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# The ISOpureR package is copyright (c) 2014 Ontario Institute for Cancer Research (OICR)
# This package and its accompanying libraries is free software; you can redistribute it and/or modify it under the terms of the GPL
# (either version 1, or at your option, any later version) or the Artistic License 2.0. Refer to LICENSE for the full license text.
# OICR makes no representations whatsoever as to the SOFTWARE contained herein. It is experimental in nature and is provided WITHOUT
# WARRANTY OF MERCHANTABILITY OR FITNESS FOR A PARTICULAR PURPOSE OR ANY OTHER WARRANTY, EXPRESS OR IMPLIED. OICR MAKES NO REPRESENTATION
# OR WARRANTY THAT THE USE OF THIS SOFTWARE WILL NOT INFRINGE ANY PATENT OR OTHER PROPRIETARY RIGHT.
# By downloading this SOFTWARE, your Institution hereby indemnifies OICR against any loss, claim, damage or liability, of whatsoever kind or
# nature, which may arise from your Institution's respective use, handling or storage of the SOFTWARE.
# If publications result from research using this SOFTWARE, we ask that the Ontario Institute for Cancer Research be acknowledged and/or
# credit be given to OICR scientists, as scientifically appropriate.
### FUNCTION: ISOpureS1.model_optimize.mm.mm_deriv_loglikelihood.R #######################################################
#
# Input variables:
# ww: the mm_weights, with G entries (not sure if a vector or matrix, check)
# tumordata: a GxD matrix representing gene expression profiles of tumor samples
# model: list containing all the parameters to be optimized
#
# Output variables:
# deriv_loglikelihood: the derivative of the part of the likelihood function relevant to optimizing
# mm. The derivative is taken not with respect to mm but with respect to unconstrained variables
# via a change of variables
ISOpureS1.model_optimize.mm.mm_deriv_loglikelihood <- function(ww, tumordata, model) {
# K = number of normal profiles + 1
K <- dim(model$log_all_rates)[1]
# G = number of genes
G <- dim(model$log_all_rates)[2]
# D = number of patients
D <- ncol(tumordata);
# reshape ww to be a 1xG matrix
ww <- as.matrix(ww, nrow=1, ncol=G);
log_cancer_rates <- t(ww) - as.numeric(ISOpure.util.logsum(ww,1));
expww <- exp(t(ww));
kappaomegaPP <- as.numeric(model$kappa) %*% t(model$omega) %*% model$PPtranspose;
log_all_rates <- rbind(model$log_BBtranspose, log_cancer_rates);
# derivative is computed not with respect to mm directly, but with respect
# to unconstrained variables via change of variables
dLdb <- matrix(0,nrow(log_cancer_rates), ncol(log_cancer_rates)) + exp(ISOpure.util.matlab_log(kappaomegaPP-1)-log_cancer_rates);
for (dd in 1:D) {
# For patient d,
# p(t_d| B, theta_d, mm) = Multinomial(t_d | alpha_d*mm + sum(theta_d_k*B_d_k))
# = sum( t_d_i )! / prod( t_d_i !) * prod_(1^G) (alpha_d*mm + sum(theta_d_k*B_d_k))_ith_component ^(t_d,i)
# The first term in t_d is a constant. Hence, if we take the logarithm, the first part is
# log (alpha_d*mm + sum(theta_d_k*B_d_k))
# theta contains both theta_d's and alpha_d, and log all rates contains both BB and mm
log_P_t_given_theta <- ISOpure.util.logsum(t(ISOpure.util.repmat(t(ISOpure.util.matlab_log(model$theta[dd,])), G, 1)) + log_all_rates, 1);
# add the derivative of loglikelihood: t_d * 1/(alpha_d*mm + sum(theta_d_k*B_d_k)) * alpha
# exp(log t_d - log P_t_given_theta + log alpha)
dLdb <- dLdb + exp(t(log(tumordata[,dd])) + ISOpure.util.matlab_log(model$theta[dd,ncol(model$theta)]) - log_P_t_given_theta);
}
# make sure bb sums up to 1
bb <- expww / sum(expww);
# The following two lines calculate dL/dbb * dbb/dww. (bb == mm)
# The code is the same as in ISOpureS1.model_optimize.omega.omega_deriv_loglikelihood for dL/domega * domega/dww.
# where the second term is explained in more detail.
deriv_loglikelihood <- exp(as.vector(ISOpure.util.logsum(ISOpure.util.matlab_log(dLdb) + ISOpure.util.matlab_log(bb), 2)) + ISOpure.util.matlab_log(bb));
deriv_loglikelihood <- -deriv_loglikelihood + (dLdb * bb);
# fix the first element of the derivative to zero, to fix the scale of the unconstrained variables
deriv_loglikelihood[1] <- 0;
# take the negative of the derivative because we are using a minimizer
deriv_loglikelihood <- -t(deriv_loglikelihood);
return(as.matrix(deriv_loglikelihood));
}
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