/** Why buildingModel2 that follows the paper instructions does not work? */
protected void buildModel2() {
for (int iter = 1; iter <= numIters; iter++) {
// Step 1: update W by fixing H
DenseMatrix trH = H.transpose();
// V * trH
DenseMatrix V_trH = DenseMatrix.mult(V, trH);
// W * H * trH
DenseMatrix W_H_trH = W.mult(H.mult(trH));
// update: W_ij = W_ij * (V_trH)_ij / (W_H_trH)_ij
for (int i = 0; i < W.numRows(); i++)
for (int j = 0; j < W.numColumns(); j++) {
double denorm = W_H_trH.get(i, j) + 1e-9;
W.set(i, j, W.get(i, j) * (V_trH.get(i, j) / denorm));
}
// Step 2: update H by fixing W
DenseMatrix trW = W.transpose();
// trW * V
DenseMatrix trW_V = trW.mult(V);
// trW * W * H
DenseMatrix trW_W_H = trW.mult(W).mult(H);
// update: H_ij = H_ij * (trW_V)_ij / (trW_W_H)_ij
for (int i = 0; i < H.numRows(); i++)
for (int j = 0; j < H.numColumns(); j++) {
double denorm = trW_W_H.get(i, j) + 1e-9;
H.set(i, j, H.get(i, j) * (trW_V.get(i, j) / denorm));
}
// compute errors
loss = 0;
errs = 0;
for (MatrixEntry me : V) {
int u = me.row();
int j = me.column();
double ruj = me.get();
if (ruj > 0) {
double pred = predict(u, j);
double euj = pred - ruj;
errs += euj * euj;
loss += euj * euj;
}
}
errs *= 0.5;
loss *= 0.5;
if (isConverged(iter)) break;
}
}
@Override
protected void buildModel() throws Exception {
// Initialize hierarchical priors
int beta = 2; // observation noise (precision)
DenseVector mu_u = new DenseVector(numFactors);
DenseVector mu_m = new DenseVector(numFactors);
// parameters of Inv-Whishart distribution
DenseMatrix WI_u = DenseMatrix.eye(numFactors);
int b0_u = 2;
int df_u = numFactors;
DenseVector mu0_u = new DenseVector(numFactors);
DenseMatrix WI_m = DenseMatrix.eye(numFactors);
int b0_m = 2;
int df_m = numFactors;
DenseVector mu0_m = new DenseVector(numFactors);
// initializing Bayesian PMF using MAP solution found by PMF
P = new DenseMatrix(numUsers, numFactors);
Q = new DenseMatrix(numItems, numFactors);
P.init(0, 1);
Q.init(0, 1);
for (int f = 0; f < numFactors; f++) {
mu_u.set(f, P.columnMean(f));
mu_m.set(f, Q.columnMean(f));
}
DenseMatrix alpha_u = P.cov().inv();
DenseMatrix alpha_m = Q.cov().inv();
// Iteration:
DenseVector x_bar = new DenseVector(numFactors);
DenseVector normalRdn = new DenseVector(numFactors);
DenseMatrix S_bar, WI_post, lam;
DenseVector mu_temp;
double df_upost, df_mpost;
int M = numUsers, N = numItems;
for (int iter = 1; iter <= numIters; iter++) {
// Sample from user hyper parameters:
for (int f = 0; f < numFactors; f++) x_bar.set(f, P.columnMean(f));
S_bar = P.cov();
DenseVector mu0_u_x_bar = mu0_u.minus(x_bar);
DenseMatrix e1e2 = mu0_u_x_bar.outer(mu0_u_x_bar).scale(M * b0_u / (b0_u + M + 0.0));
WI_post = WI_u.inv().add(S_bar.scale(M)).add(e1e2);
WI_post = WI_post.inv();
WI_post = WI_post.add(WI_post.transpose()).scale(0.5);
df_upost = df_u + M;
DenseMatrix wishrnd_u = wishart(WI_post, df_upost);
if (wishrnd_u != null) alpha_u = wishrnd_u;
mu_temp = mu0_u.scale(b0_u).add(x_bar.scale(M)).scale(1 / (b0_u + M + 0.0));
lam = alpha_u.scale(b0_u + M).inv().cholesky();
if (lam != null) {
lam = lam.transpose();
for (int f = 0; f < numFactors; f++) normalRdn.set(f, Randoms.gaussian(0, 1));
mu_u = lam.mult(normalRdn).add(mu_temp);
}
// Sample from item hyper parameters:
for (int f = 0; f < numFactors; f++) x_bar.set(f, Q.columnMean(f));
S_bar = Q.cov();
DenseVector mu0_m_x_bar = mu0_m.minus(x_bar);
DenseMatrix e3e4 = mu0_m_x_bar.outer(mu0_m_x_bar).scale(N * b0_m / (b0_m + N + 0.0));
WI_post = WI_m.inv().add(S_bar.scale(N)).add(e3e4);
WI_post = WI_post.inv();
WI_post = WI_post.add(WI_post.transpose()).scale(0.5);
df_mpost = df_m + N;
DenseMatrix wishrnd_m = wishart(WI_post, df_mpost);
if (wishrnd_m != null) alpha_m = wishrnd_m;
mu_temp = mu0_m.scale(b0_m).add(x_bar.scale(N)).scale(1 / (b0_m + N + 0.0));
lam = alpha_m.scale(b0_m + N).inv().cholesky();
if (lam != null) {
lam = lam.transpose();
for (int f = 0; f < numFactors; f++) normalRdn.set(f, Randoms.gaussian(0, 1));
mu_m = lam.mult(normalRdn).add(mu_temp);
}
// Gibbs updates over user and item feature vectors given hyper parameters:
// NOTE: in PREA, only 1 iter for gibbs where in the original Matlab code, 2 iters are used.
for (int gibbs = 0; gibbs < 2; gibbs++) {
// Infer posterior distribution over all user feature vectors
for (int u = 0; u < numUsers; u++) {
// list of items rated by user uu:
SparseVector rv = trainMatrix.row(u);
int count = rv.getCount();
if (count == 0) continue;
// features of items rated by user uu:
DenseMatrix MM = new DenseMatrix(count, numFactors);
DenseVector rr = new DenseVector(count);
int idx = 0;
for (int j : rv.getIndex()) {
rr.set(idx, rv.get(j) - globalMean);
for (int f = 0; f < numFactors; f++) MM.set(idx, f, Q.get(j, f));
idx++;
}
DenseMatrix covar = alpha_u.add((MM.transpose().mult(MM)).scale(beta)).inv();
DenseVector a = MM.transpose().mult(rr).scale(beta);
DenseVector b = alpha_u.mult(mu_u);
DenseVector mean_u = covar.mult(a.add(b));
lam = covar.cholesky();
if (lam != null) {
lam = lam.transpose();
for (int f = 0; f < numFactors; f++) normalRdn.set(f, Randoms.gaussian(0, 1));
DenseVector w1_P1_u = lam.mult(normalRdn).add(mean_u);
for (int f = 0; f < numFactors; f++) P.set(u, f, w1_P1_u.get(f));
}
}
// Infer posterior distribution over all movie feature vectors
for (int j = 0; j < numItems; j++) {
// list of users who rated item ii:
SparseVector jv = trainMatrix.column(j);
int count = jv.getCount();
if (count == 0) continue;
// features of users who rated item ii:
DenseMatrix MM = new DenseMatrix(count, numFactors);
DenseVector rr = new DenseVector(count);
int idx = 0;
for (int u : jv.getIndex()) {
rr.set(idx, jv.get(u) - globalMean);
for (int f = 0; f < numFactors; f++) MM.set(idx, f, P.get(u, f));
idx++;
}
DenseMatrix covar = alpha_m.add((MM.transpose().mult(MM)).scale(beta)).inv();
DenseVector a = MM.transpose().mult(rr).scale(beta);
DenseVector b = alpha_m.mult(mu_m);
DenseVector mean_m = covar.mult(a.add(b));
lam = covar.cholesky();
if (lam != null) {
lam = lam.transpose();
for (int f = 0; f < numFactors; f++) normalRdn.set(f, Randoms.gaussian(0, 1));
DenseVector w1_M1_j = lam.mult(normalRdn).add(mean_m);
for (int f = 0; f < numFactors; f++) Q.set(j, f, w1_M1_j.get(f));
}
}
} // end of gibbs
loss = 0;
for (MatrixEntry me : trainMatrix) {
int u = me.row();
int j = me.column();
double ruj = me.get();
double pred = predict(u, j);
double euj = ruj - pred;
loss += euj * euj;
}
loss *= 0.5;
if (isConverged(iter)) break;
}
}
