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("%f %s\n", mu[i], players[i].c_str());
  53         }
  54 #endif
  55 }
  56
  57 /*
  58  * diff(logL, mu1) = -w * (mu1 - mu2 - x) / sigma_c^2
  59  * maximizer for mu1 is given by: sum_i[ (w_i/sigma_c_i)^2 (mu1 - mu2_i - x_i) ] = 0
  60  *                                sum_i[ (w_i/sigma_c_i)^2 mu1 ] = sum_i [ (w_i/sigma_c_i)^2 ( mu2_i + x_i ) ]
  61  *                                mu1 = sum_i [ (w_i/sigma_c_i)^2 ( mu2_i + x_i ) ] / sum_i[ (w_i/sigma_c_i)^2 ]
  62  */
  63 void update_mu(float *mu, float *sigma, int player_num, const vector<match> &matches)
  64 {
  65         if (matches.empty()) {
  66                 return;
  67         }
  68
  69         float nom = 0.0f, denom = 0.0f;
  70         for (unsigned i = 0; i < matches.size(); ++i) {
  71                 float sigma1 = sigma[player_num];
  72                 float sigma2 = sigma[matches[i].other_player];
  73                 float inv_sigma_c2 = matches[i].weight / (sigma1 * sigma1 + sigma2 * sigma2);
  74                 float x = matches[i].margin; // / 70.0f;
  75
  76                 nom += (mu[matches[i].other_player] + x) * inv_sigma_c2;
  77                 denom += inv_sigma_c2;
  78         }
  79         mu[player_num] = nom / denom;
  80 }
  81
  82 /*
  83  * diff(logL, sigma1) = sigma1 (-sigma1² - sigma2² + (x - mu)²) / sigma_c²
  84  * maximizer for sigma1 is given by: sum_i[ (1/sigma_c_i)² sigma1 ((x - mu)² - (sigma1² + sigma2²) ] = 0
  85  *                                   sum_i[ (x - mu)² - sigma1² - sigma2² ] = 0                                  |: sigma1 != 0, sigma2 != 0
  86  *                                   sum_i[ (x - mu)² - sigma2² ] = sum[ sigma1² ]
  87  *                                   sigma1 = sqrt( sum_i[ (x - mu)² - sigma2² ] / N )
  88  */
  89 void update_sigma(float *mu, float *sigma, int player_num, const vector<match> &matches)
  90 {
  91         if (matches.size() < 2) {
  92                 return;
  93         }
  94
  95         float sum = 0.0f;
  96         for (unsigned i = 0; i < matches.size(); ++i) {
  97                 float mu1 = mu[player_num];
  98                 float mu2 = mu[matches[i].other_player];
  99                 float mu = mu1 - mu2;
 100                 float sigma2 = sigma[matches[i].other_player];
 101                 float x = matches[i].margin;
 102
 103                 //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);
 104                 sum += (x - mu) * (x - mu) - sigma2 * sigma2;
 105         }
 106
 107         if (sum <= 0) {
 108                 return;
 109         }
 110         //fprintf(stderr, "sum=%f\n", sum);
 111         sigma[player_num] = sqrt(sum / matches.size());
 112 }
 113
 114 /*
 115  * diff(logL, sigma) = w ( (x - mu)² - sigma² ) / sigma³
 116  * maximizer for sigma is given by: sum_i[ (w_i/sigma)³ ((x - mu)² - sigma²) ] = 0
 117  *                                   sum_i[ w_i ( (x - mu)² - sigma² ) ] = 0                            |: sigma != 0
 118  *                                   sum_i[ w_i (x - mu)² ] = sum[ w_i sigma² ]
 119  *                                   sigma = sqrt( sum_i[ w_i (x - mu)² ] / sum[w_i] )
 120  */
 121 void update_global_sigma(float *mu, float *sigma, int num_players)
 122 {
 123         float nom = 0.0f, denom = 0.0f;
 124         for (int i = 0; i < num_players; ++i) {
 125                 for (unsigned j = 0; j < matches_for_player[i].size(); ++j) {
 126                         const match& m = matches_for_player[i][j];
 127
 128                         // Only count each match once.
 129                         if (m.other_player <= i) {
 130                                 continue;
 131                         }
 132
 133                         float mu1 = mu[i];
 134                         float mu2 = mu[m.other_player];
 135                         float mu = mu1 - mu2;
 136                         float x = m.margin;
 137                         float w = m.weight;
 138
 139                         nom += w * ((x - mu) * (x - mu));
 140                         denom += w;
 141                 }
 142         }
 143
 144         float best_sigma = sqrt(nom / denom) / sqrt(2.0f);  // Divide evenly between the two players.
 145         for (int i = 0; i < num_players; ++i) {
 146                 sigma[i] = best_sigma;
 147         }
 148 }
 149
 150 void renormalize(float *mu, float *sigma, int num_players)
 151 {
 152         float avg = 0.0f;
 153         for (int i = 0; i < num_players; ++i) {
 154                 avg += mu[i];
 155         }
 156         float corr = 1500.0f - avg / num_players;
 157         for (int i = 0; i < num_players; ++i) {
 158                 mu[i] += corr;
 159         }
 160 }
 161
 162 /*
 163  * Compute Hessian matrix of the negative log-likelihood, ie. for each term in logL:
 164  *
 165  * M_ij = D_i D_j (- logL) = -w / sigma²                                for i != j
 166  *                            w / sigma²                                for i == j
 167  *
 168  * Note that this does not depend on mu or the margin at all.
 169  */
 170 double hessian[MAX_PLAYERS][MAX_PLAYERS];
 171 void construct_hessian(const float *mu, const float *sigma, int num_players)
 172 {
 173         memset(hessian, 0, sizeof(hessian));
 174
 175         for (int i = 0; i < num_players; ++i) {
 176                 double sigma1 = sigma[i];
 177
 178                 for (unsigned k = 0; k < matches_for_player[i].size(); ++k) {
 179                         int j = matches_for_player[i][k].other_player;
 180
 181                         double sigma2 = sigma[j];
 182                         double sigma_sq = sigma1 * sigma1 + sigma2 * sigma2;
 183
 184                         float w = matches_for_player[i][k].weight;
 185
 186                         hessian[i][j] -= w / sigma_sq;
 187                         hessian[i][i] += w / sigma_sq;
 188                 }
 189         }
 190
 191         for (int i = 0; i < num_players; ++i) {
 192                 for (int j = 0; j < num_players; ++j) {
 193                         printf("%.12f ", hessian[i][j]);
 194                 }
 195                 printf("\n");
 196         }
 197 }
 198
 199 int main(int argc, char **argv)
 200 {
 201         int num_players;
 202         if (scanf("%d", &num_players) != 1) {
 203                 fprintf(stderr, "Could't read number of players\n");
 204                 exit(1);
 205         }
 206
 207         if (num_players > MAX_PLAYERS) {
 208                 fprintf(stderr, "Max %d players supported\n", MAX_PLAYERS);
 209                 exit(1);
 210         }
 211
 212         vector<string> players;
 213         map<string, int> player_map;
 214
 215         for (int i = 0; i < num_players; ++i) {
 216                 char buf[256];
 217                 if (scanf("%s", buf) != 1) {
 218                         fprintf(stderr, "Couldn't read player %d\n", i);
 219                         exit(1);
 220                 }
 221
 222                 players.push_back(buf);
 223                 player_map[buf] = i;
 224         }
 225
 226         int num_matches = 0;
 227         for ( ;; ) {
 228                 char pl1[256], pl2[256];
 229                 int score1, score2;
 230                 float weight;
 231
 232                 if (scanf("%s %s %d %d %f", pl1, pl2, &score1, &score2, &weight) != 5) {
 233                         //fprintf(stderr, "Read %d matches.\n", num_matches);
 234                         break;
 235                 }
 236
 237                 ++num_matches;
 238
 239                 if (player_map.count(pl1) == 0) {
 240                         fprintf(stderr, "Unknown player '%s'\n", pl1);
 241                         exit(1);
 242                 }
 243                 if (player_map.count(pl2) == 0) {
 244                         fprintf(stderr, "Unknown player '%s'\n", pl2);
 245                         exit(1);
 246                 }
 247
 248                 match m1;
 249                 m1.other_player = player_map[pl2];
 250                 m1.margin = score1 - score2;
 251                 m1.weight = weight;
 252                 matches_for_player[player_map[pl1]].push_back(m1);
 253
 254                 match m2;
 255                 m2.other_player = player_map[pl1];
 256                 m2.margin = score2 - score1;
 257                 m2.weight = weight;
 258                 matches_for_player[player_map[pl2]].push_back(m2);
 259         }
 260
 261         float mu[MAX_PLAYERS];
 262         float sigma[MAX_PLAYERS];
 263
 264         for (int i = 0; i < num_players; ++i) {
 265                 mu[i] = 1500.0f;
 266                 sigma[i] = 70.0f / sqrt(2.0f);
 267         }
 268         renormalize(mu, sigma, num_players);
 269
 270         for (int j = 0; j < 1000; ++j) {
 271                 float old_mu[MAX_PLAYERS];
 272                 float old_sigma[MAX_PLAYERS];
 273                 memcpy(old_mu, mu, sizeof(mu));
 274                 memcpy(old_sigma, sigma, sizeof(sigma));
 275                 for (int i = 0; i < num_players; ++i) {
 276                         update_mu(mu, sigma, i, matches_for_player[i]);
 277                         renormalize(mu, sigma, num_players);
 278                 }
 279                 update_global_sigma(mu, sigma, num_players);
 280                 /* for (int i = 0; i < num_players; ++i) {
 281                         update_sigma(mu, sigma, i, matches_for_player[i]);
 282                         dump_scores(players, mu, sigma, num_players);
 283                 } */
 284
 285                 float sumdiff = 0.0f;
 286                 for (int i = 0; i < num_players; ++i) {
 287                         sumdiff += (mu[i] - old_mu[i]) * (mu[i] - old_mu[i]);
 288                         sumdiff += (sigma[i] - old_sigma[i]) * (sigma[i] - old_sigma[i]);
 289                 }
 290                 if (sumdiff < EPSILON) {
 291                         //fprintf(stderr, "Converged after %d iterations. Stopping.\n", j);
 292                         printf("%d -1\n", j + 1);
 293                         break;
 294                 }
 295         }
 296         dump_scores(players, mu, sigma, num_players);
 297         //fprintf(stderr, "Optimal sigma: %f (two-player: %f)\n", sigma[0], sigma[0] * sqrt(2.0f));
 298         printf("%f -2\n", sigma[0]);
 299
 300 //      construct_hessian(mu, sigma, num_players);
 301 }