/
demo_negmnreg.m
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demo_negmnreg.m
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%% Negative multinomial regression and sparse regression
% A demo of negative multinomial regression and sparse regression
%% Generate negative multinomial random vectors from covariates
clear;
% reset random seed
s = RandStream('mt19937ar','Seed',1);
RandStream.setGlobalStream(s);
% sample size
n = 200;
% # covariates
p = 15;
% # bins
d = 5;
% design matrix
X = randn(n,p);
% true regression coefficients
B = zeros(p,d+1);
nzidx = [1 3 5];
B(nzidx,:) = ones(length(nzidx),d+1);
eta = X*B;
alpha = exp(eta);
prob(:,d+1) = 1./(sum(alpha(:,1:d),2)+1);
prob(:,1:d) = bsxfun(@times, alpha(:,1:d), prob(:,d+1));
b= binornd(10,0.2, n, 1);
Y = negmnrnd(prob,b);
zerorows = sum(Y,2);
Y=Y(zerorows~=0, :);
X=X(zerorows~=0, :);
%% Fit negative multinomial regression - link over-disperson parameter
tic;
[B_hat, stats] = negmnreg(X,Y);
toc;
display(B_hat);
display(stats);
% Wald test of predictor significance
display('Wald test p-values:');
display(stats.wald_pvalue);
figure;
plot(stats.logL_iter);
xlabel('iteration');
ylabel('log-likelihood');
%% Fit negative multinomial regression - not linking over-disperson parameter
tic;
[B_hat, b_hat, stats] = negmnreg2(X,Y);
toc;
disp(B_hat);
disp(stats.se_B);
disp(b_hat);
disp(stats.se_b);
display(stats);
% Wald test of predictor significance
display('Wald test p-values:');
display(stats.wald_pvalue);
figure;
plot(stats.logL_iter);
xlabel('iteration');
ylabel('log-likelihood');
%% Fit negative multinomial sparse regression - lasso/group/nuclear penalty
% Regression on the over dispersion parameter
penalty = {'sweep','group','nuclear'};
ngridpt = 30;
dist = 'negmn';
for i = 1:length(penalty)
pen = penalty{i};
[~, stats] = mglm_sparsereg(X,Y,inf,'penalty',pen,'dist',dist);
maxlambda = stats.maxlambda;
lambdas = exp(linspace(log(maxlambda),log(maxlambda/100),ngridpt));
BICs = zeros(1,ngridpt);
logl =zeros(1, ngridpt);
dofs = zeros(1, ngridpt);
tic;
for j=1:ngridpt
if j==1
B0 = zeros(p,d+1);
else
B0 = B_hat;
end
[B_hat, stats] = mglm_sparsereg(X,Y,lambdas(j),'penalty',pen, ...
'dist',dist,'B0',B0);
BICs(j) = stats.BIC;
logl(j) = stats.logL;
dofs(j) = stats.dof;
end
toc;
% True signal versus estimated signal
[bestbic,bestidx] = min(BICs);
[B_best,stats] = mglm_sparsereg(X,Y,lambdas(bestidx),'penalty',pen,'dist',dist);
figure;
subplot(1,3,1);
semilogx(lambdas,BICs);
ylabel('BIC');
xlabel('\lambda');
xlim([min(lambdas) max(lambdas)]);
subplot(1,3,2);
imshow(mat2gray(-B)); title('True B');
subplot(1,3,3);
imshow(mat2gray(-B_best)); title([pen ' estimate']);
end
%% Sparse regression (not linking over-disp.) - lasso/group/nuclear penalty
% Do not run regression on the over dispersion parameter
penalty = {'sweep','group','nuclear'};
ngridpt = 30;
dist = 'negmn2';
for i = 1:length(penalty)
pen = penalty{i};
[~, stats] = mglm_sparsereg(X,Y,inf,'penalty',pen,'dist',dist);
maxlambda = stats.maxlambda;
lambdas = exp(linspace(log(maxlambda),log(maxlambda/100),ngridpt));
BICs = zeros(1,ngridpt);
logl =zeros(1, ngridpt);
dofs = zeros(1, ngridpt);
tic;
for j=1:ngridpt
if j==1
B0 = zeros(p,d);
else
B0 = B_hat;
end
[B_hat, stats] = mglm_sparsereg(X,Y,lambdas(j),'penalty',pen, ...
'dist',dist,'B0',B0);
BICs(j) = stats.BIC;
logl(j) = stats.logL;
dofs(j) = stats.dof;
end
toc;
% True signal versus estimated signal
[bestbic,bestidx] = min(BICs);
B_best = mglm_sparsereg(X,Y,lambdas(bestidx),'penalty',pen,'dist',dist);
figure;
subplot(1,3,1);
semilogx(lambdas,BICs);
ylabel('BIC');
xlabel('\lambda');
xlim([min(lambdas) max(lambdas)]);
subplot(1,3,2);
imshow(mat2gray(-B)); title('True B');
subplot(1,3,3);
imshow(mat2gray(-B_best)); title([pen ' estimate']);
end