com.linkedin.photon.ml.hyperparameter.estimators.kernels
Matern52
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package kernels
the covariance amplitude
the observation noise
the length scale of the kernel. This controls the complexity of the kernel, or the degree to which it can vary within a given region of the function's domain. Higher values allow less variation, and lower values allow more.
Applies the kernel functions to the two sets of points
Applies the kernel functions to the two sets of points
the matrix containing the first set of points, where each of the m rows is a point in the space
the matrix containing the second set of points, where each of the p rows is a point in the space
the m x p covariance matrix
Applies the kernel function to the given points
Applies the kernel function to the given points
the matrix of points, where each of the m rows is a point in the space
the m x m covariance matrix
If only one parameter value has been specified, builds a new vector with the single value repeated to fill all dimensions
If only one parameter value has been specified, builds a new vector with the single value repeated to fill all dimensions
the initial parameters
the dimensions of the final vector
the vector with all dimensions specified
Computes the Matern 5/2 kernel function from the pairwise distances between points.
Computes the Matern 5/2 kernel function from the pairwise distances between points.
the m x p matrix of pairwise distances between m and p points
the m x p covariance matrix
Builds a kernel with initial settings, based on the observations
Returns the kernel parameters as a vector
Returns the kernel parameters as a vector
the kernel parameters
Computes the log likelihood of the kernel parameters
Computes the log likelihood of the kernel parameters
the observed features
the observed labels
the log likelihood
Computes the pairwise squared distance between the points in two sets
Computes the pairwise squared distance between the points in two sets
the matrix containing the first set of points, where each of the m rows is a point in the space
the matrix containing the second set of points, where each of the p rows is a point in the space
the m x p matrix of distances
Computes the pairwise squared distances between all points
Computes the pairwise squared distances between all points
the matrix of points, where each of the m rows is a point in the space
the m x m matrix of distances
Creates a new kernel function of the same type, with the given parameters
Implements the Matérn 5/2 covariance kernel.
The Matern kernel is a generalization of the RBF kernel with an additional parameter $\nu$ that allows controlling smoothness. At $\nu = \infty$, the Matern kernel is equivalent to RBF. At $\nu = 0.5$, it's equivalent to the absolute exponential kernel. It's noted in the literature that $\nu = 2.5$ allows the kernel to closely approximate hyperparameter spaces where the smoothness of RBF causes issues (see PBO). Here we hard-code to the 5/2 value because the computation is much simpler than allowing a user-defined $\nu$.
$K(x,x') = \big(\sqrt{5r2(x,x')} + \frac{5}{3} r2(x,x') + 1\big) \exp(-\sqrt{5r^2(x,x')})$
Where $r(x,x')$ is the Euclidean distance between $x$ and $x'$.
"Practical Bayesian Optimization of Machine Learning Algorithms" (PBO), https://papers.nips.cc/paper/4522-practical-bayesian-optimization-of-machine-learning-algorithms.pdf
"Gaussian Processes for Machine Learning" (GPML), http://www.gaussianprocess.org/gpml/, Chapter 4