te')); return $arr; } /* 遍历用户所有主题 * @param $uid 用户ID * @param int $page 页数 * @param int $pagesize 每页记录条数 * @param bool $desc 排序方式 TRUE降序 FALSE升序 * @param string $key 返回的数组用那一列的值作为 key * @param array $col 查询哪些列 */ function thread_tid_find_by_uid($uid, $page = 1, $pagesize = 1000, $desc = TRUE, $key = 'tid', $col = array()) { if (empty($uid)) return array(); $orderby = TRUE == $desc ? -1 : 1; $arr = thread_tid__find($cond = array('uid' => $uid), array('tid' => $orderby), $page, $pagesize, $key, $col); return $arr; } // 遍历栏目下tid 支持数组 $fid = array(1,2,3) function thread_tid_find_by_fid($fid, $page = 1, $pagesize = 1000, $desc = TRUE) { if (empty($fid)) return array(); $orderby = TRUE == $desc ? -1 : 1; $arr = thread_tid__find($cond = array('fid' => $fid), array('tid' => $orderby), $page, $pagesize, 'tid', array('tid', 'verify_date')); return $arr; } function thread_tid_delete($tid) { if (empty($tid)) return FALSE; $r = thread_tid__delete(array('tid' => $tid)); return $r; } function thread_tid_count() { $n = thread_tid__count(); return $n; } // 统计用户主题数 大数量下严谨使用非主键统计 function thread_uid_count($uid) { $n = thread_tid__count(array('uid' => $uid)); return $n; } // 统计栏目主题数 大数量下严谨使用非主键统计 function thread_fid_count($fid) { $n = thread_tid__count(array('fid' => $fid)); return $n; } ?>c# - Trueskill with teams in Infer.Net - Stack Overflow
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c# - Trueskill with teams in Infer.Net - Stack Overflow

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I'm trying to build trueskill model with two teams and 5 players each with Infer.Net. However when inferring the skills the means of the distribution get way too big or small.

Below is code of my implementation with made up players and matches that replicates the problem. Even though I'm using made up players and matches here I get similar results with data from the real world.

using Microsoft.ML.Probabilistic.Distributions;
using Microsoft.ML.Probabilistic.Factors;
using Microsoft.ML.Probabilistic.Models;
using Microsoft.ML.Probabilistic.Collections;
using Microsoft.Data.Analysis;
using System;
using System.Collections.Generic;
using System.Linq;
using System.Numerics;
using System.Text;
using System.Threading.Tasks;
using System.Collections;
using System.Security.Cryptography;
using System.IO;
using System.Security.Policy;
using System.Reflection;

namespace ConsoleApp3
{
    internal class infernetDemo5
    {
        static void Main(string[] args)
        {

            int[][] winnerData = { 
                new[] { 0, 1, 2, 3, 4 }, 
                new[] { 0, 1, 2, 3, 5 }, 
                new[] { 5, 6, 7, 8, 9 }, 
                new[] { 5, 6, 7, 8, 9 },
                new[] { 0, 1, 2, 3, 4 },
                new[] { 0, 1, 2, 3, 5 },
                new[] { 5, 6, 7, 8, 9 },
                new[] { 5, 6, 7, 8, 9 },
                new[] { 0, 1, 2, 3, 4 },
                new[] { 0, 1, 2, 3, 5 },
                new[] { 5, 6, 7, 8, 9 },
                new[] { 5, 6, 7, 8, 9 },
                new[] { 0, 1, 2, 3, 4 },
                new[] { 0, 1, 2, 3, 5 },
                new[] { 5, 6, 7, 8, 9 },
                new[] { 5, 6, 7, 8, 9 },
                new[] { 0, 1, 2, 3, 4 },
                new[] { 0, 1, 2, 3, 5 },
                new[] { 5, 6, 7, 8, 9 },
                new[] { 5, 6, 7, 8, 9 },
                new[] { 0, 1, 2, 3, 4 },
                new[] { 0, 1, 2, 3, 5 },
                new[] { 5, 6, 7, 8, 9 },
                new[] { 5, 6, 7, 8, 9 },
                new[] { 0, 1, 2, 3, 4 },
                new[] { 0, 1, 2, 3, 5 },
                new[] { 5, 6, 7, 8, 9 },
                new[] { 5, 6, 7, 8, 9 },
                new[] { 0, 1, 2, 3, 4 },
                new[] { 0, 1, 2, 3, 5 },
                new[] { 5, 6, 7, 8, 9 },
                new[] { 5, 6, 7, 8, 9 },
            };
            int[][] loserData = { 
                new[] { 5, 6, 7, 8, 9 }, 
                new[] { 6, 7, 8, 9, 4 }, 
                new[] { 0, 1, 2, 3, 4 }, 
                new[] { 0, 1, 2, 3, 4 },
                new[] { 5, 6, 7, 8, 9 },
                new[] { 6, 7, 8, 9, 4 },
                new[] { 0, 1, 2, 3, 4 },
                new[] { 0, 1, 2, 3, 4 },
                new[] { 5, 6, 7, 8, 9 }, 
                new[] { 6, 7, 8, 9, 4 }, 
                new[] { 0, 1, 2, 3, 4 }, 
                new[] { 0, 1, 2, 3, 4 },
                new[] { 5, 6, 7, 8, 9 },
                new[] { 6, 7, 8, 9, 4 },
                new[] { 0, 1, 2, 3, 4 },
                new[] { 0, 1, 2, 3, 4 },
                new[] { 5, 6, 7, 8, 9 },
                new[] { 6, 7, 8, 9, 4 },
                new[] { 0, 1, 2, 3, 4 },
                new[] { 0, 1, 2, 3, 4 },
                new[] { 5, 6, 7, 8, 9 },
                new[] { 6, 7, 8, 9, 4 },
                new[] { 0, 1, 2, 3, 4 },
                new[] { 0, 1, 2, 3, 4 },
                new[] { 5, 6, 7, 8, 9 },
                new[] { 6, 7, 8, 9, 4 },
                new[] { 0, 1, 2, 3, 4 },
                new[] { 0, 1, 2, 3, 4 },
                new[] { 5, 6, 7, 8, 9 },
                new[] { 6, 7, 8, 9, 4 },
                new[] { 0, 1, 2, 3, 4 },
                new[] { 0, 1, 2, 3, 4 },
            };

            var nGames = 32;
            var nPlayers = 10;
            var mu = 25.0;
            var sigma = 8.333;
            var beta = 4.1667;


            var teamSize = new Range(5).Named("TeamSize");
            var games = new Range(nGames).Named("Game");
            var players = new Range(nPlayers).Named("Player");

            var playerSkills = Variable.Array<double>(players).Named("Skill");

            var winner_lineups = Variable.Array(Variable.Array<int>(teamSize), games).Named("t1Lineups");
            var loser_lineups = Variable.Array(Variable.Array<int>(teamSize), games).Named("t2Lineups");

            var w_performances = Variable.Array(Variable.Array<double>(teamSize), games);
            var l_performances = Variable.Array(Variable.Array<double>(teamSize), games);


            using (Variable.ForEach(players))
            {
                playerSkills[players] = Variable.GaussianFromMeanAndPrecision(mu, 1 / (sigma* sigma));
                
            }

            using (var game = Variable.ForEach(games))
            {
                var gameIndex = game.Index;
                using (var n = Variable.ForEach(teamSize))
                {
                    var playerIndex = n.Index;
                    w_performances[gameIndex][playerIndex] = Variable.GaussianFromMeanAndPrecision(playerSkills[winner_lineups[gameIndex][playerIndex]], 1 / (beta* beta)).Named("w_player_performance");
                    l_performances[gameIndex][playerIndex] = Variable.GaussianFromMeanAndPrecision(playerSkills[loser_lineups[gameIndex][playerIndex]], 1 / (beta* beta)).Named("l_player_perfomance");
                }

            }

            var w_performance = Variable.Sum(w_performances[games]);
            var l_performance = Variable.Sum(l_performances[games]);
            Variable.ConstrainTrue(w_performance > l_performance);

            winner_lineups.ObservedValue = winnerData;
            loser_lineups.ObservedValue = loserData;


            var inferenceEngine = new InferenceEngine();
            inferenceEngine.NumberOfIterations = 10;
            var inferredSkills = inferenceEngine.Infer<Gaussian[]>(playerSkills);

            foreach(var playerSkill in inferredSkills)
            {
                Console.WriteLine(playerSkill);
            }

        }

        
    }
}

Output:

Compiling model...done.
Iterating:
.........| 10
Gaussian(25, 69,44)
Gaussian(25, 69,44)
Gaussian(25, 69,44)
Gaussian(25, 69,44)
Gaussian(-6,574e+04, 26,68)
Gaussian(-4,68e+04, 14,8)
Gaussian(-4,889e+04, 10,78)
Gaussian(-4,889e+04, 10,78)
Gaussian(-4,889e+04, 10,78)
Gaussian(-4,889e+04, 10,78)

Using TrueskillThroughTIme .py with same sample data and values which should correspond to the same model gives the following results:

N(mu=26.223, sigma=3.618)
N(mu=26.223, sigma=3.618)
N(mu=26.223, sigma=3.618)
N(mu=26.223, sigma=3.618)
N(mu=16.821, sigma=3.618)
N(mu=33.179, sigma=3.618)
N(mu=23.777, sigma=3.618)
N(mu=23.777, sigma=3.618)
N(mu=23.777, sigma=3.618)
N(mu=23.777, sigma=3.618)

I suspect summing up the teams players performances is the issue as when constraining individual performances according to the results gives reasonable skill estimates.

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