optProject/coordDescReg.m at master · nrafidi/optProject · GitHub

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function [B, slackVar, lambda, gamma1, gamma2, totalIT, avgIT] = ...
    coordDescReg(X, Y, coordFuncs, objFunc, Psi, Theta, paramOrder)

%Parameter Selection - rough iterative grid search
lambdas = fliplr([1e-5 1e-4 0.001, 0.01, 0.1, 1, 10, 100]);
gammas = fliplr([1e-5 1e-4 0.001, 0.01, 0.1, 1, 10, 100]);
R = length(gammas);

n = size(X,1);
k = 2; %number of folds for CV
cvInd = crossvalind('Kfold', n, k);

lambda = 0;
gamma1 = 0;
gamma2 = 0;
p = size(X,2);
q = size(Y,2);
avgIT = 0;

%Choose lambda, gamma1, and gamma2 while keeping other two fixed
lambdaFirst = paramOrder(1);
gamma1First = paramOrder(2);
gamma2First = paramOrder(3);
lambdaSec = paramOrder(4);
gamma1Sec = paramOrder(5);
doPlot = 0;

if lambdaFirst
    [lambda, avgIT] = chooseLambda(p,q,R,k,cvInd,avgIT,X,Y,lambdas,gamma1, gamma2, coordFuncs, objFunc, Psi, Theta);
    fprintf('Lambda done\n');
    if doPlot
        B = coordDesc(X, Y, lambda, gamma1, gamma2, coordFuncs, objFunc, Psi, Theta, rand(p,q));
        plotB(2, B, lambda, gamma1, gamma2);
    end
    if gamma1Sec
        [gamma1, avgIT] = chooseGamma1(p,q,R,k,cvInd,avgIT,X,Y,lambda,gammas, gamma2, coordFuncs, objFunc, Psi, Theta);
        fprintf('Gamma1 done\n');
        if doPlot
            B = coordDesc(X, Y, lambda, gamma1, gamma2, coordFuncs, objFunc, Psi, Theta, rand(p,q));
            plotB(3, B, lambda, gamma1, gamma2);
        end
        [gamma2, avgIT] = chooseGamma2(p,q,R,k,cvInd,avgIT,X,Y,lambda,gamma1, gammas, coordFuncs, objFunc, Psi, Theta);
    else
        [gamma2, avgIT] = chooseGamma2(p,q,R,k,cvInd,avgIT,X,Y,lambda,gamma1, gammas, coordFuncs, objFunc, Psi, Theta);
        if doPlot
            B = coordDesc(X, Y, lambda, gamma1, gamma2, coordFuncs, objFunc, Psi, Theta, rand(p,q));
            plotB(3, B, lambda, gamma1, gamma2);
        end
        [gamma1, avgIT] = chooseGamma1(p,q,R,k,cvInd,avgIT,X,Y,lambda,gammas, gamma2, coordFuncs, objFunc, Psi, Theta);
        fprintf('Gamma1 done\n');
    end
elseif gamma2First
    [gamma2, avgIT] = chooseGamma2(p,q,R,k,cvInd,avgIT,X,Y,lambda,gamma1, gammas, coordFuncs, objFunc, Psi, Theta);
    if doPlot
        B = coordDesc(X, Y, lambda, gamma1, gamma2, coordFuncs, objFunc, Psi, Theta, rand(p,q));
        plotB(2, B, lambda, gamma1, gamma2);
    end
    if lambdaSec
        [lambda, avgIT] = chooseLambda(p,q,R,k,cvInd,avgIT,X,Y,lambdas,gamma1, gamma2, coordFuncs, objFunc, Psi, Theta);
        fprintf('Lambda done\n');
        if doPlot
            B = coordDesc(X, Y, lambda, gamma1, gamma2, coordFuncs, objFunc, Psi, Theta, rand(p,q));
            plotB(3, B, lambda, gamma1, gamma2);
        end
        [gamma1, avgIT] = chooseGamma1(p,q,R,k,cvInd,avgIT,X,Y,lambda,gammas, gamma2, coordFuncs, objFunc, Psi, Theta);
        fprintf('Gamma1 done\n');
    else
        [gamma1, avgIT] = chooseGamma1(p,q,R,k,cvInd,avgIT,X,Y,lambda,gammas, gamma2, coordFuncs, objFunc, Psi, Theta);
        fprintf('Gamma1 done\n');
        if doPlot
            B = coordDesc(X, Y, lambda, gamma1, gamma2, coordFuncs, objFunc, Psi, Theta, rand(p,q));
            plotB(3, B, lambda, gamma1, gamma2);
        end
        [lambda, avgIT] = chooseLambda(p,q,R,k,cvInd,avgIT,X,Y,lambdas,gamma1, gamma2, coordFuncs, objFunc, Psi, Theta);
        fprintf('Lambda done\n');
    end
elseif gamma1First %#ok<*UNRCH>
    [gamma1, avgIT] = chooseGamma1(p,q,R,k,cvInd,avgIT,X,Y,lambda,gammas, gamma2, coordFuncs, objFunc, Psi, Theta);
    fprintf('Gamma1 done\n');
    if doPlot
        B = coordDesc(X, Y, lambda, gamma1, gamma2, coordFuncs, objFunc, Psi, Theta, rand(p,q));
        plotB(2, B, lambda, gamma1, gamma2);
    end
    if lambdaSec
        [lambda, avgIT] = chooseLambda(p,q,R,k,cvInd,avgIT,X,Y,lambdas,gamma1, gamma2, coordFuncs, objFunc, Psi, Theta);
        fprintf('Lambda done\n');
        if doPlot
            B = coordDesc(X, Y, lambda, gamma1, gamma2, coordFuncs, objFunc, Psi, Theta, rand(p,q));
            plotB(3, B, lambda, gamma1, gamma2);
        end
        [gamma2, avgIT] = chooseGamma2(p,q,R,k,cvInd,avgIT,X,Y,lambda,gamma1, gammas, coordFuncs, objFunc, Psi, Theta);
    else
        [gamma2, avgIT] = chooseGamma2(p,q,R,k,cvInd,avgIT,X,Y,lambda,gamma1, gammas, coordFuncs, objFunc, Psi, Theta);
        if doPlot
            B = coordDesc(X, Y, lambda, gamma1, gamma2, coordFuncs, objFunc, Psi, Theta, rand(p,q));
            plotB(3, B, lambda, gamma1, gamma2);
        end
        [lambda, avgIT] = chooseLambda(p,q,R,k,cvInd,avgIT,X,Y,lambdas,gamma1, gamma2, coordFuncs, objFunc, Psi, Theta);
        fprintf('Lambda done\n');
    end
end

[B, slackVar, totalIT] = coordDesc(X, Y, lambda, gamma1, gamma2, coordFuncs, objFunc, Psi, Theta, rand(p,q));
if doPlot
    plotB(4, B, lambda, gamma1, gamma2);
    suptitle('B after Different Stages of Initial Parameter Search');
end

% Parameter Selection - gradient descent - currently unused
% tolerance = 1e-4;
% step = 1e-6;
% h = 0.1; %I have legit no idea what to make this
%
% lambdaB = rand(p,q);
% gamma1B = lambdaB;
% gamma2B = lambdaB;
% [B, slackVar] = coordDesc(X, Y, lambda, gamma1, gamma2, coordFuncs, objFunc, Psi, Theta, rand(p,q));
% currObj = feval(objFunc, X, Y, B, slackVar, lambda, gamma1, gamma2, Psi, Theta);
% prevObj = 1e10;
% while abs(currObj - prevObj) > tolerance
%     %Estimate gradient:
%     [lambdaB, lamSlack] = coordDesc(X, Y, lambda + h, gamma1, gamma2, coordFuncs, objFunc, Psi, Theta, lambdaB);
%     [gamma1B, gam1Slack] = coordDesc(X, Y, lambda, gamma1+h, gamma2, coordFuncs, objFunc, Psi, Theta, gamma1B);
%     [gamma2B, gam2Slack] = coordDesc(X, Y, lambda, gamma1, gamma2+h, coordFuncs, objFunc, Psi, Theta, gamma2B);
%
%     delLambda = - step*(feval(objFunc, X, Y, lambdaB, lamSlack, lambda, gamma1, gamma2, Psi, Theta) - currObj)/h;
%     delGamma1 = - step*(feval(objFunc, X, Y, gamma1B, gam1Slack, lambda, gamma1, gamma2, Psi, Theta) - currObj)/h;
%     delGamma2 = - step*(feval(objFunc, X, Y, gamma2B, gam2Slack, lambda, gamma1, gamma2, Psi, Theta) - currObj)/h;
%
%     lambda = lambda + delLambda;
%     gamma1 = gamma1 + delGamma1;
%     gamma2 = gamma2 + delGamma2;
%
%     prevObj = currObj;
%     [B, slackVar] = coordDesc(X, Y, lambda, gamma1, gamma2, coordFuncs, objFunc, Psi, Theta, B);
%     currObj = feval(objFunc, X, Y, B, slackVar, lambda, gamma1, gamma2, Psi, Theta);
% end
%
% %The last B learned in the above procedure is the one we return.
% figure
% imagesc(B);
% title(sprintf('\\lambda = %d, \\gamma_1 = %d, \\gamma_2 = %d', lambda, gamma1, gamma2));
end

function [lambda, avgIT] = chooseLambda(p,q,R,k,cvInd,avgIT,X,Y,lambdas,gamma1, gamma2, coordFuncs, objFunc, Psi, Theta)
Breg = rand(p,q);
cverrs = zeros(R, 1);
numIT = zeros(R, k);
for r = 1:R
    %Cross validation
    for kk = 1:k
        [Breg, ~, numIT(r,kk)] = coordDesc(X(cvInd~=kk, :), Y(cvInd~=kk,:), lambdas(r), gamma1, gamma2, coordFuncs, objFunc, Psi, Theta, Breg);
        cverrs(r) = cverrs(r) + norm(Y(cvInd==kk,:) - X(cvInd==kk,:)*Breg)/k;
    end
end
[~, ind] = min(cverrs);
avgIT = avgIT + mean(numIT(ind,:),2);
lambda = lambdas(ind);
end
function [gamma1, avgIT] = chooseGamma1(p,q,R,k,cvInd,avgIT,X,Y,lambda,gammas, gamma2, coordFuncs, objFunc, Psi, Theta)
Breg = rand(p,q);
cverrs = zeros(R, 1);
numIT = zeros(R, k);
for r = 1:R
    %Cross validation
    for kk = 1:k
        [Breg, ~, numIT(r,kk)] = coordDesc(X(cvInd~=kk, :), Y(cvInd~=kk,:), lambda, gammas(r), gamma2, coordFuncs, objFunc, Psi, Theta, Breg);
        cverrs(r) = cverrs(r) + norm(Y(cvInd==kk,:) - X(cvInd==kk,:)*Breg)/k;
    end
end
[~, ind] = min(cverrs);
avgIT = avgIT + mean(numIT(ind,:),2);
gamma1 = gammas(ind);
end
function [gamma2, avgIT] = chooseGamma2(p,q,R,k,cvInd,avgIT,X,Y,lambda,gamma1, gammas, coordFuncs, objFunc, Psi, Theta)
Breg = rand(p,q);
cverrs = zeros(R, 1);
numIT = zeros(R, k);
for r = 1:R
    %Cross validation
    for kk = 1:k
        [Breg, ~, numIT(r,kk)] = coordDesc(X(cvInd~=kk, :), Y(cvInd~=kk,:), lambda, gamma1, gammas(r), coordFuncs, objFunc, Psi, Theta, Breg);
        cverrs(r) = cverrs(r) + norm(Y(cvInd==kk,:) - X(cvInd==kk,:)*Breg)/k;
    end
end
[~, ind] = min(cverrs);
avgIT = avgIT + mean(numIT(ind,:),2);
gamma2 = gammas(ind);
end
function plotB(p, B, lambda, gamma1, gamma2)
subplot(2,2,p);
imagesc(B)
colorbar;
title(sprintf('\\lambda = %d, \\gamma_1 = %d, \\gamma_2 = %d', lambda, gamma1, gamma2));
end