Approximate Ridge Linear Mixed Models (arLMM)
Code for our UAI 2018 paper "Scalable Algorithms for Learning High-Dimensional Linear Mixed Models": https://arxiv.org/pdf/1803.04431.pdf
% Generate synthetic data
n = 1000; % 1000 observations
p = 100; % 100 fixed effects
d = 3; % 3 random effects
m = 20; % observations correspond to 20 groups
alpha = 1;% for generating approximately the same #observations per group
[X,y,Z,Beta,H,s2] = genCusData(n,p,d,m,alpha);
disp('Fitting the LMM ...')
[estBeta,~,~,estH,ests2,cr] = arLMM(X,y,Z);
disp('Real vs estimated random-effect covariances:')
disp(H); disp(estH)
pause(3);
disp('[Real_noise_var Estimated_noise_var]:')
disp([s2 ests2]);
pause(3);
disp("Corr(Real_Beta,Estimated_Beta):" + num2str(corr(Beta,estBeta)));The output would be like:
>> Example
Fitting the LMM ...
Real vs estimated random-effect covariances:
11.6581 0.1008 2.1193
0.1008 2.9977 1.6877
2.1193 1.6877 7.0714
11.7331 0.4766 6.9986
0.4766 3.2664 2.1220
6.9986 2.1220 8.1317
[Real_noise_var Estimated_noise_var]:
0.8800 0.9187
Corr(Real_Beta,Estimated_Beta):0.99933
To use the Matlab implementation, you will need to compile the SRHT mex plugin. Suppose that you are running Linux with the GCC C compiler, the compilation can be done by the following Matlab commands:
cd mex/
mex -v -g CFLAGS='-march=native -O3 -fPIC' srht.c tran_srht.c
Then, you obtain the compiled 'srht.mex*' plugin, and copy it into the parent directory. A pre-compiled plugin for 64-bit Linux is provided. Compilation for octave is similar:
cd mex/
mkoctfile --mex srht.c tran_srht.c
We used Matlab to generate a C shared library under c_dist/. The c_dist/MatlabRuntime.install is provided by Matlab 2017b which includes necessary runtime libraries.