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sparseTAM.m
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sparseTAM.m
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function [acc theta eta_t eta_a qa_te] = sparseTAM(x,K,varargin)
%function [acc theta eta_t eta_a] = sparseTAM(x,K,varargin)
%[sparse aspects alpha gamma_dirichlet te_x te_aspects vocab ...
% seed hyperprior_update_interval compute_perplexity ...
% topic_aspects verbose init_eta_t init_eta_a max_its max_mstep_its ...
% save_prefix eval_period] = ...
% process_options(varargin,'sparse',1,'aspects',ones(size(x,1),1),'alpha',1/K,...
% 'init-gamma-dirichlet',1,'te-x',[],'te-aspects',[],...
% 'vocab',[],'seed',[],'hyperprior-update-interval',1,...
% 'compute-perplexity',1,'topic-aspects',0,'verbose',1,'init-eta-t',[],...
% 'init-eta-a',[],'max-its',100,'max-mstep-its',100,'save-prefix',[],'eval-period',5);
[sparse aspects alpha gamma_dirichlet te_x te_aspects vocab ...
seed hyperprior_update_interval compute_perplexity ...
topic_aspects verbose init_eta_t init_eta_a max_its max_mstep_its ...
save_prefix eval_period] = ...
process_options(varargin,'sparse',1,'aspects',ones(size(x,1),1),'alpha',1/K,...
'init-gamma-dirichlet',1,'te-x',[],'te-aspects',[],...
'vocab',[],'seed',[],'hyperprior-update-interval',1,...
'compute-perplexity',1,'topic-aspects',0,'verbose',1,'init-eta-t',[],...
'init-eta-a',[],'max-its',100,'max-mstep-its',100,'save-prefix',[],'eval-period',5);
disp(varargin);
%screen words that have zero counts, because they mess stuff up
word_counts = sum(x); x = x(:,word_counts>0);
if ~isempty(te_x), te_x = te_x(:,word_counts>0); end
if ~isempty(vocab), vocab = vocab(word_counts > 0); end
alpha = alpha * ones(1,K); acc = 0;
[D W] = size(x); theta = zeros(D,K); A = max(aspects);
if A > 1, compute_perplexity = 0; end
%% corpus initialization
if ~isempty(seed), rand('seed',seed); end
%mean
m = makeLogProbs(sum(x))';
%eta_t (topics)
if sparse
if ~isempty(init_eta_t),eta_t = init_eta_t; else
eta_t = zeros(W,K);
%need enough words to get a good initialization
D_init = round(10000 / (full(sum(sum(x))) / size(x,1)))
if K>1,
for k = 1:K,
%consider initializing non-sparsely
dsamp = randsample(D,D_init);
%eta_t_nonsparse = computeBetaVariational(full(sum(x(dsamp,:))'),m,'precision',1);
eta_t(:,k) = computeBetaSparseVariational(full(sum(x(dsamp,:))'),m,'max-its',max_mstep_its,'verbose',0);
end
end
end
%eta_a (aspects)
if ~isempty(init_eta_a), eta_a = init_eta_a; else
eta_a = zeros(W,A);
if A>1
for j = 1:A
eta_a(:,j) = computeBetaSparseVariational(full(sum(x(aspects==j,:))'),m,'max-its',max_mstep_its);
end
end
end
%eta_ta (interactions)
eta_ta = zeros(W,K,A); if topic_aspects && A>1, for j = 1:A, for k = 1:K, eta_ta(:,k,j) = 0.1 * (eta_t(:,k) + eta_a(:,j)); end; end; end
%sums
eta_sum = makeEtaSum(m,eta_a,eta_t,eta_ta);
else
assert(A==1); %can't do non-sparse aspect models now
for k = 1:K
eta_sum(:,k) = computeBetaDirichlet(full(sum(x(randsample(D,10),:))),gamma_dirichlet);
end
gamma_dirichlet = gamma_dirichlet * ones(1,W);
end
sigma = repmat(sum(x,2)/K,1,K) + repmat(alpha,D,1);
q_a = zeros(D+1,max(aspects)); q_a(end,:) = 1/max(aspects); %prior
eta_lv_score = 0; eta_ta_lv_score = 0; prior_prob = 0;
%iter = newIterator(max_its,'debug',true,'thresh',1e-5);
iter = newDeltaIterator(max_its,'debug',true,'thresh',0);
ecounts = zeros(W,K,A);
while ~iter.done
%% E-step
word_score = 0; estep_lv_score = 0;
old_ecounts = ecounts;
ecounts = zeros(W,K,A);
for i = 1:D
if (rem(i,100)==0), fprintf('+'); end
old_sigma = sigma(i,:);
log_p_a = digamma(sum(q_a)) - digamma(sum(sum(q_a)));
%[theta(i,:) q_a(i,:) new_counts sigma(i,:) score doc_lv_score
%doc_word_score] = tamEStep(x(i,:),eta_sum,alpha,log_p_a,old_sigma);
[theta(i,:) q_a(i,:) new_counts sigma(i,:) score doc_lv_score doc_word_score] = tamEStep(x(i,:),eta_sum(:,:,aspects(i)),alpha,0,old_sigma);
q_a(i,:) = 0; q_a(i,aspects(i)) = 1;
ecounts(:,:,aspects(i)) = ecounts(:,:,aspects(i)) + full(new_counts);
doc_lv_score = doc_lv_score + digamma(sum(q_a(:,aspects(i)))) - digamma(sum(sum(q_a))); %E[log P(a_i)] - E[log Q(a_i)]
word_score = word_score + doc_word_score;
estep_lv_score = estep_lv_score + doc_lv_score;
end
fprintf('fro norm of counts: %.3f\n',norm(reshape(ecounts,W,K*A)-reshape(old_ecounts,W,K*A),'fro'));
estep_lv_score = estep_lv_score - kldirichlet(sum(q_a),q_a(end,:));
fprintf('\n');
computeScore(word_score,estep_lv_score,eta_lv_score,prior_prob,'print',1);
%% M-step.
if A>1 && K > 1, max_its = 10; else max_its = 0; end
mstep_iter = newIterator(max_its,'thresh',1e-5,'debug',true);
if sparse
eta_t_lv_score = zeros(K,1); eta_a_lv_score = zeros(A,1);
old_eta_t = eta_t;
while ~mstep_iter.done
if K > 1,
for k = 1:K
eq_m = logNormalizeRows(reshape(eta_sum(:,k,:),W,A)' - repmat(eta_t(:,k),1,A)');
eta_t(:,k) = computeBetaSparseVariational(reshape(ecounts(:,k,:),W,A),eq_m','max-its',max_mstep_its);
eta_sum = makeEtaSum(m,eta_a,eta_t,eta_ta);
end
end
fprintf(' ');
if A > 1,
for j = 1:A
if sparse
eq_m = logNormalizeRows(eta_sum(:,:,j)' - repmat(eta_a(:,j),1,K)');
eta_a(:,j) = computeBetaSparseVariational(ecounts(:,:,j),eq_m','max-its',max_mstep_its);
eta_sum = makeEtaSum(m,eta_a,eta_t,eta_ta);
else
assert(K==1);
eta_a(:,j) = computeBetaDirichlet(ecounts(:,1,j)');
end
end
end
fprintf(' ');
if topic_aspects, for k = 1:K, for j=1:A,
assert(sparse==1);
eq_m = logNormalizeRows(eta_sum(:,k,j)' - eta_ta(:,k,j)');
eta_ta(:,k,j) = computeBetaSparseVariational(ecounts(:,k,j),eq_m','max-its',max_mstep_its);
end; end;
eta_sum = makeEtaSum(m,eta_a,eta_t,eta_ta);
end
word_score = 0;
for j = 1:A, for k = 1:K
word_score = word_score + scoreWords(ecounts(:,k,j),eta_sum(:,k,j));
end; end
eta_lv_score = sum(eta_t_lv_score) + sum(eta_a_lv_score) + sum(sum(eta_ta_lv_score));
fprintf('\n');
total_score = computeScore(word_score,estep_lv_score,eta_lv_score,prior_prob,'print',0);
density_t = sum(sum(abs(eta_t) > 1e-4)) / numel(eta_t);
density_a = sum(sum(abs(eta_a) > 1e-4)) / numel(eta_a);
density_ta = sum(sum(sum(abs(eta_ta)>1e-4))) / numel(eta_ta);
fprintf('%.3f\tT=%.3f A=%.3f TA=%.3f norm diff=%.3f\n',total_score,density_t,density_a,density_ta,norm(eta_t-old_eta_t,'fro'));
%mstep_iter = updateIterator(mstep_iter,word_score + eta_lv_score);
mstep_iter = updateDeltaIterator(mstep_iter,reshape(eta_sum,W,A*K));
end
else
if A == 1
eta_sum(:,:,1) = computeBetaDirichlet(ecounts(:,:,1)',gamma_dirichlet)';
elseif K == 1
for a = 1:A
eta_sum(:,1,a) = computeBetaDirichlet(ecounts(:,1,a)',gamma_dirichlet);
end
else
error('in non-sparse model, either K or A must be 1');
end
end
%% status
%iter = updateIterator(iter,total_score);
iter = updateDeltaIterator(iter,[reshape(theta,D*K,1)]);% reshape(q_a(1:end-1),D*A,1)]);
if ~isempty(vocab)
if sparse
if K > 1
fprintf(' ----- topics ----- \n');
if topic_aspects %print interaction terms
for k = 1:K
for j = 1:A
fprintf('K%dA%d\t ',k,j);
%makeTopicReport(eta_sum(1:numel(vocab),k,j)',vocab,'N',10,'background',m'); %i'm not sure supplying the background is a good idea
makeTopicReport(eta_ta(1:numel(vocab),k,j)',vocab,'N',10); %i'm not sure supplying the background is a good idea
end
fprintf('\n');
end
end
%same as above (for topics)
makeTopicReport(tprod(mean(q_a)',[-3],eta_sum,[1 2 -3],'n')',vocab,'N',20);
end
if A > 1
fprintf(' ----- aspects ----- \n');
makeTopicReport(eta_a(1:numel(vocab),:)',vocab,'N',20,'background',zeros(1,W));
end
else
if A > K
for k = 1:K,
if K>1, fprintf(' ----- topic %d ----- ',k); end
makeTopicReport(reshape(eta_sum(1:numel(vocab),k,:),W,A)',vocab,'N',20);
end
else
for a = 1:A
if A > 1, fprintf(' ----- aspect %d ----- \n', a); end
makeTopicReport(eta_sum(1:numel(vocab),:,a)',vocab,'N',20);
end
end
end
end
%% hyperpriors
prior_prob = 0;
if rem(iter.its,hyperprior_update_interval) == 0
%topics might be too sparse? consider removing this.
if K > 1
e_log_theta = digamma(sigma) - repmat(digamma(sum(sigma,2)),1,K);
alpha = fitDirichletPrior(e_log_theta);
end
if verbose > 0, fprintf('new alpha: %s\n',sprintf('%.2f ',alpha)); end
if ~sparse
%gamma = fitDirichletPrior(reshape(eta_sum,W,K*A)');
%here is a newton step that will increase your bound...
for i = 1:10
g_gamma = K * A * W * (digamma(W*gamma_dirichlet(1)) - digamma(gamma_dirichlet(1))) + sum(sum(sum(eta_sum)));
g_gamma = g_gamma - 2/gamma_dirichlet(1) + 1/(gamma_dirichlet(1)^2); %from IG(1,1) prior
h_gamma = K * A * W * (W * trigamma(W*gamma_dirichlet(1)) - trigamma(gamma_dirichlet(1)));
h_gamma = h_gamma + 2/(gamma_dirichlet(1)^2) - 2/(gamma_dirichlet(1)^3); %from IG(1,1) prior
gamma_dirichlet = gamma_dirichlet - 0.2 * g_gamma / h_gamma;
end
prior_prob = prior_prob - 2 * log(gamma_dirichlet(1)) - 1 / gamma_dirichlet(1); %from IG(1,1) prior
if verbose > 0, fprintf('new mean gamma = %.5f\n',mean(gamma_dirichlet)); end
end
end
%% TEST SET
qa_te = [];
if ~isempty(te_x)
theta_te = zeros(size(te_x,1),K);
qa_te = zeros(size(te_x,1),max(aspects));
e_log_a = digamma(sum(q_a)) - digamma(sum(sum(q_a)));
%use the Chib estimator from Wallach et al
if rem(iter.its,compute_perplexity)==0
if sparse, pred_topics = logToSimplex2(eta_sum');
else, pred_topics = logToSimplex2(computeBetaDirichlet(ecounts',gamma_dirichlet)); end
fprintf('PERPLEX %d: %.5f\n',iter.its,computePerplexity(te_x,pred_topics,alpha));
end
if A > 1 && rem(iter.its,eval_period)==0
for i = 1:size(te_x,1)
[theta_te(i,:) qa_te(i,:)] = tamEStep(te_x(i,:),eta_sum(:,:,1:max(aspects)),alpha,e_log_a);
end
[ig preds] = max(qa_te');
acc = mean(preds==te_aspects);
fprintf('ACC %d: = %.3f\n',iter.its,acc);
end
end
if ~isempty(save_prefix) && rem(iter.its,2)==1
save(sprintf('%s.%d.mat',save_prefix,iter.its));
end
end
if ~isempty(te_x)
if compute_perplexity
if sparse, pred_topics = normalize_rows(exp(eta_sum'));
else, pred_topics = logToSimplex2(computeBetaDirichlet(ecounts',gamma_dirichlet)); end
fprintf('FINAL PERPLEX\t%.5f\t%.5f\n',computePerplexity(te_x,pred_topics,alpha),iter.prev(1));
end
if A>1 && ~isempty(te_aspects )
for i = 1:size(te_x,1)
[theta_te(i,:) qa_te(i,:)] = tamEStep(te_x(i,:),eta_sum(:,:,1:max(aspects)),alpha,e_log_a);
end
[ig preds] = max(qa_te');
acc = mean(preds==te_aspects);
fprintf('FINAL ACC\t%.5f\t%.5f\n',acc,iter.prev(1));
end
end
if ~sparse %can't remember why i was doing this...
eta_t = eta_sum(:,:,1) - repmat(m,1,K);
eta_a = eta_sum(:,1,:) - repmat(m,1,A);
end
end
function eta_sum = makeEtaSum(m,eta_a,eta_t,eta_ta)
[W K A] = size(eta_ta);
eta_sum = zeros(W,K,A);
for j = 1:A
for k = 1:K
eta_sum(:,k,j) = logNormalizeVec(m + eta_a(:,j) + eta_t(:,k) + eta_ta(:,k,j));
end
end
end
function total_score = computeScore(word_score, estep_lv_score, eta_lv_score, prior_score, varargin)
[print] = process_options(varargin,'print',0);
total_score = word_score + estep_lv_score + eta_lv_score + prior_score;
if print,
fprintf('%.3f\t=\t%.3f\t+\t%.3f\t+\t%.3f\t+\t%.3f\n',total_score,word_score,estep_lv_score,eta_lv_score,prior_score);
end
end