R/ZIPLDA.R

In zhangli1109/CAEN: Category encoding method for selecting feature genes for the classification of single-cell RNA-seq

#' Classify observations using a Zero-inflated Poisson model.
#' @description Classify observations using a Zero-inflated Poisson model.
#' @usage ZIPLDA(x, y, xte=NULL, rho = 0, beta = 1, rhos = NULL, prob0=NULL,
#' type=c("mle","deseq","quantile"),prior = NULL, transform=TRUE, alpha=NULL)
#' @param x A n-by-p training data matrix; n observations and p features.
#' Used to train the classifier.
#' @param y A numeric vector of class labels of length n: 1, 2, ...., K
#' if there are K classes.Each element of y corresponds to a row of x;
#' i.e. these are the class labels for the observations in x.
#' @param xte A m-by-p data matrix: m test observations and p features.
#' The classifier fit on the training data set x will be tested on this
#' data set. If NULL, then testing will be performed on the training set.
#' @param rho Tuning parameter controlling the amount of soft thresholding
#'  performed, i.e. the level of sparsity, i.e. number of nonzero features
#'  in classifier. Rho=0 means that there is no soft-thresolding,
#'  i.e. all  features used in classifier. Larger rho means that fewer
#'  features will be used.
#' @param beta A smoothing term. A Gamma(beta,beta) prior is used to fit
#'  the Zero-inflated Poisson model.Recommendation is to just leave it
#'  at 1, the default value.
#' @param rhos A vector of tuning parameters that control the amount of
#' soft thresholding performed. If "rhos" is provided then a number of models
#'  will be fit (one for each element of "rhos"), and a number of predicted
#'  class labels will be output (one for each element of "rhos").
#' @param prob0  The probability that the read is 0
#' @param type How should the observations be normalized within the
#' Zero-inflated Poisson model, i.e. how should the size factors be estimated?
#'  Options are "quantile" or "deseq" (more robust) or "mle" (less robust).
#' In greater detail: "quantile" is quantile normalization approach of
#' Bullard et al 2010 BMC Bioinformatics,"deseq" is median of the ratio of
#' an observation to a pseudoreference obtained by taking the geometric mean,
#' described in Anders and Huber 2010 Genome Biology and implemented in
#' Bioconductor package "DESeq", and "mle" is the sum of counts for each
#' sample; this is the maximum likelihood estimate under a simple Zero-inflated
#' Poisson model.
#' @param prior vector of length equal to the number of classes, representing
#'  prior probabilities for each class.If NULL then uniform priors are used
#' (i.e. each class is equally likely)
#' @param transform should data matrices x and xte first be power transformed
#' so that it more closely fits the Zero-inflated Poisson model? TRUE or FALSE.
#' Power transformation is especially useful if the data are overdispersed
#' relative to the Zero-inflated Poisson model.
#' @param alpha if transform=TRUE, this determines the power to which the
#' data matrices x and xte are transformed.If alpha=NULL then the transformation
#' that makes the Zero-inflated Poisson model best fit the data matrix x is
#' computed.(Note that alpha is computed based on x, not based on xte).
#' Or a value of alpha, 0<alpha<=1, can be entered by the user.
#' @return list(.) A list of output, "ytehat" represents The predicted class
#' labels for each of the test observations(rows of xte)."discriminant"
#' represents A m-by-K matrix, where K is the number of classes. The (i,k)
#' element is large if the ith element of xte belongs to class k."ds" A
#' K-by-p matrix indicating the extent to which each feature is under-or
#' over-expressed in each class. The (k,j) element is >1 if feature j is
#' over-expressed in class k, and is <1 if feature j is under-expressed in
#' class k. When rho is large then many of the elemtns of this matrix
#' are shrunken towards 1(no over- or under-expression)."alpha" represents
#' Power transformation used (if transform=TRUE).
#' @examples
#' library(SummarizedExperiment)
#' dat <- newCountDataSet(n=40,p=500, K=4, param=10, sdsignal=0.1,drate=0.4)
#' x <- t(assay(dat$sim_train_data))
#' y <- as.numeric(colnames(dat$sim_train_data))
#' xte <- t(assay(dat$sim_test_data))
#' prob<-estimatep(x=x, y=y, xte=x, beta=1, type="mle", prior=NULL)
#' prob0<-estimatep(x=x, y=y, xte=xte, beta=1,type="mle", prior=NULL)
#' cv.out <- ZIPDA.cv(x=x, y=y, prob0=t(prob))
#' out <- ZIPLDA(x=x, y=y, xte=xte, rho=cv.out$bestrho, prob0=t(prob0))
#' @export

ZIPLDA <-
    function(x, y, xte=NULL, rho=0, beta=1, rhos=NULL, prob0=NULL,
             type=c("mle","deseq","quantile"),
             prior=NULL, transform=TRUE, alpha=NULL){
        if (is.null(xte)) {
            xte <- x
            warning("Since no xte was provided, testing was
            performed on training data set.")
        }
        if (!is.null(rho) && length(rho) > 1)
            stop("Can only enter 1 value of rho. If you would like
            to enter multiple values, use rhos argument.")
        type <- match.arg(type)
        if (!transform && !is.null(alpha)) stop("You have asked for
                NO transformation but have entered alpha.")
        if (transform && is.null(alpha)) 
            alpha <- PoiClaClu::FindBestTransform(x)
        if (transform) {
            if (alpha <= 0 || alpha > 1) stop("alpha must be between 0 and 1")
            x <- x^alpha
            xte <- xte^alpha
        }
        if (is.null(prior)) 
            prior <- rep(1/length(unique(y)), length(unique(y)))
        if (is.null(rho) && is.null(rhos)) stop("Must enter rho or rhos.")
        null.out <- PoiClaClu::NullModel(x, type = type)
        ns <- null.out$n
        nste <- PoiClaClu::NullModelTest(null.out,x,xte,type = type)$nste
        uniq <- sort(unique(y))
        signx <- sign(xte == 0)
        if (is.null(rhos)) {
            ds <- GetD(ns,x,y,rho,beta)
            discriminant <- matrix(NA, nrow = nrow(xte), ncol = length(uniq))
            for (k in seq_len(length(uniq))) {
                for (i in seq_len(nrow(xte))) {
                    dstar = ds[k,]
                    part2 = nste[i,]*dstar
                    part1 = prob0[i,] + (1 - prob0[i,])*exp(-part2)
                    part1[part1 == 0] = 1
                    discriminant[i,k] <- sum(signx[i,]*log(part1)) +
                        sum(xte[i,]*(1 - signx[i,])*log(dstar)) -
                        sum((1 - signx[i,])*part2) + log(prior[k])
                }
            }
            save <- list(ns = ns, nste = nste, ds = ds,
                         discriminant = discriminant,
                         ytehat = uniq[apply(discriminant,1,which.max)],
                         alpha = alpha,rho = rho,x = x,y = y,xte = xte,
                         type = type)
            return(save)
        } else {
            save <- list()
            ds.list <- GetD(ns,x,y,rho = NULL, rhos = rhos,beta)
            for (rho in rhos) {
                ds <- ds.list[[which(rhos == rho)]]
                discriminant <- matrix(NA, nrow = nrow(xte), 
                                       ncol = length(uniq))
                for (k in seq_len(length(uniq))) {
                    for (i in seq_len(nrow(xte))) {
                        dstar = ds[k,]
                        part2 = nste[i,]*dstar
                        part1 = prob0[i] + (1 - prob0[i])*exp(-part2)
                        part1[part1 == 0] = 1
                        discriminant[i,k] <- sum(signx[i,]*log(part1)) +
                            sum(xte[i,]*(1 - signx[i,])*log(dstar)) -
                            sum((1 - signx[i,])*part2) + log(prior[k])
                    }
                }
                save[[which(rhos == rho)]] <- 
                    list(ns = ns,nste = nste,ds = ds, 
                         discriminant = discriminant,
                         ytehat = uniq[apply(discriminant,1,which.max)],
                         alpha = alpha, rho = rho,x = x,y = y,
                         xte = xte,type = type)
            }
            return(save)
        }
    }