using namespace std;
#define PRIOR_MU 1500
-#define PRIOR_SIGMA 100
#define MAX_PLAYERS 4096
float mu[MAX_PLAYERS];
float sigma[MAX_PLAYERS];
+float prior_sigma = 70.0f;
#define EPSILON 1e-3
// Prior.
{
- float inv_sigma2 = 1.0f / (PRIOR_SIGMA * PRIOR_SIGMA);
+ float inv_sigma2 = 1.0f / (prior_sigma * prior_sigma);
nom += PRIOR_MU * inv_sigma2;
denom += inv_sigma2;
}
}
}
-void renormalize(float *mu, float *sigma, int num_players)
+/*
+ * diff(priorlogL, sigma) = w ( (x - mu)² - sigma² ) / sigma³
+ * maximizer for sigma is given by: sum_i[ (w_i/sigma)³ ((x - mu)² - sigma²) ] = 0
+ * sum_i[ w_i ( (x - mu)² - sigma² ) ] = 0 |: sigma != 0
+ * sum_i[ w_i (x - mu)² ] = sum[ w_i sigma² ]
+ * sigma = sqrt( sum_i[ w_i (x - mu)² ] / sum[w_i] )
+ */
+void update_prior_sigma(float *mu, float *sigma, int num_players)
{
- float avg = 0.0f;
- for (int i = 0; i < num_players; ++i) {
- avg += mu[i];
- }
- float corr = 1500.0f - avg / num_players;
+ float nom = 0.0f, denom = 0.0f;
for (int i = 0; i < num_players; ++i) {
- mu[i] += corr;
+ for (unsigned j = 0; j < matches_for_player[i].size(); ++j) {
+ const match& m = matches_for_player[i][j];
+
+ // Only count each match once.
+ if (m.other_player <= i) {
+ continue;
+ }
+
+ float mu1 = mu[i];
+
+ nom += ((mu1 - PRIOR_MU) * (mu1 - PRIOR_MU));
+ denom += 1.0f;
+ }
}
+
+ prior_sigma = sqrt(nom / denom);
}
/*
mu[i] = 1500.0f;
sigma[i] = 70.0f / sqrt(2.0f);
}
- renormalize(mu, sigma, num_players);
for (int j = 0; j < 1000; ++j) {
float old_mu[MAX_PLAYERS];
float old_sigma[MAX_PLAYERS];
+ float old_prior_sigma = prior_sigma;
memcpy(old_mu, mu, sizeof(mu));
memcpy(old_sigma, sigma, sizeof(sigma));
for (int i = 0; i < num_players; ++i) {
update_mu(mu, sigma, i, matches_for_player[i]);
- renormalize(mu, sigma, num_players);
}
update_global_sigma(mu, sigma, num_players);
+ update_prior_sigma(mu, sigma, num_players);
/* for (int i = 0; i < num_players; ++i) {
update_sigma(mu, sigma, i, matches_for_player[i]);
dump_scores(players, mu, sigma, num_players);
sumdiff += (mu[i] - old_mu[i]) * (mu[i] - old_mu[i]);
sumdiff += (sigma[i] - old_sigma[i]) * (sigma[i] - old_sigma[i]);
}
+ sumdiff += (prior_sigma - old_prior_sigma) * (prior_sigma - old_prior_sigma);
if (sumdiff < EPSILON) {
//fprintf(stderr, "Converged after %d iterations. Stopping.\n", j);
printf("%d -1\n", j + 1);
dump_scores(players, mu, sigma, num_players);
//fprintf(stderr, "Optimal sigma: %f (two-player: %f)\n", sigma[0], sigma[0] * sqrt(2.0f));
printf("%f -2\n", sigma[0]);
+ printf("%f -3\n", prior_sigma);
// construct_hessian(mu, sigma, num_players);
}