# IterativeHardThresholding

IterativeHardThresholding is part of the HADES.

# Introduction

IterativeHardThresholding is an R package for performing L_0-based regressions using Cyclops

# Examples

• Cox’s Proportional Hazards Model
library(Cyclops)
library(IterativeHardThresholding)
library(survival)

## data dimension
p <- 20    # number of covariates
n <- 300   # sample size

## tuning parameters
lambda <- log(n)  # BAR penalty (BIC)
xi     <- 0.1     # initial ridge penalty

## Cox model parameters
true.beta <- c(1, 0.1, 0, -1, 1, rep(0, p - 5))

## simulate data from an exponential model
x        <- matrix(rnorm(p * n, mean = 0, sd = 1), ncol = p)
ti       <- rweibull(n, shape = 1, scale = exp(-x%*%true.beta))
ui       <- runif(n, 0, 10) # Controls censoring
ci       <- rweibull(n, shape = 1, scale = ui * exp(-x%*%true.beta))
survtime <- pmin(ti, ci)
delta    <- ti == survtime; mean(delta)

cyclopsData <- createCyclopsData(Surv(survtime, delta) ~ x, modelType = "cox")
ihtPrior    <- createIhtPrior(K = 3, penalty = "bic")

cyclopsFit <- fitCyclopsModel(cyclopsData,
prior = ihtPrior)
coef(cyclopsFit)
• Generalized Linear Model
library(Cyclops)
library(IterativeHardThresholding)

## data dimension
p <- 20    # number of covariates
n <- 300   # sample size

## tuning parameters
lambda <- log(n)  # BAR penalty (BIC)
xi     <- 0.1     # initial ridge penalty

## logistic model parameters
itcpt     <- 0.2 # intercept
true.beta <- c(1, 0.3, 0, -1, 1, rep(0, p - 5))

## simulate data from logistic model
x <- matrix(rnorm(p * n, mean = 0, sd = 1), ncol = p)
y <- rbinom(n, 1, 1 / (1 + exp(-itcpt - x%*%true.beta)))

# fit BAR model
cyclopsData <- createCyclopsData(y ~ x, modelType = "lr")
ihtPrior    <- createIhtPrior(K  = 3, penalty = "bic", exclude = c("(Intercept)"))

cyclopsFit <- fitCyclopsModel(cyclopsData,
prior = ihtPrior)
coef(cyclopsFit)

# System Requirements

Requires R (version 3.2.0 or higher). Installation on Windows requires RTools (devtools >= 1.12 required for RTools34, otherwise RTools33 works fine).

• Cyclops

# Getting Started

1. On Windows, make sure RTools is installed.
2. In R, use the following commands to download and install IterativeHardThresholding:
install.packages("devtools")
library(devtools)
install_github("ohdsi/Cyclops")
install_github("ohdsi/IterativeHardThresholding")
1. To perform a L_0-based Cyclops model fit with IHT, use the following commands in R:
library(IterativeHardThresholding)
cyclopsData <- createCyclopsData(formula, modelType = "modelType") ## TODO: Update
ihtPrior    <- createIhtPrior(K = 5, penalty = "bic")
cyclopsFit  <- fitCyclopsModel(cyclopsData, prior = ihtPrior)
coef(cyclopsFit) #Extract coefficients