flash_add_intercept {flashier}

Add "intercept" to a flash object

Description

Adds an all-ones vector as a fixed set of loadings (if rowwise = TRUE) or fixed factor (if rowwise = FALSE). Assuming (without loss of generality) that the fixed factor/loadings is indexed as k = 1, a fixed set of loadings gives:

\mathbf{y}_{i \cdot} \approx \mathbf{f}_1 + \sum_{k = 2}^K \ell_{i k} \mathbf{f}_k,

so that the (estimated) factor \mathbf{f}_1 \in \mathbf{R}^p is shared by all row-wise observations \mathbf{y}_{i \cdot} \in \mathbf{R}^p. A fixed factor gives:

\mathbf{y}_{\cdot j} \approx \boldsymbol{\ell}_1 + \sum_{k = 2}^K f_{j k} \boldsymbol{\ell}_k,

so that the (estimated) set of loadings \ell_1 \in \mathbf{R}^n is shared by all column-wise observations y_{\cdot j} \in \mathbf{R}^n.

Usage

flash_add_intercept(flash, rowwise = TRUE, ebnm_fn = ebnm_point_normal)

Arguments

flash

A flash or flash_fit object to which an "intercept" is to be added.

rowwise

Should the all-ones vector be added as a fixed set of loadings ("row-wise") or a fixed factor ("column-wise")? See above for details.

ebnm_fn

As with other factor/loadings pairs, a prior is put on the estimated factor (if rowwise = TRUE) or set of loadings (if rowwise = FALSE). Parameter ebnm_fn specifies the function used to estimate that prior; see flash for details.

Details

The estimated factor (if rowwise = TRUE) or set of loadings (if rowwise = FALSE) is initialized at the column- or row-wise means of the data (or, if factor/loadings pairs have previously been added, at the column- or row-wise means of the matrix of residuals) and then backfit via function flash_backfit.

Value

The flash object from argument flash, with an "intercept" added.

Examples

# The following are equivalent:
init <- list(matrix(rowMeans(gtex), ncol = 1),
             matrix(1, nrow = ncol(gtex)))
fl <- flash_init(gtex) %>%
  flash_factors_init(init) %>%
  flash_factors_fix(kset = 1, which_dim = "factors") %>%
  flash_backfit(kset = 1)

fl <- flash_init(gtex) %>%
  flash_add_intercept(rowwise = FALSE)