git.sesse.net Git - wloh/blob - bayeswf.cpp

   1 #include <stdio.h>
   2 #include <math.h>
   3 #include <string.h>
   4 #include <stdlib.h>
   5
   6 #include <map>
   7 #include <vector>
   8 #include <string>
   9 #include <algorithm>
  10
  11 using namespace std;
  12
  13 #define MAX_PLAYERS 4096
  14
  15 float mu[MAX_PLAYERS];
  16 float sigma[MAX_PLAYERS];
  17
  18 #define EPSILON 1e-3
  19
  20 /*
  21  * L(mu_vec, sigma_vec, matches) = product[ L(mu_A, sigma_A, mu_B, sigma_B, score_AB - score_BA) ]
  22  * log-likelihood = sum[ log( L(mu_A, sigma_A, mu_B, sigma_B, score_AB - score_BA) ) ]
  23  *
  24  * L(mu1, sigma1, mu2, sigma2, score2 - score1) = sigmoid(mu2 - mu1, sqrt(sigma1² + sigma2²), (score2 - score1))
  25  *
  26  * pdf := 1/(sigma * sqrt(2*Pi)) * exp(-(x - mu)^2 / (2 * sigma^2));
  27  * pdfs := subs({ mu = mu1 - mu2, sigma = sqrt(sigma1^2 + sigma2^2) }, pdf);
  28  * diff(log(pdfs), mu1);
  29  */
  30
  31 struct match {
  32         int other_player;
  33         int margin;
  34         float weight;
  35 };
  36 map<int, vector<match> > matches_for_player;
  37
  38 void dump_scores(const vector<string> &players, const float *mu, const float *sigma, int num_players)
  39 {
  40 #if 0
  41         for (int i = 0; i < num_players; ++i) {
  42                 printf("%s=[%5.1f, %4.1f] ", players[i].c_str(), mu[i], sigma[i]);
  43         }
  44         printf("\n");
  45 #elif 0
  46         for (int i = 0; i < num_players; ++i) {
  47                 printf("%5.1f ", mu[i]);
  48         }
  49         printf("\n");
  50 #else
  51         for (int i = 0; i < num_players; ++i) {
  52                 printf("%5.1f %s\n", mu[i], players[i].c_str());
  53         }
  54         printf("\n");
  55 #endif
  56 }
  57
  58 /*
  59  * diff(logL, mu1) = -w * (mu1 - mu2 - x) / sigma_c^2
  60  * maximizer for mu1 is given by: sum_i[ (w_i/sigma_c_i)^2 (mu1 - mu2_i - x_i) ] = 0
  61  *                                sum_i[ (w_i/sigma_c_i)^2 mu1 ] = sum_i [ (w_i/sigma_c_i)^2 ( mu2_i + x_i ) ]
  62  *                                mu1 = sum_i [ (w_i/sigma_c_i)^2 ( mu2_i + x_i ) ] / sum_i[ (w_i/sigma_c_i)^2 ]
  63  */
  64 void update_mu(float *mu, float *sigma, int player_num, const vector<match> &matches)
  65 {
  66         if (matches.empty()) {
  67                 return;
  68         }
  69
  70         float nom = 0.0f, denom = 0.0f;
  71         for (unsigned i = 0; i < matches.size(); ++i) {
  72                 float sigma1 = sigma[player_num];
  73                 float sigma2 = sigma[matches[i].other_player];
  74                 float inv_sigma_c2 = matches[i].weight / (sigma1 * sigma1 + sigma2 * sigma2);
  75                 float x = matches[i].margin; // / 70.0f;
  76
  77                 nom += (mu[matches[i].other_player] + x) * inv_sigma_c2;
  78                 denom += inv_sigma_c2;
  79         }
  80         mu[player_num] = nom / denom;
  81 }
  82
  83 /*
  84  * diff(logL, sigma1) = sigma1 (-sigma1² - sigma2² + (x - mu)²) / sigma_c²
  85  * maximizer for sigma1 is given by: sum_i[ (1/sigma_c_i)² sigma1 ((x - mu)² - (sigma1² + sigma2²) ] = 0
  86  *                                   sum_i[ (x - mu)² - sigma1² - sigma2² ] = 0                                  |: sigma1 != 0, sigma2 != 0
  87  *                                   sum_i[ (x - mu)² - sigma2² ] = sum[ sigma1² ]
  88  *                                   sigma1 = sqrt( sum_i[ (x - mu)² - sigma2² ] / N )
  89  */
  90 void update_sigma(float *mu, float *sigma, int player_num, const vector<match> &matches)
  91 {
  92         if (matches.size() < 2) {
  93                 return;
  94         }
  95
  96         float sum = 0.0f;
  97         for (unsigned i = 0; i < matches.size(); ++i) {
  98                 float mu1 = mu[player_num];
  99                 float mu2 = mu[matches[i].other_player];
 100                 float mu = mu1 - mu2;
 101                 float sigma2 = sigma[matches[i].other_player];
 102                 float x = matches[i].margin;
 103
 104                 //fprintf(stderr, "x=%f mu=%f sigma2=%f   add %f-%f = %f\n", x, mu, sigma2, (x-mu)*(x-mu), sigma2*sigma2, (x - mu) * (x - mu) - sigma2 * sigma2);
 105                 sum += (x - mu) * (x - mu) - sigma2 * sigma2;
 106         }
 107
 108         if (sum <= 0) {
 109                 return;
 110         }
 111         //fprintf(stderr, "sum=%f\n", sum);
 112         sigma[player_num] = sqrt(sum / matches.size());
 113 }
 114
 115 /*
 116  * diff(logL, sigma) = w ( (x - mu)² - sigma² ) / sigma³
 117  * maximizer for sigma is given by: sum_i[ (w_i/sigma)³ ((x - mu)² - sigma²) ] = 0
 118  *                                   sum_i[ w_i ( (x - mu)² - sigma² ) ] = 0                            |: sigma != 0
 119  *                                   sum_i[ w_i (x - mu)² ] = sum[ w_i sigma² ]
 120  *                                   sigma = sqrt( sum_i[ w_i (x - mu)² ] / sum[w_i] )
 121  */
 122 void update_global_sigma(float *mu, float *sigma, int num_players)
 123 {
 124         float nom = 0.0f, denom = 0.0f;
 125         for (int i = 0; i < num_players; ++i) {
 126                 for (unsigned j = 0; j < matches_for_player[i].size(); ++j) {
 127                         const match& m = matches_for_player[i][j];
 128
 129                         // Only count each match once.
 130                         if (m.other_player <= i) {
 131                                 continue;
 132                         }
 133
 134                         float mu1 = mu[i];
 135                         float mu2 = mu[m.other_player];
 136                         float mu = mu1 - mu2;
 137                         float x = m.margin;
 138                         float w = m.weight;
 139
 140                         nom += w * ((x - mu) * (x - mu));
 141                         denom += w;
 142                 }
 143         }
 144
 145         float best_sigma = sqrt(nom / denom) / sqrt(2.0f);  // Divide evenly between the two players.
 146         for (int i = 0; i < num_players; ++i) {
 147                 sigma[i] = best_sigma;
 148         }
 149 }
 150
 151 void renormalize(float *mu, float *sigma, int num_players)
 152 {
 153         float avg = 0.0f;
 154         for (int i = 0; i < num_players; ++i) {
 155                 avg += mu[i];
 156         }
 157         float corr = 1500.0f - avg / num_players;
 158         for (int i = 0; i < num_players; ++i) {
 159                 mu[i] += corr;
 160         }
 161 }
 162
 163 /*
 164  * Compute Hessian matrix of the negative log-likelihood, ie. for each term in logL:
 165  *
 166  * M_ij = D_i D_j (- logL) = -1 / sigma²                                for i != j
 167  *                            1 / sigma²                                for i == j
 168  *
 169  * Note that this does not depend on mu or the margin at all.
 170  */
 171 double hessian[MAX_PLAYERS][MAX_PLAYERS];
 172 void construct_hessian(const float *mu, const float *sigma, int num_players)
 173 {
 174         memset(hessian, 0, sizeof(hessian));
 175
 176         for (int i = 0; i < num_players; ++i) {
 177                 double sigma1 = sigma[i];
 178
 179                 for (unsigned k = 0; k < matches_for_player[i].size(); ++k) {
 180                         int j = matches_for_player[i][k].other_player;
 181
 182                         double sigma2 = sigma[j];
 183                         double sigma_sq = sigma1 * sigma1 + sigma2 * sigma2;
 184
 185                         hessian[i][j] -= 1.0f / sigma_sq;
 186                         hessian[i][i] += 1.0f / sigma_sq;
 187                 }
 188         }
 189
 190         for (int i = 0; i < num_players; ++i) {
 191                 for (int j = 0; j < num_players; ++j) {
 192                         printf("%.12f ", hessian[i][j]);
 193                 }
 194                 printf("\n");
 195         }
 196 }
 197
 198 int main(int argc, char **argv)
 199 {
 200         int num_players;
 201         if (scanf("%d", &num_players) != 1) {
 202                 fprintf(stderr, "Could't read number of players\n");
 203                 exit(1);
 204         }
 205
 206         if (num_players > MAX_PLAYERS) {
 207                 fprintf(stderr, "Max %d players supported\n", MAX_PLAYERS);
 208                 exit(1);
 209         }
 210
 211         vector<string> players;
 212         map<string, int> player_map;
 213
 214         for (int i = 0; i < num_players; ++i) {
 215                 char buf[256];
 216                 if (scanf("%s", buf) != 1) {
 217                         fprintf(stderr, "Couldn't read player %d\n", i);
 218                         exit(1);
 219                 }
 220
 221                 players.push_back(buf);
 222                 player_map[buf] = i;
 223         }
 224
 225         int num_matches = 0;
 226         for ( ;; ) {
 227                 char pl1[256], pl2[256];
 228                 int score1, score2;
 229                 float weight;
 230
 231                 if (scanf("%s %s %d %d %f", pl1, pl2, &score1, &score2, &weight) != 5) {
 232                         fprintf(stderr, "Read %d matches.\n", num_matches);
 233                         break;
 234                 }
 235
 236                 ++num_matches;
 237
 238                 if (player_map.count(pl1) == 0) {
 239                         fprintf(stderr, "Unknown player '%s'\n", pl1);
 240                         exit(1);
 241                 }
 242                 if (player_map.count(pl2) == 0) {
 243                         fprintf(stderr, "Unknown player '%s'\n", pl2);
 244                         exit(1);
 245                 }
 246
 247                 match m1;
 248                 m1.other_player = player_map[pl2];
 249                 m1.margin = score1 - score2;
 250                 m1.weight = weight;
 251                 matches_for_player[player_map[pl1]].push_back(m1);
 252
 253                 match m2;
 254                 m2.other_player = player_map[pl1];
 255                 m2.margin = score2 - score1;
 256                 m2.weight = weight;
 257                 matches_for_player[player_map[pl2]].push_back(m2);
 258         }
 259
 260         float mu[MAX_PLAYERS];
 261         float sigma[MAX_PLAYERS];
 262
 263         for (int i = 0; i < num_players; ++i) {
 264                 mu[i] = 1500.0f;
 265                 sigma[i] = 70.0f / sqrt(2.0f);
 266         }
 267         renormalize(mu, sigma, num_players);
 268
 269         for (int j = 0; j < 1000; ++j) {
 270                 float old_mu[MAX_PLAYERS];
 271                 float old_sigma[MAX_PLAYERS];
 272                 memcpy(old_mu, mu, sizeof(mu));
 273                 memcpy(old_sigma, sigma, sizeof(sigma));
 274                 for (int i = 0; i < num_players; ++i) {
 275                         update_mu(mu, sigma, i, matches_for_player[i]);
 276                         renormalize(mu, sigma, num_players);
 277                 }
 278                 update_global_sigma(mu, sigma, num_players);
 279                 /* for (int i = 0; i < num_players; ++i) {
 280                         update_sigma(mu, sigma, i, matches_for_player[i]);
 281                         dump_scores(players, mu, sigma, num_players);
 282                 } */
 283
 284                 float sumdiff = 0.0f;
 285                 for (int i = 0; i < num_players; ++i) {
 286                         sumdiff += (mu[i] - old_mu[i]) * (mu[i] - old_mu[i]);
 287                         sumdiff += (sigma[i] - old_sigma[i]) * (sigma[i] - old_sigma[i]);
 288                 }
 289                 if (sumdiff < EPSILON) {
 290                         fprintf(stderr, "Converged after %d iterations. Stopping.\n", j);
 291                         break;
 292                 }
 293         }
 294         dump_scores(players, mu, sigma, num_players);
 295         fprintf(stderr, "Optimal sigma: %f (two-player: %f)\n", sigma[0], sigma[0] * sqrt(2.0f));
 296
 297         construct_hessian(mu, sigma, num_players);
 298 }