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function cwr = cwr_em(X, Y, nc, varargin)
% CWR_LEARN Fit the parameters of a cluster weighted regression model using EM
% function cwr = cwr_learn(X, Y, ...)
%
% X(:, t) is the t'th input example
% Y(:, t) is the t'th output example
% nc is the number of clusters
%
% Kevin Murphy, May 2003
[max_iter, thresh, cov_typeX, cov_typeY, clamp_weights, ...
muX, muY, SigmaX, SigmaY, weightsY, priorC, create_init_params, ...
cov_priorX, cov_priorY, verbose, regress, clamp_covX, clamp_covY] = process_options(...
varargin, 'max_iter', 10, 'thresh', 1e-2, 'cov_typeX', 'full', ...
'cov_typeY', 'full', 'clamp_weights', 0, ...
'muX', [], 'muY', [], 'SigmaX', [], 'SigmaY', [], 'weightsY', [], 'priorC', [], ...
'create_init_params', 1, 'cov_priorX', [], 'cov_priorY', [], 'verbose', 0, ...
'regress', 1, 'clamp_covX', 0, 'clamp_covY', 0);
[nx N] = size(X);
[ny N2] = size(Y);
if N ~= N2
error(sprintf('nsamples X (%d) ~= nsamples Y (%d)', N, N2));
end
%if N < nx
% fprintf('cwr_em warning: dim X (%d) > nsamples X (%d)\n', nx, N);
%end
if (N < nx) & regress
fprintf('cwr_em warning: dim X = %d, nsamples X = %d\n', nx, N);
end
if (N < ny)
fprintf('cwr_em warning: dim Y = %d, nsamples Y = %d\n', ny, N);
end
if (nc > N)
error(sprintf('cwr_em: more centers (%d) than data', nc))
end
if nc==1
% No latent variable, so there is a closed-form solution
w = 1/N;
WYbig = Y*w;
WYY = WYbig * Y';
WY = sum(WYbig, 2);
WYTY = sum(diag(WYbig' * Y));
cwr.priorC = 1;
cwr.SigmaX = [];
if ~regress
% This is just fitting an unconditional Gaussian
cwr.weightsY = [];
[cwr.muY, cwr.SigmaY] = ...
mixgauss_Mstep(1, WY, WYY, WYTY, ...
'cov_type', cov_typeY, 'cov_prior', cov_priorY);
% There is a much easier way...
assert(approxeq(cwr.muY, mean(Y')))
assert(approxeq(cwr.SigmaY, cov(Y') + 0.01*eye(ny)))
else
% This is just linear regression
WXbig = X*w;
WXX = WXbig * X';
WX = sum(WXbig, 2);
WXTX = sum(diag(WXbig' * X));
WXY = WXbig * Y';
[cwr.muY, cwr.SigmaY, cwr.weightsY] = ...
clg_Mstep(1, WY, WYY, WYTY, WX, WXX, WXY, ...
'cov_type', cov_typeY, 'cov_prior', cov_priorY);
end
if clamp_covY, cwr.SigmaY = SigmaY; end
if clamp_weights, cwr.weightsY = weightsY; end
return;
end
if create_init_params
[cwr.muX, cwr.SigmaX] = mixgauss_init(nc, X, cov_typeX);
[cwr.muY, cwr.SigmaY] = mixgauss_init(nc, Y, cov_typeY);
cwr.weightsY = zeros(ny, nx, nc);
cwr.priorC = normalize(ones(nc,1));
else
cwr.muX = muX; cwr.muY = muY; cwr.SigmaX = SigmaX; cwr.SigmaY = SigmaY;
cwr.weightsY = weightsY; cwr.priorC = priorC;
end
if clamp_covY, cwr.SigmaY = SigmaY; end
if clamp_covX, cwr.SigmaX = SigmaX; end
if clamp_weights, cwr.weightsY = weightsY; end
previous_loglik = -inf;
num_iter = 1;
converged = 0;
while (num_iter <= max_iter) & ~converged
% E step
[likXandY, likYgivenX, post] = cwr_prob(cwr, X, Y);
loglik = sum(log(likXandY));
% extract expected sufficient statistics
w = sum(post,2); % post(c,t)
WYY = zeros(ny, ny, nc);
WY = zeros(ny, nc);
WYTY = zeros(nc,1);
WXX = zeros(nx, nx, nc);
WX = zeros(nx, nc);
WXTX = zeros(nc, 1);
WXY = zeros(nx,ny,nc);
%WYY = repmat(reshape(w, [1 1 nc]), [ny ny 1]) .* repmat(Y*Y', [1 1 nc]);
for c=1:nc
weights = repmat(post(c,:), ny, 1);
WYbig = Y .* weights;
WYY(:,:,c) = WYbig * Y';
WY(:,c) = sum(WYbig, 2);
WYTY(c) = sum(diag(WYbig' * Y));
weights = repmat(post(c,:), nx, 1); % weights(nx, nsamples)
WXbig = X .* weights;
WXX(:,:,c) = WXbig * X';
WX(:,c) = sum(WXbig, 2);
WXTX(c) = sum(diag(WXbig' * X));
WXY(:,:,c) = WXbig * Y';
end
% M step
% Q -> X is called Q->Y in Mstep_clg
[cwr.muX, cwr.SigmaX] = mixgauss_Mstep(w, WX, WXX, WXTX, ...
'cov_type', cov_typeX, 'cov_prior', cov_priorX);
for c=1:nc
assert(is_psd(cwr.SigmaX(:,:,c)))
end
if clamp_weights % affects estimate of mu and Sigma
W = cwr.weightsY;
else
W = [];
end
[cwr.muY, cwr.SigmaY, cwr.weightsY] = ...
clg_Mstep(w, WY, WYY, WYTY, WX, WXX, WXY, ...
'cov_type', cov_typeY, 'clamped_weights', W, ...
'cov_prior', cov_priorY);
%'xs', X, 'ys', Y, 'post', post); % debug
%a = linspace(min(Y(2,:)), max(Y(2,:)), nc+2);
%cwr.muY(2,:) = a(2:end-1);
cwr.priorC = normalize(w);
for c=1:nc
assert(is_psd(cwr.SigmaY(:,:,c)))
end
if clamp_covY, cwr.SigmaY = SigmaY; end
if clamp_covX, cwr.SigmaX = SigmaX; end
if clamp_weights, cwr.weightsY = weightsY; end
if verbose, fprintf(1, 'iteration %d, loglik = %f\n', num_iter, loglik); end
num_iter = num_iter + 1;
converged = em_converged(loglik, previous_loglik, thresh);
previous_loglik = loglik;
end
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