flash_backfit {flashier}

Backfit a flash object

Description

Backfits existing flash factor/loadings pairs. Whereas a "greedy" fit optimizes each newly added factor/loadings pair in one go without returning to optimize previously added pairs, a "backfit" updates all existing pairs in a cyclical fashion. See flash for examples of usage.

Usage

flash_backfit(
  flash,
  kset = NULL,
  extrapolate = TRUE,
  warmstart = TRUE,
  maxiter = 500,
  tol = NULL,
  verbose = NULL
)

Arguments

flash

A flash or flash_fit object.

kset

A vector of integers specifying which factors to backfit. If kset = NULL, then all existing factors will be backfitted.

extrapolate

Whether to use an extrapolation technique inspired by Ang and Gillis (2019) to accelerate the fitting process. Control parameters are handled via global options and can be set by calling options("extrapolate.control") <- control.param.

warmstart

Whether to use "warmstarts" when solving the EBNM subproblems by initializing solutions at the previous value of the fitted prior \hat{g}. An important side effect of warmstarts for ashr-like prior families is to fix the grid at its initial setting. Fixing the grid can lead to poor fits if there are large changes in the scale of the estimated prior over the course of the fitting process. However, allowing the grid to vary can occasionally result in decreases in ELBO.

maxiter

The maximum number of backfitting iterations. An "iteration" is defined such that all factors in kset get updated at each iteration.

tol

The convergence tolerance parameter. After each update, the fit is compared to the fit from before the update using a convergence criterion function (by default, the difference in ELBO, but the criterion can be changed via flash_set_conv_crit). The backfit is considered to have "converged" when the value of the convergence criterion function over successive updates to all factor/loadings pairs is less than or equal to tol. If, for example, factor/loadings pairs 1, \ldots, K are being sequentially backfitted, then fits are compared before and after the update to factor/loadings 1, before and after the update to factor/loadings 2, and so on through factor/loadings K, and backfitting only terminates when the convergence criterion function returns a value less than or equal to tol for all K updates. Note that specifying tol here will override any value set by flash_set_conv_crit; to use the "global" tolerance parameter, tol must be left unspecified (NULL). If tol = NULL and a global tolerance parameter has not been set, then the default tolerance used is np\sqrt{\epsilon}, where n is the number of rows in the dataset, p is the number of columns, and \epsilon is equal to .Machine$double.eps.

verbose

When and how to display progress updates. Set to 0 for none, 1 for updates after a factor is added or a backfit is completed, 2 for additional notifications about the variational lower bound, and 3 for updates after every iteration. It is also possible to output a single tab-delimited table of values using function flash_set_verbose with verbose = -1.

Value

The flash object from argument flash, backfitted as specified.