Last updated: 2018-11-29

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    Rmd 521f70b zouyuxin 2018-11-29 wflow_publish(“analysis/EstimateCorMaxMVProblem.Rmd”)

A brief introduction of the algorithm to estimate the null correlation matrix \(V\) is in pdf. This is the current algorithm we used in mash. However, I encountered a problem with one simulated dataset. The log likelihood decreases during the update of parameters.

The simulated data is \[ \hat{\mathbf{c}}_{j} | \mathbf{c}_{j} \sim N_{10}(\mathbf{c}_{j}, I) \\ \mathbf{c}_{j} = \mu_{j}\mathbf{1} \] We subtract the median from each observation, and estimate \(V\).

library(mashr)
Loading required package: ashr
set.seed(1)
data = sim_contrast1(nsamp = 10000, ncond = 10, err_sd = 1)
colnames(data$C) = colnames(data$Chat) = colnames(data$Shat) = 1:10
m.data = mash_set_data(data$Chat, data$Shat)
delta.median = t(apply(data$C, 1, function(x) x - median(x)))
deltahat.median = t(apply(data$Chat, 1, function(x) x - median(x)))

data.median = mash_set_data(deltahat.median, Shat = 1, alpha = 1)
U.c = cov_canonical(data.median)

Using the current algorithm, the log likelihood decreases.

estV.orig = estimate_null_correlation(data.median, U.c)
plot(estV.orig$loglik)

The problem is the EM step to update V.

One more example

source('../code/generateDataV.R')
set.seed(1)
Sigma = cbind(c(1,0.7,0.2), c(0.7,1,0.4), c(0.2,0.4,1))
U0 = matrix(0,3,3)
U1 = matrix(0,3,3); U1[1,1] = 1
U2 = diag(3); U2[3,3] = 0
U3 = matrix(1,3,3)
data = generate_data(n=4000, p=3, V=Sigma, Utrue = list(U0=U0, U1=U1,U2=U2,U3=U3))
m.data = mash_set_data(data$Bhat, data$Shat)
m.1by1 = mash_1by1(m.data)
strong = get_significant_results(m.1by1)

U.pca = cov_pca(m.data, 3, subset = strong)
U.ed = cov_ed(m.data, U.pca, subset = strong)
U.c = cov_canonical(m.data)
Vhat = estimate_null_correlation(m.data, c(U.c,U.ed), max_iter = 100, tol=1e-2)
plot(Vhat$loglik)

Session information

sessionInfo()
R version 3.5.1 (2018-07-02)
Platform: x86_64-apple-darwin15.6.0 (64-bit)
Running under: macOS  10.14.1

Matrix products: default
BLAS: /Library/Frameworks/R.framework/Versions/3.5/Resources/lib/libRblas.0.dylib
LAPACK: /Library/Frameworks/R.framework/Versions/3.5/Resources/lib/libRlapack.dylib

locale:
[1] en_US.UTF-8/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8

attached base packages:
[1] stats     graphics  grDevices utils     datasets  methods   base     

other attached packages:
[1] mashr_0.2.19.0547 ashr_2.2-23      

loaded via a namespace (and not attached):
 [1] Rcpp_1.0.0        knitr_1.20        whisker_0.3-2    
 [4] magrittr_1.5      workflowr_1.1.1   REBayes_1.3      
 [7] MASS_7.3-50       pscl_1.5.2        doParallel_1.0.14
[10] SQUAREM_2017.10-1 lattice_0.20-35   foreach_1.4.4    
[13] plyr_1.8.4        stringr_1.3.1     tools_3.5.1      
[16] parallel_3.5.1    grid_3.5.1        R.oo_1.22.0      
[19] rmeta_3.0         git2r_0.23.0      htmltools_0.3.6  
[22] iterators_1.0.10  assertthat_0.2.0  abind_1.4-5      
[25] yaml_2.2.0        rprojroot_1.3-2   digest_0.6.18    
[28] Matrix_1.2-14     codetools_0.2-15  R.utils_2.7.0    
[31] evaluate_0.12     rmarkdown_1.10    stringi_1.2.4    
[34] compiler_3.5.1    Rmosek_8.0.69     backports_1.1.2  
[37] R.methodsS3_1.7.1 mvtnorm_1.0-8     truncnorm_1.0-8

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