package gpr

  1. Overview
  2. Docs

Module Gpr.InterfacesSource

Representations of (sparse) derivative matrices

Sourcemodule Sparse_indices = Utils.Int_vec

Representation of indices into sparse matrices

Sourcetype common_mat_deriv = [
  1. | `Dense of Lacaml.D.mat
  2. | `Sparse_rows of Lacaml.D.mat * Sparse_indices.t
  3. | `Const of float
  4. | `Factor of float
]

Derivative representations for both symmetric and unsymmetric matrices.

  • Dense: matrix is dense.
  • Sparse_rows: matrix is zero everywhere except for rows whose index is stored in the sparse index argument. The rows in the matrix correspond to the given indices.
  • Const: matrix is constant everywhere.
  • Factor: matrix is the non-derived matrix times the given factor (useful with exponential functions).
Sourcetype mat_deriv = [
  1. | common_mat_deriv
  2. | `Sparse_cols of Lacaml.D.mat * Sparse_indices.t
]

Only general matrices support sparse column representations.

  • Sparse_cols: matrix is zero everywhere except for columns whose index is stored in the sparse index argument. The columns in the matrix correspond to the given indices.
Sourcetype symm_mat_deriv = [
  1. | common_mat_deriv
  2. | `Diag_vec of Lacaml.D.vec
  3. | `Diag_const of float
]

Only symmetric (square) matrices support diagonal vectors and diagonal constants as derivatives.

  • Diag_vec: matrix is zero everywhere except for the diagonal whose values are given in the argument.
  • Diag_const: matrix is zero everywhere except for the diagonal whose values are set to the given constant.

Note that sparse rows do not need to compute or store all elements for symmetric matrices. Entries that have already appeared in previous rows by symmetry can be left uninitialized.

Sourcetype diag_deriv = [
  1. | `Vec of Lacaml.D.vec
  2. | `Sparse_vec of Lacaml.D.vec * Sparse_indices.t
  3. | `Const of float
  4. | `Factor of float
]

Derivatives of diagonal matrices.

  • Vec: the derivatives of the diagonal given in a dense vector.
  • Sparse_vec: matrix is zero everywhere except at those indices along the diagonal that are mentioned in the sparse indices argument. The element associated with such an index is stored in the vector argument.
  • Const: the derivative of the diagonal matrix is a constant.
  • Factor: the derivative of the diagonal is the the non-derived diagonal matrix times the given factor (useful with exponential functions).
Sourcemodule Specs : sig ... end

Specifications of covariance functions (= kernels) and their derivatives

Sourcemodule Sigs : sig ... end

Signatures for learning sparse Gaussian processes with inducing inputs