R/zzPathCalc.r

In SGL: Fit a GLM (or Cox Model) with a Combination of Lasso and Group Lasso Regularization

betterPathCalc <- function(data, index, alpha = 0.95, min.frac = 0.05, nlam = 20, type = "linear"){

reset <- 10
step <- 1
gamma <- 0.8

inner.iter <- 1000
outer.iter <- 1000
thresh = 10^(-3)
outer.thresh = thresh
  
  n <- nrow(data$x)

  if(type == "linear"){

  X <- data$x
  resp <- data$y
  n <- nrow(X)
  p <- ncol(X)

  ## Setting up group lasso stuff ##
     
  ord <- order(index)
  index <- index[ord]
  X <- X[,ord]
  unOrd <- match(1:length(ord),ord)

  ## Coming up with other C++ info ##
    
  groups <- unique(index)
  num.groups <- length(groups)
  range.group.ind <- rep(0,(num.groups+1))
  for(i in 1:num.groups){
    range.group.ind[i] <- min(which(index == groups[i])) - 1
  }
  range.group.ind[num.groups + 1] <- ncol(X)
  
  group.length <- diff(range.group.ind)
  
  }

  if(type == "logit"){

  X <- data$x
  y <- data$y
  n <- nrow(X)
  p <- ncol(X)

  ## Setting up group lasso stuff ##
     
  ord <- order(index)
  index <- index[ord]
  X <- X[,ord]
  unOrd <- match(1:length(ord),ord)

  ## Coming up with other C++ info ##
    
  groups <- unique(index)
  num.groups <- length(groups)
  range.group.ind <- rep(0,(num.groups+1))
  for(i in 1:num.groups){
    range.group.ind[i] <- min(which(index == groups[i])) - 1
  }
  range.group.ind[num.groups + 1] <- ncol(X)
  
  group.length <- diff(range.group.ind)
  beta.naught <- rep(0,ncol(X))
  beta <- beta.naught
  
  beta.is.zero <- rep(1, num.groups)
  beta.old <- rep(0, ncol(X))
  betas <- matrix(0, nrow = ncol(X), ncol = nlam)

  eta <- rep(0,n)

  intercepts <- mean(y)

  eta = eta + intercepts

  m.y <- mean(y)

  resp <- m.y*m.y*(1-m.y) - (y-m.y)

  }

  if(type == "cox"){

  covariates <- data$x
  n <- nrow(covariates)
  p <- ncol(covariates)  
  time <- data$time
  status <- data$status

  ## Ordering Response and Removing any Censored obs before first death ##
  death.order <- order(time)
  ordered.time <- sort(time)  

  X <- covariates[death.order,]  
  ordered.status <- status[death.order]

  first.blood <- min(which(ordered.status == 1))

  X <- X[first.blood:n,]
  ordered.status <- ordered.status[first.blood:n]
  ordered.time <- ordered.time[first.blood:n]
  death.order <- death.order[first.blood:n]
  n <- n-first.blood+1
  
 death.times <- unique(ordered.time[which(ordered.status == 1)])  ## Increasing list of times when someone died (censored ends not included) ##

  ## Calculating Risk Sets ##
  
  risk.set <- rep(0,n)
  for(i in 1:n){
    risk.set[i] <- max(which(death.times <= ordered.time[i]))
  }

  ## Calculating risk set beginning/ending indices ##
  
  risk.set.ind <- rep(0,(length(death.times)+1))  
  for(i in 1:length(death.times)){
    risk.set.ind[i] <- min(which(ordered.time >= death.times[i]))
  }
  risk.set.ind[length(risk.set.ind)] <- length(ordered.time) + 1

  ## Calculating number of deaths at each death time ##
  num.deaths <- rep(0,length(death.times))
  for(i in 1:length(ordered.time)){
    if(ordered.status[i] == 1){
      num.deaths[which(death.times == ordered.time[i])] <-  num.deaths[which(death.times == ordered.time[i])] + 1
    }
  }
    
    ## Finding death indices and number of deaths ##
    death.index <- which(ordered.status == 1)
    total.deaths <- length(death.index)
    
    ## Setting up group lasso stuff ##
    
    ord <- order(index)
    index <- index[ord]
    X <- X[,ord]
    unOrd <- match(1:length(ord),ord)
    
    ## Coming up with other C++ info ##
    
    groups <- unique(index)
    num.groups <- length(groups)
    range.group.ind <- rep(0,(num.groups+1))
    for(i in 1:num.groups){
      range.group.ind[i] <- min(which(index == groups[i])) - 1
    }
    range.group.ind[num.groups + 1] <- ncol(X)

    group.length <- diff(range.group.ind)
    beta.naught <- rep(0,ncol(X))
    beta <- beta.naught

    beta.is.zero <- rep(1, num.groups)
    beta.old <- rep(0, ncol(X))
    beta <- array(0, c(ncol(X),nlam,nlam))

    beta.is.zero <- rep(1, num.groups)
  
  eta <- rep(0,n)

  ## DONE SETTING UP COX MODEL STUFF


  junk1 <- .C("Cox", riskSetInd = as.integer(risk.set.ind), riskSet = as.integer(risk.set), numDeath = as.integer(num.deaths), status = as.integer(ordered.status), ndeath = as.integer(length(death.times)), nrow = as.integer(n), ncol = as.integer(p), beta = as.double(rep(0,p)), eta = as.double(rep(0,n)), y = as.double(rep(0,n)), weights = as.double(rep(0,n)))

  resp <- junk1$y * junk1$weights
}
lambda.max <- rep(0,num.groups)

if((alpha != 0)*(alpha != 1)){

for(i in 1:num.groups){
  ind <- groups[i]
  X.fit <- X[,which(index == ind)]
  cors <- t(X.fit) %*% resp
  ord.cors <- sort(abs(cors), decreasing = TRUE)

  if(length(ord.cors) > 1){ 
  norms <- rep(0,length(cors)-1)

  lam <- ord.cors/alpha



  for(j in 1:(length(ord.cors)-1)){
    norms[j] <- sqrt(sum((ord.cors[1:j]-ord.cors[j+1])^2))
  }
  if(norms[1] >= lam[2] * (1-alpha)*sqrt(group.length[i])){
    our.cors <- ord.cors[1]
    our.range <- c(ord.cors[2], ord.cors[1])/alpha
  }else{
    if(norms[length(ord.cors)-1] <= lam[length(ord.cors)] * (1-alpha)*sqrt(group.length[i])){
      our.cors <- ord.cors
      our.range <- c(0, ord.cors[length(ord.cors)])/alpha
    } else{
      my.ind <- max(which(norms[-length(norms)] <= lam[2:(length(norms))] * (1-alpha) * sqrt(group.length[i]))) + 1
      our.cors <- ord.cors[1:my.ind]
      our.range <- c(ord.cors[my.ind+1], ord.cors[my.ind])/alpha
    }
  }
  nn <- length(our.cors)
  if(alpha == 0.5){
    alpha = 0.500001
  }
  
  A.term <- nn*alpha^2 - (1 - alpha)^2*group.length[i]
  B.term <- - 2 * alpha * sum(our.cors)
  C.term <- sum(our.cors^2)

  lams <- c((-B.term + sqrt(B.term^2 - 4 * A.term * C.term))/(2*A.term), (-B.term - sqrt(B.term^2 - 4 * A.term * C.term))/(2*A.term))
  
  
  lambda.max[i] <- min(subset(lams, lams >= our.range[1] & lams <= our.range[2]))
  }
     if(length(ord.cors) == 1){
       lambda.max[i] <- ord.cors
     }
}
}
if(alpha == 1){
  lambda.max <- abs(t(X) %*% resp)
}
if(alpha == 0){
  for(i in 1:num.groups){
  ind <- groups[i]
  X.fit <- X[,which(index == ind)]
  cors <- t(X.fit) %*% resp
  lambda.max[i] <- sqrt(sum(cors^2)) / sqrt(group.length[i])
  }
}
max.lam <- max(lambda.max)
min.lam <- min.frac*max.lam
lambdas <- exp(seq(log(max.lam),log(min.lam), (log(min.lam) - log(max.lam))/(nlam-1)))
return(lambdas/nrow(X))
}