=None):
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super(Latent, self).__init__(mean_func, cov_func)
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@@ -69,6 +108,29 @@ def _build_prior(self, name, X, n_points, reparameterize=True):
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return f
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def prior(self, name, X, n_points=None, reparameterize=True):
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R"""
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Returns the GP prior distribution evaluated over the input
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locations `X`. This is the prior probability over the space
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of functions described by its mean and covariance function.
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.. math::
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f \mid X \sim \text{MvNormal}\left(\boldsymbol\mu, \mathbf{K}\right)
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Parameters
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----------
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name : string
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Name of the random variable
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X : array-like
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Function input values.
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n_points : int, optional
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Required if `X` is a random variable or a Theano object.
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This is the number of points the GP is evaluated over, the
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number of rows in `X`.
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reparameterize : bool
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Reparameterize the distribution by rotating the random
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variable by the Cholesky factor of the covariance matrix.
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"""
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n_points = infer_shape(X, n_points)
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f = self._build_prior(name, X, n_points, reparameterize)
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self.X = X
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return mu, cov
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def conditional(self, name, Xnew, n_points=None, given=None):
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R"""
166+
Returns the conditional distribution evaluated over new input
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locations `Xnew`. Given a set of function values `f` that
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the GP prior was over, the conditional distribution over a
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set of new points, `f_*` is
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.. math::
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f^* \mid f, X, X_{\text{new}} \sim \mathcal{GP}\left(\mu(x), k(x, x')\right)
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Parameters
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----------
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name : string
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Name of the random variable
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Xnew : array-like
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Function input values.
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n_points : int, optional
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Required if `Xnew` is a random variable or a Theano object.
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This is the number of points the GP is evaluated over, the
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number of rows in `Xnew`.
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given : keyword arguments
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The `gp.Latent` argument can optionally take as keyword args,
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`X`, `f`, and `gp`. See the tutorial on additive GP models in
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PyMC3 for more information.
189+
"""
103190
givens = self._get_given_vals(**given)
104191
mu, cov = self._build_conditional(Xnew, *givens)
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chol = cholesky(stabilize(cov))

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