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Kernel and RKHS methods

morie_kernel_methods.Rd

Kernel matrices, reproducing-kernel Hilbert space regression, kernel BLUP, and the Nystrom and eigenvalue compressions used to make them scale.

Usage

morie_kernel_matrix(X, kernel = "linear", gamma = NULL, degree = 2, coef0 = 1, Z = NULL) 

morie_rkhs_fit(K, y, lambda = 1) 

morie_rkhs_predict(K_new, beta, eta0 = 0) 

morie_rkhs_mixed_equations(C, K, y, lambda = 1, sigma2_e = 1, form = "direct") 

morie_arccos_kernel(X, Z = NULL, depth = 1L, normalize_median = FALSE) 

morie_bayesian_kernel_blup(y, K, sigma2_u = 1, sigma2_e = 1, mu = NULL) 

morie_kernel_blup_gxe(Z_u1, K, Z_E, sigma2_u1 = 1, sigma2_u2 = 1) 

morie_kernel_blup_replicated(Z, K, sigma2_u = 1) 

morie_kernel_eigen_design(K, tol = 1e-10) 

morie_nystrom(X, m_index, kernel = "linear", gamma = NULL) 

morie_sparse_kernel_design(X, m_index, kernel = "linear", gamma = NULL, tol = 1e-10)

Arguments

X

numeric matrix of inputs, one row per observation

y

numeric response vector

kernel

kernel name, one of linear, gaussian, polynomial, exponential, sigmoid or arccos

gamma

argument gamma; not described in the source.

degree

argument degree; not described in the source.

coef0

argument coef0; not described in the source.

Z

argument Z; not described in the source.

K

argument K; not described in the source.

lambda

argument lambda; not described in the source.

K_new

argument K_new; not described in the source.

beta

argument beta; not described in the source.

eta0

argument eta0; not described in the source.

C

argument C; not described in the source.

sigma2_e

argument sigma2_e; not described in the source.

form

argument form; not described in the source.

depth

argument depth; not described in the source.

normalize_median

argument normalize_median; not described in the source.

sigma2_u

argument sigma2_u; not described in the source.

mu

argument mu; not described in the source.

Z_u1

argument Z_u1; not described in the source.

Z_E

argument Z_E; not described in the source.

sigma2_u1

argument sigma2_u1; not described in the source.

sigma2_u2

argument sigma2_u2; not described in the source.

tol

argument tol; not described in the source.

m_index

argument m_index; not described in the source.

Value

A list holding the fitted quantities for the method called: point estimates, fitted values and any diagnostics it produces. See the individual method descriptions above for the components each returns.

Details

These functions mirror, in R, the implementations in the Python package morie; the two are checked against each other by the parity tests in tests/testthat/.

Examples

set.seed(1)
X <- matrix(rnorm(20), 10, 2)
morie_kernel_matrix(X, kernel = "gaussian", gamma = 0.5)
#>               [,1]       [,2]      [,3]         [,4]        [,5]        [,6]
#>  [1,] 1.000000e+00 0.38385091 0.1005834 8.178777e-05 0.587571210 0.292146095
#>  [2,] 3.838509e-01 1.00000000 0.3567918 1.242329e-02 0.755167901 0.549560938
#>  [3,] 1.005834e-01 0.35679179 1.0000000 1.463680e-02 0.110434925 0.846893967
#>  [4,] 8.178777e-05 0.01242329 0.0146368 1.000000e+00 0.001699098 0.005134027
#>  [5,] 5.875712e-01 0.75516790 0.1104349 1.699098e-03 1.000000000 0.260405803
#>  [6,] 2.921461e-01 0.54956094 0.8468940 5.134027e-03 0.260405803 1.000000000
#>  [7,] 1.673420e-01 0.87934806 0.3470509 4.829680e-02 0.515020620 0.424980947
#>  [8,] 3.353465e-01 0.73543742 0.0851452 4.722759e-03 0.904870636 0.181999593
#>  [9,] 3.824638e-01 0.84372422 0.1304994 5.927825e-03 0.926403739 0.259274292
#> [10,] 6.232589e-01 0.86901416 0.4152551 3.181533e-03 0.709962745 0.714116806
#>            [,7]        [,8]        [,9]       [,10]
#>  [1,] 0.1673420 0.335346506 0.382463815 0.623258942
#>  [2,] 0.8793481 0.735437422 0.843724223 0.869014161
#>  [3,] 0.3470509 0.085145203 0.130499350 0.415255092
#>  [4,] 0.0482968 0.004722759 0.005927825 0.003181533
#>  [5,] 0.5150206 0.904870636 0.926403739 0.709962745
#>  [6,] 0.4249809 0.181999593 0.259274292 0.714116806
#>  [7,] 1.0000000 0.611219138 0.701501641 0.606296816
#>  [8,] 0.6112191 1.000000000 0.979485944 0.545585514
#>  [9,] 0.7015016 0.979485944 1.000000000 0.660956522
#> [10,] 0.6062968 0.545585514 0.660956522 1.000000000