klkeys / ExchangeLeastsq.jl

ExchangeLeastsq

ExchangeLeastsq.jl is a module to perform sparse model selection in least squares regression without shrinkage.

Installation

From a Julia prompt, type

Pkg.clone("https://github.com/klkeys/ExchangeLeastsq.jl")

Usage

The workhorse of ExchangeLeastsq.jl is the function exlstsq which requires only two arguments:

• x, the statistical design matrix
• y, the response vector

The function exlstsq returns a sparse matrix betas of estimated models:

betas = exlstsq(x, y) 

Optional arguments with defaults include:

• v = ELSQVariables(x, y) is a container object of temporary arrays for exlstsq
• models is the integer vector of model sizes to test. It defaults to collect(1:p), where p = min(20, size(x,2)).
• window = maximum(models) is a window size of active predictors that exlstsq uses when searching through active predictors. Generally a smaller value of window means that exlstsq sifts through fewer active models, thereby increasing speed and sacrificing accuracy.
• max_iter = 100 is the maximum number of iterations that exlstsq will take in any inner loop
• tol = 1e-6 is the convergence tolerance
• quiet = true controls output to the console. Setting quiet = false causes exlstsq to print all inner loop information.

Crossvalidation

ExchangeLeastsq.jl is best used to obtain the ideal model size to predict y. It furnishes a crossvalidation routine for this purpose. ExchangeLeastsq.jl makes use of SharedArrays to enable crossvalidation in a multicore shared memory environment. Users can perform q-fold crossvalidation for a vector models of model sizes by calling

cv_output = cv_exlstsq(x, y)

Important optional arguments include:

• models = collect(1:min(20,p)), with p = size(x,2), is the Int vector of model sizes to test.
• q = 5 is the number of crossvalidation folds
• folds controls the fold structure. The default RegressionTools.cv_get_folds(y, q) distributes data to q folds as evenly as possible.

Here cv_output is an ELSQCrossvalidationResults container object with the following fields:

• mses contains the vector of mean squared errors
• k is the best crossvalidated model size
• b and bidx contain the coefficients and indices, respectively, of the model size k.

GWAS

ExchangeLeastsq.jl interfaces with the PLINK.jl package to enable GWAS analysis. PLINK.jl furnishes both multicore and GPU interfaces for GWAS analysis. The multicore environment makes heavy used of SharedArray interfaces.

For genotype data housed in a PLINK.BEDFile object x and a SharedVector y, the function call to exlstsq is unchanged:

output = exlstsq(x, y)

However, the call to cv_exlstsq changes dramatically in order to accomodate SharedArray computing. Most users should use the call

cv_output = cv_exlstsq("PATH_TO_BEDFILE.bed", "PATH_TO_COVARIATES.txt", "PATH_TO_Y.bin")

Note the file extensions! The first file path points to the BED file, the second points to the covariates stored in a delimited text file, and the last points to the response variable y stored as a binary file.

GPU

PLINK.jl also ships with a GPU interface for GWAS analysis. The GPU environment uses OpenCL.jl wrappers to port the computational bottleneck x' * y to the GPU. PLINK.jl automatically loads the OpenCL kernels into the variables PLINK.gpucode64 (for 64-bit kernels) and PLINK.gpucode32 (for 32-bit kernels). Assuming that a suitable device is available, then the calls from ExchangeLeastsq.jl to use GPUs are

output = exlstsq(x, y, PLINK.gpucode64)
cv_output = cv_exlstsq("PATH_TO_BEDFILE.bed", "PATH_TO_COVARIATES.txt", "PATH_TO_RESPONSE.bin", PLINK.gpucode64)