gpflow.expectations¶
gpflow.expectations.expectation¶
- gpflow.expectations.expectation(p, obj1, obj2=None, nghp=None)[source]¶
Compute the expectation <obj1(x) obj2(x)>_p(x) Uses multiple-dispatch to select an analytical implementation, if one is available. If not, it falls back to quadrature.
- Parameters
nghp (int) – passed to _quadrature_expectation to set the number of Gauss-Hermite points used: num_gauss_hermite_points
- Return type
Tensor- Returns
a 1-D, 2-D, or 3-D tensor containing the expectation
Allowed combinations
- Psi statistics:
>>> eKdiag = expectation(p, kernel) (N) # Psi0 >>> eKxz = expectation(p, (kernel, inducing_variable)) (NxM) # Psi1 >>> exKxz = expectation(p, identity_mean, (kernel, inducing_variable)) (NxDxM) >>> eKzxKxz = expectation(p, (kernel, inducing_variable), (kernel, inducing_variable)) (NxMxM) # Psi2
- kernels and mean functions:
>>> eKzxMx = expectation(p, (kernel, inducing_variable), mean) (NxMxQ) >>> eMxKxz = expectation(p, mean, (kernel, inducing_variable)) (NxQxM)
- only mean functions:
>>> eMx = expectation(p, mean) (NxQ) >>> eM1x_M2x = expectation(p, mean1, mean2) (NxQ1xQ2) .. note:: mean(x) is 1xQ (row vector)
- different kernels. This occurs, for instance, when we are calculating Psi2 for Sum kernels:
>>> eK1zxK2xz = expectation(p, (kern1, inducing_variable), (kern2, inducing_variable)) (NxMxM)
- Parameters
p (
Union[ProbabilityDistribution,Tuple[Union[ndarray,Tensor,Variable, Parameter],Union[ndarray,Tensor,Variable, Parameter]]]) –obj1 (
Union[Kernel,MeanFunction,None,Tuple[Kernel,InducingVariables]]) –obj2 (
Union[Kernel,MeanFunction,None,Tuple[Kernel,InducingVariables]]) –nghp (
Optional[int]) –
gpflow.expectations.quadrature_expectation¶
- gpflow.expectations.quadrature_expectation(p, obj1, obj2=None, nghp=None)[source]¶
Compute the expectation <obj1(x) obj2(x)>_p(x) Uses Gauss-Hermite quadrature for approximate integration.
- Parameters
num_gauss_hermite_points (int) – passed to _quadrature_expectation to set the number of Gauss-Hermite points used
- Return type
Tensor- Returns
a 1-D, 2-D, or 3-D tensor containing the expectation
- Parameters
p (
Union[ProbabilityDistribution,Tuple[Union[ndarray,Tensor,Variable, Parameter],Union[ndarray,Tensor,Variable, Parameter]]]) –obj1 (
Union[Kernel,MeanFunction,None,Tuple[Kernel,InducingVariables]]) –obj2 (
Union[Kernel,MeanFunction,None,Tuple[Kernel,InducingVariables]]) –nghp (
Optional[int]) –