lori {lori}

The lori method implements a method to analyze and impute incomplete count tables. An important feature of the method is that it can take into account main effects of rows and columns, as well as effects of continuous or categorical covariates, and interaction. The estimation procedure is based on minimizing a Poisson loss penalized by a Lasso type penalty (sparse vector of covariate effects) and a nuclear norm penalty inducing a low-rank interaction matrix (a few latent factors summarize the interactions).

Description

The lori method implements a method to analyze and impute incomplete count tables. An important feature of the method is that it can take into account main effects of rows and columns, as well as effects of continuous or categorical covariates, and interaction. The estimation procedure is based on minimizing a Poisson loss penalized by a Lasso type penalty (sparse vector of covariate effects) and a nuclear norm penalty inducing a low-rank interaction matrix (a few latent factors summarize the interactions).

Usage

lori(
  Y,
  cov = NULL,
  lambda1 = NULL,
  lambda2 = NULL,
  intercept = T,
  reff = T,
  ceff = T,
  rank.max = 2,
  algo = c("alt", "mcgd"),
  thresh = 1e-05,
  maxit = 100,
  trace.it = F,
  parallel = F
)

Arguments

Y

[matrix, data.frame] count table (nxp).

cov

[matrix, data.frame] design matrix (np*q) in order row1xcol1,row2xcol2,..,rownxcol1,row1xcol2,row2xcol2,...,...,rownxcolp

lambda1

[positive number] the regularization parameter for the interaction matrix.

lambda2

[positive number] the regularization parameter for the covariate effects.

intercept

[boolean] whether an intercept should be fitted, default value is FALSE

reff

[boolean] whether row effects should be fitted, default value is TRUE

ceff

[boolean] whether column effects should be fitted, default value is TRUE

rank.max

[integer] maximum rank of interaction matrix (smaller than min(n-1,p-1))

algo

type of algorithm to use, either one of "mcgd" (mixed coordinate gradient descent, adapted to large dimensions) or "alt" (alternating minimization, adapted to small dimensions)

thresh

[positive number] convergence tolerance of algorithm, by default 1e-6.

maxit

[integer] maximum allowed number of iterations.

trace.it

[boolean] whether convergence information should be printed

parallel

[boolean] whether computations should be performed in parallel on multiple cores

Value

A list with the following elements

X

nxp matrix of log of expected counts

alpha

row effects

beta

column effects

epsilon

covariate effects

theta

nxp matrix of row-column interactions

imputed

nxp matrix of imputed counts

means

nxp matrix of expected counts (exp(X))

cov

npxK matrix of covariates

Examples