# potts: Linearized Bregman solver for composite conditionally... In Libra: Linearized Bregman Algorithms for Generalized Linear Models

## Description

Solver for the entire solution path of coefficients.

## Usage

 1 2 potts(X, kappa, alpha, c = 1, tlist, nt = 100, trate = 100, group = FALSE, intercept = TRUE, print = FALSE)

## Arguments

 X An n-by-p matrix of variables. kappa The damping factor of the Linearized Bregman Algorithm that is defined in the reference paper. See details. alpha Parameter in Linearized Bregman algorithm which controls the step-length of the discretized solver for the Bregman Inverse Scale Space. See details. c Normalized step-length. If alpha is missing, alpha is automatically generated by alpha=c*n/(kappa*||XX^T*XX||_2), where XX is 0-1 indicator matrix induced by the class of each Xi. Default is 1. It should be in (0,2). If beyond this range the path may be oscillated at large t values. tlist Parameters t along the path. nt Number of t. Used only if tlist is missing. Default is 100. trate tmax/tmin. Used only if tlist is missing. Default is 100. group Whether to use a block-wise group penalty, Default is FALSE intercept if TRUE, an intercept is included in the model (and not penalized), otherwise no intercept is included. Default is TRUE. print If TRUE, the percentage of finished computation is printed.

## Details

The data matrix X is transformed into a 0-1 indicator matrix D with each column D_{jk} means 1(X_j)==k. The Potts model here used is described as following:

P(x) \sim \exp(∑_{jk} a_{0,jk}1(x_i=1) + d^T Θ d/2)

where Θ is p-by-p symmetric and 0 on diagnal. Then conditional on x_{-j}

P(x_j=k) \sim exp(∑_{k} a_{0,jk} + ∑_{i\neq j,r}θ_{jk,ir}d_{ir})

then the composite conditional likelihood is like this:

- ∑_{j} condloglik(X_j | X_{-j})

## Value

A "potts" class object is returned. The list contains the call, the path, the intercept term a0 and value for alpha, kappa, t.

Jiechao Xiong

## Examples

 1 2 X = matrix(floor(runif(200*10)*3),200,10) obj = potts(X,10,nt=100,trate=10,group=TRUE)

Libra documentation built on May 2, 2019, 3:55 p.m.