From: Steinar H. Gunderson <Steinar H. Gunderson sesse@debian.org>
Date: Sat, 17 Mar 2012 00:12:59 +0000 (+0100)
Subject: Optimize global sigma.
X-Git-Url: https://git.sesse.net/?a=commitdiff_plain;h=b48d3244dd4ed5f61e4e1e1d21bca88e918ccff9;p=wloh

Optimize global sigma.
---

diff --git a/bayeswf.cpp b/bayeswf.cpp
index f518edd..48d5232 100644
--- 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);
 }