Optimize global sigma.

[wloh] / bayeswf.cpp

diff --git a/bayeswf.cpp b/bayeswf.cpp
index f518edd7ca2987f9ae3c6551be9a0deaa1613706..48d52325620c0542b4f61553e2d0d075d906371c 100644 (file)
--- a/bayeswf.cpp
+++ b/bayeswf.cpp
@@ -112,6 +112,42 @@ void update_sigma(float *mu, float *sigma, int player_num, const vector<match> &
        sigma[player_num] = sqrt(sum / matches.size());
 }
 
+/*
+ * diff(logL, 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_global_sigma(float *mu, float *sigma, int num_players)
+{
+       float nom = 0.0f, denom = 0.0f;
+       for (int i = 0; i < num_players; ++i) {
+               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];
+                       float mu2 = mu[m.other_player];
+                       float mu = mu1 - mu2;
+                       float x = m.margin;
+                       float w = m.weight;
+
+                       nom += w * ((x - mu) * (x - mu));
+                       denom += w;
+               }
+       }
+
+       float best_sigma = sqrt(nom / denom) / sqrt(2.0f);  // Divide evenly between the two players.
+       for (int i = 0; i < num_players; ++i) {
+               sigma[i] = best_sigma;
+       }
+}
+
 void renormalize(float *mu, float *sigma, int num_players)
 {
        float avg = 0.0f;
@@ -247,6 +283,7 @@ int main(int argc, char **argv)
                        update_mu(mu, sigma, i, matches_for_player[i]);
                        renormalize(mu, sigma, num_players);
                }
+               update_global_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);
@@ -263,6 +300,7 @@ int main(int argc, char **argv)
                }
        }
        dump_scores(players, mu, sigma, num_players);
+       fprintf(stderr, "Optimal sigma: %f (two-player: %f)\n", sigma[0], sigma[0] * sqrt(2.0f));
 
 //     construct_fim(mu, sigma, num_players);
 }