ldf: LDF method for flash and flash fit objects

In willwerscheid/flashier: Empirical Bayes Matrix Factorization

LDF method for flash and flash fit objects

Description

Given a flash or flash_fit object, returns the LDF decomposition Y \approx LDF'.

Usage

ldf(object, type)

## S3 method for class 'flash'
ldf(object, type = "f")

## S3 method for class 'flash_fit'
ldf(object, type = "f")

Arguments

object	An object inheriting from class flash or flash_fit.
type	Takes identical arguments to function norm. Use "f" or "2" for the 2-norm (Euclidean norm); "o" or "1" for the 1-norm (taxicab norm); and "i" or "m" for the infinity norm (maximum norm).

Details

When the prior families G_\ell^{(k)} and G_f^{(k)} are closed under scaling (as is typically the case), then the EBMF model (as described in the documention to function flash) is only identifiable up to scaling by a diagonal matrix D:

Y = LDF' + E.

Method ldf scales columns \ell_k and f_k so that, depending on the argument to parameter type, their 1-norms, 2-norms, or infinity norms are equal to 1.

Value

A list with fields L, D, and F, each of which corresponds to one of the matrices in the decomposition Y \approx LDF' (with the columns of L and F scaled according to argument type). Note that D is returned as a vector rather than a matrix (the vector of diagonal entries in D). Thus, "fitted values" LDF' can be recovered as L %*% diag(D) %*% t(F).

Methods (by class)

• ldf(flash): LDF decomposition for flash objects

• ldf(flash_fit): LDF decomposition for flash_fit objects

willwerscheid/flashier documentation built on Jan. 30, 2025, 11:27 p.m.