public static void compute_gradient2(int iteration) {
double[][][] tmp_grad_h_hat_prime_s = new double[T - t0][n][K];
/*
* compute
* nti[t][i] = \sum_{j} { n_{ij} }
* and
* nti_h[t][j][k] = \sum_{i} { n_{ij}^{t} h_{ik}^{t} }
*/
double[][] nti = new double[T - t0][n];
double[][][] nti_h = new double[T - t0][n][K];
for (int t = 0; t < T - t0; t++) {
double[][] G_t = GS.get(t);
double[][] h_t = h_s.get(t); // h^{t}
for (int i = 0; i < n; i++)
for (int j = 0; j < n; j++) {
nti[t][i] += G_t[i][j];
for (int k = 0; k < K; k++) {
nti_h[t][j][k] += G_t[i][j] * h_t[i][k];
}
}
}
for (int t = 0; t < T - t0; t++) {
double delta_t = delta_prime_s.get(t);
double[][] h_t = h_s.get(t); // h^{t}
double[][] h_hat_prime_t = h_hat_prime_s.get(t); // \hat{h}^{t}
double[][] mu_hat_t = mu_hat_s.get(t); // \hat{\mu}^{t}
double[][] mu_hat_prime_t = mu_hat_prime_s.get(t); // \hat{\mu}'^{t}
double[][] h_prime_t = h_prime_s.get(t);
if (t != 0) {
Matrix a = new Matrix(AS.get(t - 1));
Matrix hprime_pre_t = new Matrix(h_prime_s.get(t - 1));
Matrix ave_neighbors = a.times(hprime_pre_t);
double[][] G_pre_t = GS.get(t - 1); // G^{t-1}
double[][] A_pre_t = AS.get(t - 1); // A^{t-1}
double[][] h_pre_t = h_s.get(t - 1); // h^{t-1}
double[][] mu_hat_prime_pre_t = mu_hat_prime_s.get(t - 1); // \hat{\mu}'^{t-1} [t]
for (int s = 0; s < T - t0; s++) {
double[][] grad_mu_hat_prime_t = grad_mu_hat_prime_s.get(t * (T - t0) + s);
double[][] grad_mu_hat_prime_pre_t = grad_mu_hat_prime_s.get((t - 1) * (T - t0) + s);
double[] h2delta2 = new double[n];
for (int i = 0; i < n; i++)
for (int k = 0; k < K; k++) {
h2delta2[i] += 0.5 * h_t[i][k] * h_t[i][k] * delta_t * delta_t;
}
/* compute weighted_exp for later use */
double[][][] weighted_exp_num = new double[K][n][n];
double[][] weighted_exp_den = new double[K][n];
double[][][] weighted_exp = new double[K][n][n];
for (int i = 0; i < n; i++)
for (int j = 0; j < n; j++) {
double h_muhp = Operations.inner_product(h_t[j], mu_hat_prime_t[i], K);
for (int k = 0; k < K; k++) {
weighted_exp_num[k][i][j] = h_t[j][k] * Math.exp(h_muhp + h2delta2[j]);
weighted_exp_den[k][j] += Math.exp(h_muhp + h2delta2[j]);
}
}
for (int i = 0; i < n; i++)
for (int j = 0; j < n; j++)
for (int k = 0; k < K; k++) {
weighted_exp[k][i][j] = weighted_exp_num[k][i][j] / weighted_exp_den[k][j];
}
/* compute sum_mu_hat_prime for later use */
double[] sum_mu_hat_prime = new double[K];
for (int i = 0; i < n; i++)
for (int k = 0; k < K; k++) {
sum_mu_hat_prime[k] += mu_hat_prime_pre_t[i][k];
}
for (int i = 0; i < n; i++)
for (int k = 0; k < K; k++) {
/* first term */
double g1 = nti_h[t][i][k] * grad_mu_hat_prime_t[i][k];
tmp_grad_h_hat_prime_s[s][i][k] += g1;
/* second term */
double g2 = 0;
for (int j = 0; j < n; j++) {
g2 -= nti[t][j] * weighted_exp[k][i][j] * grad_mu_hat_prime_t[i][k];
}
tmp_grad_h_hat_prime_s[s][i][k] += g2;
/* third term */
for (int j = 0; j < n; j++)
if (G_pre_t[j][i] != 0) {
// double g3 = ( h_t[j][k] - (1-lambda) * h_pre_t[j][k] - lambda *
// A_pre_t[j][i] * sum_mu_hat_prime[k] )
double g3 =
(h_t[j][k]
- (1 - lambda) * h_pre_t[j][k]
- lambda * A_pre_t[j][i] * mu_hat_prime_pre_t[i][k])
* lambda
* A_pre_t[j][i]
* grad_mu_hat_prime_pre_t[i][k]
/ (sigma * sigma);
tmp_grad_h_hat_prime_s[s][j][k] += g3; // j instead of i!
}
}
/* fourth term */
for (int i = 0; i < n; i++)
for (int k = 0; k < K; k++) {
double g4 =
-(mu_hat_prime_t[i][k] - mu_hat_prime_pre_t[i][k])
* (grad_mu_hat_prime_t[i][k] - grad_mu_hat_prime_pre_t[i][k])
/ (sigma * sigma);
tmp_grad_h_hat_prime_s[s][i][k] += g4;
}
}
} else {
/*
for (int s = 0; s < T-t0; s++) {
double[] grad_mu_hat_prime_t = grad_mu_hat_prime_s.get(t * (T-t0) + s);
for (int i = 0; i < n; i++) {
// first term
double g1 = nti_hp[t][i] * grad_mu_hat_prime_t[i];
tmp_grad_h_hat_prime_s[s][i] += g1;
// second term
double g2 = 0;
for (int _j = 0; _j < NEG; _j++) {
double weighted_exp_num = 0, weighted_exp_den = 0;
int j = neg_samples.get(t)[i][_j];
double htj = h_t[j][0]; double muhti = mu_hat_t[i];
weighted_exp_num += htj * Math.exp(htj * muhti + 0.5 * htj * htj * delta_t * delta_t);
for (int _k = 0; _k < NEG; _k++) {
int k = neg_samples.get(t)[i][_k];
double muhtk = mu_hat_t[k];
weighted_exp_den += Math.exp(htj * muhtk + 0.5 * htj * htj * delta_t * delta_t);
}
g2 -= nti[t][j] * weighted_exp_num / weighted_exp_den * grad_mu_hat_prime_t[i];
}
tmp_grad_h_hat_prime_s[s][i] += g2;
}
// fourth term (if any)
if (s == t) for (int i = 0; i < n; i++) {
double g4 = -h_hat_prime_t[i][0] / (sigma*sigma);
tmp_grad_h_hat_prime_s[s][i] += g4;
}
}
*/
}
}
/* update global gradient */
for (int t = 0; t < T - t0; t++) {
double[][] grad = new double[n][K];
for (int i = 0; i < n; i++)
for (int k = 0; k < K; k++) {
grad[i][k] = tmp_grad_h_hat_prime_s[t][i][k];
}
grad_h_hat_prime_s.set(t, grad);
}
FileParser.output_2d(grad_h_hat_prime_s, "./grad/grad_prime_" + iteration + ".txt");
return;
}
public static void compute_gradient1(int iteration) {
double[][][] tmp_grad_h_hat_s = new double[T - t0][n][K];
for (int t = 0; t < T - t0; t++) {
// System.out.println("compute gradient 1, t = " + t);
double delta_t = delta_s.get(t);
double[][] G_t = GS.get(t);
double[][] h_prime_t = h_prime_s.get(t);
double[][] mu_hat_t = mu_hat_s.get(t);
if (t != 0) {
double[][] mu_hat_pre_t = mu_hat_s.get(t - 1);
Matrix a = new Matrix(AS.get(t - 1));
Matrix hprime_pre_t = new Matrix(h_prime_s.get(t - 1));
Matrix ave_neighbors = a.times(hprime_pre_t);
/* TODO: check whether we can save computation by comparing s and t */
for (int s = 0; s < T - t0; s++) {
double[][] grad_hat_t = grad_mu_hat_s.get(t * (T - t0) + s);
double[][] grad_hat_pre_t = grad_mu_hat_s.get((t - 1) * (T - t0) + s);
double[] hp2delta2 = new double[n];
for (int i = 0; i < n; i++)
for (int k = 0; k < K; k++) {
hp2delta2[i] += 0.5 * h_prime_t[i][k] * h_prime_t[i][k] * delta_t * delta_t;
}
for (int i = 0; i < n; i++) {
/* first term */
double[] weighted_exp_num = new double[K];
double weighted_exp_den = 0;
for (int l = 0; l < n; l++) {
double hp_muh = Operations.inner_product(h_prime_t[l], mu_hat_t[i], K);
double e = Math.exp(hp_muh + hp2delta2[l]);
if (Double.isNaN(e)) {
/* check if e explodes */
System.out.println("ERROR2");
Scanner sc = new Scanner(System.in);
int gu;
gu = sc.nextInt();
}
for (int k = 0; k < K; k++) {
weighted_exp_num[k] += h_prime_t[l][k] * e;
weighted_exp_den += e;
}
}
for (int j = 0; j < n; j++)
for (int k = 0; k < K; k++) {
double weighted_exp = weighted_exp_num[k] / weighted_exp_den;
double gi1 = G_t[i][j] * grad_hat_t[i][k] * (h_prime_t[j][k] - weighted_exp);
tmp_grad_h_hat_s[s][i][k] += gi1;
}
/* second term */
for (int k = 0; k < K; k++) {
double gi2 =
-(mu_hat_t[i][k]
- (1 - lambda) * mu_hat_pre_t[i][k]
- lambda * ave_neighbors.get(i, k))
* (grad_hat_t[i][k] - (1 - lambda) * grad_hat_pre_t[i][k])
/ (sigma * sigma);
tmp_grad_h_hat_s[s][i][k] += gi2;
}
}
}
} else {
/* no such term (t=0) in ELBO */
/*
for (int s = 0; s < T-t0; s++) {
double[] grad_hat_t = grad_mu_hat_s.get(t * (T-t0) + s);
for (int i = 0; i < n; i++) {
double n_it = 0;
for (int j = 0; j < n; j++) n_it += G_t[i][j];
// first term
double gi1 = -mu_hat_t[i] * grad_hat_t[i] / (sigma * sigma);
tmp_grad_h_hat_s[s][i] += gi1;
// second term
double gi2 = 0;
double weighted_exp_num = 0, weighted_exp_den = 0;
for (int j = 0; j < NEG; j++) {
int l = neg_samples.get(t)[i][j];
double hpl = h_prime_t[l][0];
double muit = mu_hat_t[i];
double e = Math.exp(hpl * muit + 0.5 * hpl * hpl * delta_t * delta_t);
// TODO: check if e explodes
if (Double.isNaN(e)) {
System.out.println("ERROR3");
Scanner sc = new Scanner(System.in);
int gu; gu = sc.nextInt();
}
weighted_exp_num += hpl * e;
weighted_exp_den += e;
}
double weighted_exp = weighted_exp_num / weighted_exp_den;
for (int j = 0; j < n; j++) {
gi2 += G_t[i][j] * grad_hat_t[i] * (h_prime_t[j][0] - weighted_exp);
}
tmp_grad_h_hat_s[s][i] += gi2;
}
}
*/
}
/* end if-else */
}
/* update global gradient */
for (int t = 0; t < T - t0; t++) {
double[][] grad = new double[n][K];
for (int i = 0; i < n; i++)
for (int k = 0; k < K; k++) {
grad[i][k] = tmp_grad_h_hat_s[t][i][k];
}
grad_h_hat_s.set(t, grad);
}
FileParser.output_2d(grad_h_hat_s, "./grad/grad_" + iteration + ".txt");
return;
}
/** compute_objective2: return the lower bound when h is fixed */
public static double compute_objective2() {
double res = 0;
for (int t = 0; t < T - t0; t++) {
if (t != 0) {
double[][] G_t = GS.get(t);
double[][] G_t_pre = GS.get(t - 1);
double[][] h_t = h_s.get(t);
double[][] h_pre_t = h_s.get(t - 1);
double[][] mu_hat_prime_t = mu_hat_prime_s.get(t);
double[][] mu_hat_prime_pre_t = mu_hat_prime_s.get(t - 1);
double delta_t = delta_s.get(t);
double[][] a_pre = AS.get(t - 1);
double[][] ave_neighbors = new double[n][K];
for (int i = 0; i < n; i++)
for (int j = 0; j < n; j++)
if (G_t_pre[i][j] != 0) {
for (int k = 0; k < K; k++) {
ave_neighbors[i][k] += a_pre[i][j] * mu_hat_prime_pre_t[j][k];
}
}
for (int i = 0; i < n; i++) {
/* first term */
double h2delta2 = 0;
for (int k = 0; k < K; k++) {
h2delta2 += 0.5 * h_t[i][k] * h_t[i][k] * delta_t * delta_t;
}
List<Double> powers = new ArrayList<Double>();
for (int l = 0; l < n; l++) {
double h_muhp = Operations.inner_product(h_t[i], mu_hat_prime_t[l], K);
powers.add(h_muhp + h2delta2);
}
double lse = log_sum_exp(powers);
for (int j = 0; j < n; j++)
if (G_t[i][j] != 0) {
double h_muhp = Operations.inner_product(h_t[i], mu_hat_prime_t[j], K);
res += G_t[i][j] * (h_muhp - lse);
}
/* second term */
for (int k = 0; k < K; k++) {
double diff = h_t[i][k] - (1 - lambda) * h_pre_t[i][k] - lambda * ave_neighbors[i][k];
res -= 0.5 * diff * diff / (sigma * sigma);
}
/* third term */
for (int k = 0; k < K; k++) {
double diff_3 = mu_hat_prime_t[i][k] - mu_hat_prime_pre_t[i][k];
res -= 0.5 * diff_3 * diff_3 / (sigma * sigma);
}
}
} else {
/*
double[][] G_t = GS.get(t);
double[][] h_t = h_s.get(t);
double[] mu_hat_prime_t = mu_hat_prime_s.get(t);
double delta_t = delta_s.get(t);
int[][] neg_sam_t = neg_samples.get(t);
for (int i = 0; i < n; i++) {
// first term
for (int j = 0; j < n; j++) if (G_t[i][j] != 0) {
List<Double> powers = new ArrayList<Double>();
for (int _l = 0; _l < NEG; _l++) {
int l = neg_sam_t[i][_l];
powers.add(h_t[i][0] * mu_hat_prime_t[l]
+ 0.5 * h_t[i][0] * h_t[i][0] * delta_t * delta_t);
}
double lse = log_sum_exp(powers);
res += G_t[i][j] * (h_t[i][0] * mu_hat_prime_t[j] - lse);
}
}
*/
}
}
return res;
}
/** compute_objective1: return the lower bound when h' is fixed */
public static double compute_objective1() {
double res = 0;
for (int t = 0; t < T - t0; t++) {
if (t != 0) {
double[][] G_t = GS.get(t);
double[][] h_prime_t = h_prime_s.get(t);
double[][] h_prime_pre_t = h_prime_s.get(t - 1);
double[][] mu_hat_t = mu_hat_s.get(t);
double[][] mu_hat_pre_t = mu_hat_s.get(t - 1);
double delta_t = delta_s.get(t);
Matrix a = new Matrix(AS.get(t - 1));
Matrix hprime_pre_t = new Matrix(h_prime_s.get(t - 1));
Matrix ave_neighbors = a.times(hprime_pre_t);
double[] hp2delta2 = new double[n];
for (int i = 0; i < n; i++)
for (int k = 0; k < K; k++) {
hp2delta2[i] += 0.5 * h_prime_t[i][k] * h_prime_t[i][k] * delta_t * delta_t;
}
for (int i = 0; i < n; i++) {
/* first term */
List<Double> powers = new ArrayList<Double>();
for (int l = 0; l < n; l++) {
double hp_muh = Operations.inner_product(h_prime_t[l], mu_hat_t[i], K);
powers.add(hp_muh + hp2delta2[l]);
}
double lse = log_sum_exp(powers);
for (int j = 0; j < n; j++)
if (G_t[i][j] != 0) {
double hp_muh = Operations.inner_product(h_prime_t[j], mu_hat_t[i], K);
res += G_t[i][j] * (hp_muh - lse);
}
/* second term */
for (int k = 0; k < K; k++) {
double diff =
mu_hat_t[i][k]
- (1 - lambda) * mu_hat_pre_t[i][k]
- lambda * ave_neighbors.get(i, k);
res -= 0.5 * diff * diff / (sigma * sigma);
}
}
} else {
/*
double[][] G_t = GS.get(t);
double[][] h_prime_t = h_prime_s.get(t);
double[] mu_hat_t = mu_hat_s.get(t);
double delta_t = delta_s.get(t);
int[][] neg_sam_t = neg_samples.get(t);
for (int i = 0; i < n; i++) {
// first term
for (int j = 0; j < n; j++) if (G_t[i][j] != 0) {
List<Double> powers = new ArrayList<Double>();
for (int _l = 0; _l < NEG; _l++) {
int l = neg_sam_t[i][_l];
powers.add(h_prime_t[l][0] * mu_hat_t[i]
+ 0.5 * h_prime_t[l][0] * h_prime_t[l][0] * delta_t * delta_t);
}
double lse = log_sum_exp(powers);
res += G_t[i][j] * (h_prime_t[j][0] * mu_hat_t[i] - lse);
}
}
*/
}
}
return res;
}