R/base_deconCorePET.R

In dpeak: dPeak (Deconvolution of Peaks in ChIP-seq Analysis)

# Deconvolution, based on the generative model

.deconCorePET <- function( S, E, L, fragRange, peak, psize=21, niter=50,
    mu_init, pi_init, pi0_init, gamma_init,
    L_table, alpha, stop_eps=1e-6, verbose=FALSE ) {

    # construct grid

    grid_min <- peak[1]
    grid_max <- peak[2]
        # search binding site only within peak region
    grid_vec <- c(seq(from = grid_min, to = grid_max))

    # initialization

    N <- length(S)
    n_group <- length(mu_init)
        # pi for background: 0.1
    L <- E - S + 1
    R <- grid_max - grid_min + 1

    mu <- mu_init
    pi <- pi_init
    pi0 <- pi0_init
    gamma <- gamma_init

    # EM step

    mu_mat <- matrix( NA, niter, n_group )
    mu_mat[1,] <- mu_init

    pi_mat <- matrix( NA, niter, n_group )
    pi0_vec <- rep( NA, niter )
    pi_mat[1,] <- pi_init
    pi0_vec[1] <- pi0_init

    gamma_vec <- rep( NA, niter )
    gamma_vec[1] <- gamma_init

    ll <- rep( NA, niter )
    ll[1] <- -Inf

    for ( i in seq(from = 2, to = niter) ) {
        if ( verbose ) {
            message( paste("------------ iteration:",i,"------------") )
        }

        ########################################################################
        #                                                                      #
        #                       E step: update Z                               #
        #                                                                      #
        ########################################################################

        muRange <- IRanges( start=mu, end=mu )
        mm <- as.matrix( findOverlaps( muRange, fragRange ) )
        mms <- split( mm[,2], mm[,1] )

        Z <- matrix( NA, N, n_group )
        for ( g in seq_len(n_group) ) {
            if ( any( names(mms) == g ) ) {
				Z[ , g ] <- pi[g] * ( gamma / (R-1) )
				Z[ mms[[ as.character(g) ]], g ] <- pi[g] * ( ( 1 - gamma ) / L )
            } else {
				Z[,g] <- gamma / (R-1)
            }

            # check at least one element in Z[,g] is non-zero

            if ( verbose ) {
                if ( sum(Z[,g]) == 0 ) {
                    message( "Warning: all elements in Z vector is zero." )
                    message( "peak region: ", grid_min, "-", grid_max )
                    message( "event number: ", g )
                }
            }
        }

        Z0 <- pi0 / ( R + L - 1 )

        Znorm <- .ff_normalize( cbind(Z0,Z) )
        Z0 <- Znorm[ , 1 ]
        Z <- Znorm[ , -1, drop=FALSE ]

        ########################################################################
        #                                                                      #
        #                      CM step: update mu                              #
        #                                                                      #
        ########################################################################

        # M step: update mu

        for ( g in seq_len(n_group) ) {
            yvar <- .ff_score( grid_vec, S, E, L, Z[,g], R, gamma  )
            mu_max <- grid_vec[ yvar == max(yvar) ]
            mu[g] <- median(mu_max)
        }

        if ( length(mu) == 0 || all(is.na(mu)) ) {
	        mu_old <- mu_mat[ (i-1), ]
	        mu_old <- mu_old[ !is.na(mu_old) ]

	        n_group <- length(mu_old)
	        mu <- sample( (S+E)/2, n_group, replace=FALSE )
	        gamma <- 0.1
		    pi <- rep( 0.90/n_group, n_group )
		    pi0 <- 0.10

		    next;
        }

        # M step: update pi
		pi <- colSums(Z) / N
        pi0 <- sum(Z0) / N

        # safe guard for pi0: when signal is weak, do not use pi0

        if ( pi0 > max(pi) ) {
            pi0 <- 0
            pi <- pi / sum(pi)
        }

        # M step: update gamma

        muRange <- IRanges( start=mu, end=mu )
        mm <- as.matrix( findOverlaps( muRange, fragRange ) )
        mms <- split( mm[,2], mm[,1] )

        gamma <- 0
        for ( g in seq_len(n_group) ) {
            if ( any( names(mms) == g ) ) {
				gamma <- gamma + sum( Z[ -mms, g ] )
            } else {
				gamma <- gamma + sum( Z[ , g ] )
            }
        }
        gamma <- gamma / N

        # safe guard: prevent NaN in calculating score

        if ( gamma < 0.01 ) {
            gamma <- 0.01
        } else if ( gamma > 0.50 ) {
            gamma <- 0.50
        }

        ########################################################################
        #                                                                      #
        #      Identifiability, over-fitting, track estimates & loglik         #
        #                                                                      #
        ########################################################################

        # identifiability problem: order constraint on \mu values

        pi <- pi[ order(mu) ]
        mu <- mu[ order(mu) ]

        # check over-fitting -> reduce dimension
        # (avoid identifiability problem due to over-fitting)
        # condition: distance <= psize

        if ( n_group >= 2 ) {
            mu_new <- pi_new <- c()
            mu_current <- mu[1]
            pi_current <- pi[1]

            for ( g in seq(from = 2, to = n_group) ) {
                if ( abs( mu[g] - mu_current ) <= psize ) {
                    mu_current <- ( mu_current + mu[g] ) / 2
                    pi_current <- pi_current + pi[g]
                } else {
                    mu_new <- c( mu_new, mu_current )
                    pi_new <- c( pi_new, pi_current )

                    mu_current <- mu[g]
                    pi_current <- pi[g]
                }
            }

            mu_new <- c( mu_new, mu_current )
            pi_new <- c( pi_new, pi_current )

            mu <- mu_new
            pi <- pi_new
            n_group <- length(mu)

            # check over-fitting \pi < 0.01 -> reduce dimension
            # (avoid identifiability problem due to over-fitting)

            if ( any( pi < 0.01 ) ) {
                # safeguard: reduce dim only if there is at least one remaining component
                #             if nothing remains, just stop

                if ( length(which( pi > 0.01 )) > 0 ) {
                    mu <- mu[ pi > 0.01 ]
                    pi <- pi[ pi > 0.01 ]
                    n_group <- length(mu)
                } else {

                    # use estimates in the last iteration

                    mu <- mu_mat[ (i-1), !is.na(mu_mat[(i-1),]) ]
                    mu_mat[ i, ] <- NA
                    mu_mat[ i, seq_len(length(mu)) ] <- mu

                    pi <- pi_mat[ (i-1), !is.na(pi_mat[(i-1),]) ]
                    pi_mat[ i, ] <- NA
                    pi_mat[ i, seq_len(length(pi)) ] <- pi

                    pi0 <- pi0_vec[(i-1)]
                    pi0_vec[i] <- pi0

                    gamma <- gamma_vec[(i-1)]
                    gamma_vec[i] <- gamma

                    # stop iteration

                    mu_mat <- mu_mat[ seq_len(i), , drop=FALSE ]
                    pi_mat <- pi_mat[ seq_len(i), , drop=FALSE ]
                    pi0_vec <- pi0_vec[ seq_len(i) ]
                    gamma_vec <- gamma_vec[ seq_len(i) ]
                    ll <- ll[ seq_len(i) ]

                    break;
                }
            }

            pi <- pi / sum(pi)
        }

        # safeguard: if only one component & pi decrases, just stop

        if ( n_group == 1 & pi[1] < 0.01 ) {

            # use estimates in the last iteration

            mu <- mu_mat[ (i-1), !is.na(mu_mat[(i-1),]) ]
            mu_mat[ i, ] <- NA
            mu_mat[ i, seq_len(length(mu)) ] <- mu

            pi <- pi_mat[ (i-1), !is.na(pi_mat[(i-1),]) ]
            pi_mat[ i, ] <- NA
            pi_mat[ i, seq_len(length(pi)) ] <- pi

            pi0 <- pi0_vec[(i-1)]
            pi0_vec[i] <- pi0

            gamma <- gamma_vec[(i-1)]
            gamma_vec[i] <- gamma

            # stop iteration

            mu_mat <- mu_mat[ seq_len(i), , drop=FALSE ]
            pi_mat <- pi_mat[ seq_len(i), , drop=FALSE ]
            pi0_vec <- pi0_vec[ seq_len(i) ]
            gamma_vec <- gamma_vec[ seq_len(i) ]
            ll <- ll[ seq_len(i) ]
            break;

        }

        # track estimates

        mu_mat[ i, seq_len(length(mu)) ] <- mu
        pi_mat[ i, seq_len(length(pi)) ] <- pi
        pi0_vec[i] <- pi0
        gamma_vec[i] <- gamma

        if ( verbose ) {
            message( "mu: " )
            message( mu )
            message( "pi: " )
            message( pi )
            message( "pi0: " )
            message( pi0 )
            message( "gamma: " )
            message( gamma )
        }

        # track complete log likelihood

        ll[i] <- .loglikPET( fragRange, L, mu, pi, pi0, gamma, R, alpha )
        if ( verbose ) {
            message( "increment in loglik:" )
            message( ll[i]-ll[(i-1)] )
        }

        # if loglik decreases, stop iteration

        if ( ll[i] < ll[(i-1)] ) {

            # use estimates in the last iteration

            mu <- mu_mat[ (i-1), !is.na(mu_mat[(i-1),]) ]
            mu_mat[ i, ] <- NA
            mu_mat[ i, seq_len(length(mu)) ] <- mu

            pi <- pi_mat[ (i-1), !is.na(pi_mat[(i-1),]) ]
            pi_mat[ i, ] <- NA
            pi_mat[ i, seq_len(length(pi)) ] <- pi

            pi0 <- pi0_vec[(i-1)]
            pi0_vec[i] <- pi0

            gamma <- gamma_vec[(i-1)]
            gamma_vec[i] <- gamma

            # stop iteration

            mu_mat <- mu_mat[ seq_len(i), , drop=FALSE ]
            pi_mat <- pi_mat[ seq_len(i), , drop=FALSE ]
            pi0_vec <- pi0_vec[ seq_len(i) ]
            gamma_vec <- gamma_vec[ seq_len(i) ]
            ll <- ll[ seq_len(i) ]
            break;
        }

        # check whether to stop iterations

        if ( ll[i] - ll[(i-1)] < stop_eps ) {
            # stop if no improvement in loglik

            if ( verbose ) {
                message( "stop because there is no improvements in likelihood." )
            }

            mu_mat <- mu_mat[ seq_len(i), , drop=FALSE ]
            pi_mat <- pi_mat[ seq_len(i), , drop=FALSE ]
            pi0_vec <- pi0_vec[ seq_len(i) ]
            gamma_vec <- gamma_vec[ seq_len(i) ]
            ll <- ll[ seq_len(i) ]
            break;
        } else {
            # stop if no improvement in estimates

            if ( length(which(!is.na(mu_mat[i,]))) == length(which(!is.na(mu_mat[(i-1),]))) &&
            all( abs( mu_mat[i,!is.na(mu_mat[i,])] - mu_mat[(i-1),!is.na(mu_mat[(i-1),])] ) < stop_eps ) &&
            all( abs( pi_mat[i,!is.na(pi_mat[i,])] - pi_mat[(i-1),!is.na(pi_mat[(i-1),])] ) < stop_eps ) &&
            abs( pi0_vec[i] - pi0_vec[(i-1)] ) < stop_eps &&
            abs( gamma_vec[i] - gamma_vec[(i-1)] ) < stop_eps ) {
                if ( verbose ) {
                    message( "stop because there is no improvements in estimates." )
                }

                mu_mat <- mu_mat[ seq_len(i), , drop=FALSE ]
                pi_mat <- pi_mat[ seq_len(i), , drop=FALSE ]
                pi0_vec <- pi0_vec[ seq_len(i) ]
                gamma_vec <- gamma_vec[ seq_len(i) ]
                ll <- ll[ seq_len(i) ]
                break;
            }
        }
    }

    aicValue <- -2 * .loglikPET( fragRange, L, mu, pi, pi0, gamma, R, alpha ) +
        (2*n_group+2) * 2
    bicValue <- -2 * .loglikPET( fragRange, L, mu, pi, pi0, gamma, R, alpha ) +
        (2*n_group+2) * log(N)

    return( list( mu=mu, pi=pi, pi0=pi0, gamma=gamma,
        mu_mat=mu_mat, pi_mat=pi_mat, gamma_vec=gamma_vec, Z=Z,
        loglik=ll, AIC=aicValue, BIC=bicValue ) )
}