R/big_oem.R

In oem: Orthogonalizing EM: Penalized Regression for Big Tall Data

#' Orthogonalizing EM for big.matrix objects
#'
#' @param x input big.matrix object pointing to design matrix 
#' Each row is an observation, each column corresponds to a covariate
#' @param y numeric response vector of length nobs.
#' @param family \code{"gaussian"} for least squares problems, \code{"binomial"} for binary response. 
#' \code{"binomial"} currently not available.
#' @param penalty Specification of penalty type. Choices include:
#' \itemize{
#'    \item{\code{"elastic.net"}}{ - elastic net penalty, extra parameters: \code{"alpha"}}
#'    \item{\code{"lasso"}}{ - lasso penalty}
#'    \item{\code{"ols"}}{ - ordinary least squares}
#'    \item{\code{"mcp"}}{ - minimax concave penalty, extra parameters: \code{"gamma"}}
#'    \item{\code{"scad"}}{ - smoothly clipped absolute deviation, extra parameters: \code{"gamma"}}
#'    \item{\code{"mcp.net"}}{ - minimax concave penalty + l2 penalty, extra parameters: 
#'    \code{"gamma"}, \code{"alpha"}}
#'    \item{\code{"scad.net"}}{ - smoothly clipped absolute deviation + l2 penalty, extra parameters: 
#'    \code{"gamma"}, \code{"alpha"}}
#'    \item{\code{"grp.lasso"}}{ - group lasso penalty}
#'    \item{\code{"grp.lasso.net"}}{ - group lasso penalty + l2 penalty, extra parameters: \code{"alpha"}}
#'    \item{\code{"grp.mcp"}}{ - group minimax concave penalty, extra parameters: \code{"gamma"}}
#'    \item{\code{"grp.scad"}}{ - group smoothly clipped absolute deviation, extra parameters: \code{"gamma"}}
#'    \item{\code{"grp.mcp.net"}}{ - group minimax concave penalty + l2 penalty, extra parameters: \code{"gamma"}, \code{"alpha"}}
#'    \item{\code{"grp.scad.net"}}{ - group smoothly clipped absolute deviation + l2 penalty, extra parameters: \code{"gamma"}, \code{"alpha"}}
#'    \item{\code{"sparse.grp.lasso"}}{ - sparse group lasso penalty (group lasso + lasso), extra parameters: \code{"tau"}}
#' }
#' Careful consideration is required for the group lasso, group MCP, and group SCAD penalties. Groups as specified by the \code{groups} argument 
#' should be chosen in a sensible manner.
#' @param weights observation weights. Not implemented yet. Defaults to 1 for each observation (setting weight vector to 
#' length 0 will default all weights to 1)
#' @param lambda A user supplied lambda sequence. By default, the program computes
#' its own lambda sequence based on \code{nlambda} and \code{lambda.min.ratio}. Supplying
#' a value of lambda overrides this.
#' @param nlambda The number of lambda values - default is 100.
#' @param lambda.min.ratio Smallest value for lambda, as a fraction of \code{lambda.max}, the (data derived) entry
#' value (i.e. the smallest value for which all coefficients are zero). The default
#' depends on the sample size nobs relative to the number of variables nvars. If
#' \code{nobs > nvars}, the default is 0.0001, close to zero. If \code{nobs < nvars}, the default
#' is 0.01. A very small value of \code{lambda.min.ratio} will lead to a saturated fit
#' when \code{nobs < nvars}.
#' @param alpha mixing value for \code{elastic.net}, \code{mcp.net}, \code{scad.net}, \code{grp.mcp.net}, \code{grp.scad.net}. 
#' penalty applied is (1 - alpha) * (ridge penalty) + alpha * (lasso/mcp/mcp/grp.lasso penalty)
#' @param gamma tuning parameter for SCAD and MCP penalties. must be >= 1
#' @param tau mixing value for \code{sparse.grp.lasso}. penalty applied is (1 - tau) * (group lasso penalty) + tau * (lasso penalty)
#' @param groups A vector of describing the grouping of the coefficients. See the example below. All unpenalized variables
#' should be put in group 0
#' @param penalty.factor Separate penalty factors can be applied to each coefficient. 
#' This is a number that multiplies lambda to allow differential shrinkage. Can be 0 for some variables, 
#' which implies no shrinkage, and that variable is always included in the model. Default is 1 for all 
#' variables. 
#' @param group.weights penalty factors applied to each group for the group lasso. Similar to \code{penalty.factor}, 
#' this is a number that multiplies lambda to allow differential shrinkage. Can be 0 for some groups, 
#' which implies no shrinkage, and that group is always included in the model. Default is sqrt(group size) for all
#' groups. 
#' @param standardize Logical flag for x variable standardization, prior to fitting the models. 
#' The coefficients are always returned on the original scale. Default is \code{standardize = TRUE}. If 
#' variables are in the same units already, you might not wish to standardize. Keep in mind that 
#' standardization is done differently for sparse matrices, so results (when standardized) may be
#' slightly different for a sparse matrix object and a dense matrix object
#' @param intercept Should intercept(s) be fitted (\code{default = TRUE}) or set to zero (\code{FALSE})
#' @param maxit integer. Maximum number of OEM iterations
#' @param tol convergence tolerance for OEM iterations
#' @param irls.maxit integer. Maximum number of IRLS iterations
#' @param irls.tol convergence tolerance for IRLS iterations. Only used if \code{family != "gaussian"}
#' @param compute.loss should the loss be computed for each estimated tuning parameter? Defaults to \code{FALSE}. Setting
#' to \code{TRUE} will dramatically increase computational time
#' @param gigs maximum number of gigs of memory available. Used to figure out how to break up calculations
#' involving the design matrix x
#' @param hessian.type only for logistic regression. if \code{hessian.type = "full"}, then the full hessian is used. If
#' \code{hessian.type = "upper.bound"}, then an upper bound of the hessian is used. The upper bound can be dramatically
#' faster in certain situations, ie when n >> p
#' @return An object with S3 class "oem" 
#' @import Rcpp
#' @import Matrix
#' @import bigmemory
#' @importFrom bigmemory is.big.matrix
#' @export
#' @references Huling. J.D. and Chien, P. (2022), Fast Penalized Regression and Cross Validation for Tall Data with the oem Package.
#' Journal of Statistical Software 104(6), 1-24. doi:10.18637/jss.v104.i06
#' @examples
#' \dontrun{
#' set.seed(123)
#' nrows <- 50000
#' ncols <- 100
#' bkFile <- "bigmat.bk"
#' descFile <- "bigmatk.desc"
#' bigmat <- filebacked.big.matrix(nrow=nrows, ncol=ncols, type="double",
#'                                 backingfile=bkFile, backingpath=".",
#'                                 descriptorfile=descFile,
#'                                 dimnames=c(NULL,NULL))
#'
#' # Each column value with be the column number multiplied by
#' # samples from a standard normal distribution.
#' set.seed(123)
#' for (i in 1:ncols) bigmat[,i] = rnorm(nrows)*i
#'
#' y <- rnorm(nrows) + bigmat[,1] - bigmat[,2]
#' 
#' fit <- big.oem(x = bigmat, y = y, 
#'                penalty = c("lasso", "elastic.net", 
#'                            "ols", 
#'                            "mcp",       "scad", 
#'                            "mcp.net",   "scad.net",
#'                            "grp.lasso", "grp.lasso.net",
#'                            "grp.mcp",   "grp.scad",
#'                            "sparse.grp.lasso"), 
#'                groups = rep(1:20, each = 5))
#'                
#' fit2 <- oem(x = bigmat[,], y = y, 
#'             penalty = c("lasso", "grp.lasso"), 
#'             groups = rep(1:20, each = 5))   
#'            
#' max(abs(fit$beta[[1]] - fit2$beta[[1]]))            
#' 
#' layout(matrix(1:2, ncol = 2))
#' plot(fit)
#' plot(fit, which.model = 2)
#' }
#' 
big.oem <- function(x, 
                    y, 
                    family = c("gaussian", "binomial"),
                    penalty = c("elastic.net", 
                                "lasso", 
                                "ols", 
                                "mcp",           "scad", 
                                "mcp.net",       "scad.net",
                                "grp.lasso",     "grp.lasso.net",
                                "grp.mcp",       "grp.scad",
                                "grp.mcp.net",   "grp.scad.net",
                                "sparse.grp.lasso"),
                    weights = numeric(0),
                    lambda = numeric(0),
                    nlambda = 100L,
                    lambda.min.ratio = NULL,
                    alpha = 1,
                    gamma = 3,
                    tau   = 0.5,
                    groups = numeric(0),
                    penalty.factor = NULL,
                    group.weights = NULL,
                    standardize = TRUE,
                    intercept = TRUE,
                    maxit = 500L, 
                    tol = 1e-7,
                    irls.maxit = 100L,
                    irls.tol = 1e-3,
                    compute.loss = FALSE,
                    gigs         = 4.0,
                    hessian.type = c("full", "upper.bound")) 
{
    family       <- match.arg(family)
    penalty      <- match.arg(penalty, several.ok = TRUE)
    hessian.type <- match.arg(hessian.type)
    
    if (!is.big.matrix(x)) stop("matrix x must be big.matrix object")
    if (!is.numeric(y))    stop("y must be numeric for now, not big.matrix object or otherwise")
    if (family == "binomial") stop("binomial case not implemented yet")
    
    dims   <- dim(x)
    
    if (is.null(dims))
    {
        stop("x must have at least two columns")
    }
    
    n      <- dims[1]
    p      <- dims[2]
    y      <- drop(y)
    y.vals <- unique(y)
    
    if (p < 2)
    {
        stop("x must have at least two columns")
    }
    
    if (length(weights) > 0) stop("weights not implemented yet.")
    
    if (length(y) != n) {
        stop("x and y lengths do not match")
    }
    
    if (family == "binomial" & length(y.vals) > 2) {
        stop("y must be a binary outcome")
    }
    
    if (is.null(penalty.factor)) {
        penalty.factor <- rep(1, p)
    }
    
    varnames <- colnames(x)
    if(is.null(varnames)) varnames = paste("V", seq(p), sep="")
    
    if (length(weights))
    {
        if (length(weights) != n)
        {
            stop("length of weights not same as number of observations in x")
        }
        
    }
    
    if (length(penalty.factor) != p) {
        stop("penalty.factor must have same length as number of columns in x")
    }
    penalty.factor <- drop(penalty.factor)
    
    if (any(grep("grp", penalty) > 0)) {
        if (length(groups) != p) {
            stop("groups must have same length as number of columns in x")
        }
        
        unique.groups <- sort(unique(groups))
        zero.idx <- unique.groups[which(unique.groups == 0)]
        groups <- drop(groups)
        if (!is.null(group.weights))
        {
            
            if (length(zero.idx) > 0)
            {
                # force group weight for 0 group to be zero
                group.weights[zero.idx] <- 0
            } else 
            {
                if (intercept)
                {
                    ## add group for zero term if it's not here
                    ## and add penalty weight of zero
                    unique.groups <- c(0, unique.groups)
                    group.weights <- c(0, group.weights)
                }
            }
            group.weights <- drop(group.weights)
            if (length(group.weights) != length(unique.groups)) {
                stop("group.weights must have same length as the number of groups")
            }
            group.weights <- as.numeric(group.weights)
        } else {
            # default to sqrt(group size) for each group weight
            group.weights <- numeric(0)
            
            if (length(zero.idx) == 0)
            {
                if (intercept)
                {
                    ## add group for zero term if it's not here
                    unique.groups <- sort(c(0, unique.groups))
                }
            }
        }
        
        
        
        if (intercept)
        {
            ## add intercept to group with no penalty
            groups <- c(0, groups)
        }
        
        
    } else {
        unique.groups <- numeric(0)
        group.weights <- numeric(0)
    }
    
    
    if (is.null(lambda.min.ratio)) {
        lambda.min.ratio <- ifelse(nrow(x) < ncol(x), 0.01, 0.0001)
    } else {
        lambda.min.ratio <- as.numeric(lambda.min.ratio)
    }
    
    if(lambda.min.ratio >= 1 | lambda.min.ratio <= 0) 
    {
        stop("lambda.min.ratio must be between 0 and 1")
    }
    
    if(nlambda[1] <= 0) 
    {
        stop("nlambda must be a positive integer")
    }
    
    if (!is.list(lambda))
    {
        lambda <- sort(as.numeric(lambda), decreasing = TRUE)
        
        ## ensure is double type
        if (length(lambda) > 0)
        {
            lambda    <- as.double(lambda)
        }
        
        lambda <- rep(list(lambda), length(penalty))
        
    } else 
    {
        if (length(lambda) != length(penalty))
        {
            stop("If list of lambda vectors is provided, it must be 
                 the same length as the number of penalties fit")
        }
        nlambda.tmp <- length(lambda[[1]])
        for (l in 1:length(lambda))
        {
            
            ## check to make sure all things in the list are actually vectors
            if ( is.null(lambda[[l]]) || length(lambda[[l]]) < 1 )
            {
                stop("Provided lambda vector must have at least one value")
            }
            
            if (length(lambda[[l]]) != nlambda.tmp)
            {
                stop("All provided lambda vectors must have same length")
            }
            
            ## ensure is double type
            lambda[[l]] <- as.double(sort(as.numeric(lambda[[l]]), decreasing = TRUE))
            
        }
    }
    
    ##    ensure types are correct
    ##    before sending to c++
    
    groups        <- as.integer(groups)
    unique.groups <- as.integer(unique.groups)
    nlambda       <- as.integer(nlambda)
    alpha         <- as.double(alpha)
    gamma         <- as.double(gamma)
    tau           <- as.double(tau)
    tol           <- as.double(tol)
    irls.tol      <- as.double(irls.tol)
    gigs          <- as.double(gigs)
    irls.maxit    <- as.integer(irls.maxit)
    maxit         <- as.integer(maxit)
    standardize   <- as.logical(standardize)
    intercept     <- as.logical(intercept)
    compute.loss  <- as.logical(compute.loss)
    
    if(maxit <= 0 | irls.maxit <= 0)
    {
        stop("maxit and irls.maxit should be positive")
    }
    if(tol < 0 | irls.tol < 0)
    {
        stop("tol and irls.tol should be nonnegative")
    }
    
    
    options <- list(maxit        = maxit,
                    tol          = tol,
                    irls_maxit   = irls.maxit,
                    irls_tol     = irls.tol,
                    hessian.type = hessian.type,
                    gigs         = gigs)
    
    res <- switch(family,
                  "gaussian" = oemfit.big.gaussian(x@address, 
                                                   y, 
                                                   family, 
                                                   penalty, 
                                                   weights,
                                                   groups,
                                                   unique.groups,
                                                   group.weights,
                                                   lambda, 
                                                   nlambda,
                                                   lambda.min.ratio,
                                                   alpha,
                                                   gamma,
                                                   tau,
                                                   penalty.factor,
                                                   standardize,
                                                   intercept,
                                                   compute.loss,
                                                   is_filebacked = is.filebacked(x),
                                                   options),
                  "binomial" = oemfit.big.binomial(x@address, 
                                                   y, 
                                                   family, 
                                                   penalty, 
                                                   weights,
                                                   groups,
                                                   unique.groups,
                                                   group.weights,
                                                   lambda, 
                                                   nlambda,
                                                   lambda.min.ratio,
                                                   alpha,
                                                   gamma,
                                                   tau,
                                                   penalty.factor,
                                                   standardize,
                                                   intercept,
                                                   compute.loss,
                                                   is_filebacked = is.filebacked(x),
                                                   options)
    )
    
    for (i in 1:length(penalty))
    {
        if (penalty[i] == "ols") res$beta[[i]] <- matrix(res$beta[[i]], ncol = 1)
        rownames(res$beta[[i]]) <- c("(Intercept)", varnames)
    }
    
    names(res$beta) <- penalty
    
    nz <- lapply(1:length(res$beta), function(m) 
        sapply(predict.oem(res, type = "nonzero", which.model = m), length)
    )
    
    res$nobs     <- n
    res$nvars    <- p
    res$penalty  <- penalty
    res$family   <- family
    res$varnames <- varnames
    res$nzero    <- nz
    
    class(res)   <- c(class(res), "oem")
    res
}


oemfit.big.gaussian <- function(x, 
                                y, 
                                family, 
                                penalty, 
                                weights,
                                groups,
                                unique.groups,
                                group.weights,
                                lambda, 
                                nlambda,
                                lambda.min.ratio,
                                alpha,
                                gamma,
                                tau,
                                penalty.factor,
                                standardize,
                                intercept,
                                compute.loss,
                                is_filebacked,
                                options)
{
    if (is_filebacked)
    {
        ret <- .Call("oem_fit_fb_big", 
                     x, y, 
                     family, 
                     penalty, 
                     weights,
                     groups,
                     unique.groups,
                     group.weights,
                     lambda, 
                     nlambda,
                     lambda.min.ratio,
                     alpha,
                     gamma,
                     tau,
                     penalty.factor,
                     standardize,
                     intercept,
                     compute.loss,
                     options,
                     PACKAGE = "oem")
    } else 
    {
        ret <- .Call("oem_fit_big", 
                     x, y, 
                     family, 
                     penalty, 
                     weights,
                     groups,
                     unique.groups,
                     group.weights,
                     lambda, 
                     nlambda,
                     lambda.min.ratio,
                     alpha,
                     gamma,
                     tau,
                     penalty.factor,
                     standardize,
                     intercept,
                     compute.loss,
                     options,
                     PACKAGE = "oem")
    }
    class(ret) <- "oemfit_gaussian"
    ret
}


oemfit.big.binomial <- function(x, 
                                y, 
                                family, 
                                penalty, 
                                weights,
                                groups,
                                unique.groups,
                                group.weights,
                                lambda, 
                                nlambda,
                                lambda.min.ratio,
                                alpha,
                                gamma,
                                tau,
                                penalty.factor,
                                standardize,
                                intercept,
                                compute.loss,
                                is_filebacked,
                                options)
{
    ret <- .Call("oem_fit_big_logistic", 
                 x, y, 
                 family, 
                 penalty, 
                 weights,
                 groups,
                 unique.groups,
                 group.weights,
                 lambda, 
                 nlambda,
                 lambda.min.ratio,
                 alpha,
                 gamma,
                 tau,
                 penalty.factor,
                 standardize,
                 intercept,
                 compute.loss,
                 options,
                 PACKAGE = "oem")
    class(ret) <- "oemfit_binomial"
    ret
}