flash_factors_init {flashier}

Initialize flash factors at specified values

Description

Initializes factor/loadings pairs at values specified by init. This function has two primary uses: 1. One can initialize multiple factor/loadings pairs at once using an SVD-like function and then optimize them via function flash_backfit. Sometimes this results in a better fit than adding them one at a time via flash_greedy. 2. One can initialize factor/loadings pairs and then fix the factor (or loadings) via function flash_factors_fix to incorporate "known" factors into a flash object. See below for examples of both use cases.

Usage

flash_factors_init(flash, init, ebnm_fn = ebnm_point_normal)

Arguments

flash

A flash or flash_fit object to which factors are to be added.

init

An SVD-like object (specifically, a list containing fields u, d, and v), a flash or flash_fit object, or a list of matrices specifying the values at which factors and loadings are to be initialized (for a data matrix of size n \times p, this should be a list of length two, with the first element a matrix of size n \times k and the second a matrix of size p \times k). If a flash fit is supplied, then it will be used to initialize both the first and second moments of posteriors on loadings and factors. Otherwise, the supplied values will be used to initialize posterior means, with posterior second moments initialized as the squared values of the first moments. Missing entries are not allowed.

ebnm_fn

The function or functions used to solve the empirical Bayes normal means (EBNM) subproblems. Most importantly, these functions specify the families of distributions G_\ell^{(k)} and G_f^{(k)} to which the priors on loadings and factors g_\ell^{(k)} and g_f^{(k)} are assumed to belong. If the same function is to be used for both loadings L and factors F, then ebnm_fn can be a single function. If one function is to be used for loadings and a second for factors, then ebnm_fn should be a list of length two, with the first element giving the function for loadings and the second the function for factors. If different functions are to be used for different values of k, then factor/loadings pairs must be added successively using multiple calls to either flash_greedy or flash_factors_init.

Any EBNM function provided by package ebnm can be used as input. Non-default arguments to parameters can be supplied using the helper function flash_ebnm. Custom EBNM functions can also be used: for details, see flash_ebnm.

Value

The flash object from argument flash, with factors and loadings initialized as specified.

Examples

# Initialize several factors at once and backfit.
fl <- flash_init(gtex) %>%
  flash_factors_init(init = svd(gtex, nu = 5, nv = 5)) %>%
  flash_backfit()

# Add fixed loadings with \ell_i identically equal to one. This can be
#   interpreted as giving a "mean" factor that accounts for different
#   row-wise means.
ones <- matrix(1, nrow = nrow(gtex), ncol = 1)
# Initialize the factor at the least squares solution.
ls_soln <- t(solve(crossprod(ones), crossprod(ones, gtex)))
fl <- flash_init(gtex) %>%
  flash_factors_init(init = list(ones, ls_soln)) %>%
  flash_factors_fix(kset = 1, which_dim = "loadings") %>%
  flash_backfit() %>%
  flash_greedy(Kmax = 5L)