Initial commit.
This commit is contained in:
540
src/game.rs
Normal file
540
src/game.rs
Normal file
@@ -0,0 +1,540 @@
|
||||
use std::cmp::Reverse;
|
||||
use std::collections::HashSet;
|
||||
|
||||
use crate::{message::DiffMessages, utils, variable::TeamVariable, Gaussian, Player, N00};
|
||||
|
||||
pub struct Game {
|
||||
teams: Vec<Vec<Player>>,
|
||||
result: Vec<u16>,
|
||||
p_draw: f64,
|
||||
pub likelihoods: Vec<Vec<Gaussian>>,
|
||||
pub evidence: f64,
|
||||
}
|
||||
|
||||
impl Game {
|
||||
pub fn new(teams: Vec<Vec<Player>>, result: Vec<u16>, p_draw: f64) -> Self {
|
||||
if !result.is_empty() {
|
||||
assert!(
|
||||
teams.len() == result.len(),
|
||||
"len(result) and (len(teams) != len(result))"
|
||||
);
|
||||
}
|
||||
|
||||
assert!(p_draw >= 0.0 && p_draw < 1.0, "0.0 <= p_draw < 1.0");
|
||||
|
||||
if p_draw == 0.0 {
|
||||
assert!(
|
||||
result.iter().collect::<HashSet<_>>().len() == result.len(),
|
||||
"(p_draw == 0.0) and (len(result) > 0) and (len(set(result)) != len(result))"
|
||||
);
|
||||
}
|
||||
|
||||
let mut this = Self {
|
||||
teams,
|
||||
result,
|
||||
p_draw,
|
||||
likelihoods: Vec::new(),
|
||||
evidence: 0.0,
|
||||
};
|
||||
|
||||
this.compute_likelihoods();
|
||||
|
||||
this
|
||||
}
|
||||
|
||||
fn performance(&self, index: usize) -> Gaussian {
|
||||
self.teams[index]
|
||||
.iter()
|
||||
.fold(N00, |sum, p| sum + p.performance())
|
||||
}
|
||||
|
||||
fn partial_evidence(&mut self, d: &[DiffMessages], margin: &[f64], tie: &[bool], e: usize) {
|
||||
let mu = d[e].prior.mu();
|
||||
let sigma = d[e].prior.sigma();
|
||||
|
||||
if tie[e] {
|
||||
self.evidence *= utils::cdf(margin[e], mu, sigma) - utils::cdf(-margin[e], mu, sigma)
|
||||
} else {
|
||||
self.evidence *= 1.0 - utils::cdf(margin[e], mu, sigma);
|
||||
}
|
||||
}
|
||||
|
||||
fn graphical_model(
|
||||
&mut self,
|
||||
) -> (
|
||||
Vec<usize>,
|
||||
Vec<TeamVariable>,
|
||||
Vec<DiffMessages>,
|
||||
Vec<bool>,
|
||||
Vec<f64>,
|
||||
) {
|
||||
if self.result.is_empty() {
|
||||
self.result = (0..self.teams.len() as u16).rev().collect::<Vec<_>>();
|
||||
}
|
||||
|
||||
let r = &self.result;
|
||||
let o = sortperm(r);
|
||||
|
||||
let t = (0..self.teams.len())
|
||||
.map(|e| TeamVariable {
|
||||
prior: self.teams[o[e]]
|
||||
.iter()
|
||||
.fold(N00, |sum, p| sum + p.performance()),
|
||||
..Default::default()
|
||||
})
|
||||
.collect::<Vec<_>>();
|
||||
|
||||
let d = t
|
||||
.windows(2)
|
||||
.map(|window| DiffMessages {
|
||||
prior: window[0].prior - window[1].prior,
|
||||
..Default::default()
|
||||
})
|
||||
.collect::<Vec<_>>();
|
||||
|
||||
let tie = (0..d.len())
|
||||
.map(|e| r[o[e]] == r[o[e + 1]])
|
||||
.collect::<Vec<_>>();
|
||||
|
||||
let margin = (0..d.len())
|
||||
.map(|e| {
|
||||
if self.p_draw == 0.0 {
|
||||
0.0
|
||||
} else {
|
||||
let a: f64 = self.teams[o[e]].iter().map(|a| a.beta.powi(2)).sum();
|
||||
let b: f64 = self.teams[o[e + 1]].iter().map(|a| a.beta.powi(2)).sum();
|
||||
|
||||
utils::compute_margin(self.p_draw, (a + b).sqrt())
|
||||
}
|
||||
})
|
||||
.collect::<Vec<_>>();
|
||||
|
||||
self.evidence = 1.0;
|
||||
|
||||
(o, t, d, tie, margin)
|
||||
}
|
||||
|
||||
fn likelihood_analitico(&mut self) -> Vec<Vec<Gaussian>> {
|
||||
let (o, t, d, tie, margin) = self.graphical_model();
|
||||
|
||||
self.partial_evidence(&d, &margin, &tie, 0);
|
||||
|
||||
let d = d[0].prior;
|
||||
let (mu_trunc, sigma_trunc) = utils::trunc(d.mu(), d.sigma(), margin[0], tie[0]);
|
||||
|
||||
let (delta_div, theta_div_pow2) = if d.sigma() == sigma_trunc {
|
||||
(
|
||||
d.sigma().powi(2) * mu_trunc - sigma_trunc.powi(2) * d.mu(),
|
||||
f64::INFINITY,
|
||||
)
|
||||
} else {
|
||||
(
|
||||
(d.sigma().powi(2) * mu_trunc - sigma_trunc.powi(2) * d.mu())
|
||||
/ (d.sigma().powi(2) - sigma_trunc.powi(2)),
|
||||
(sigma_trunc.powi(2) * d.sigma().powi(2))
|
||||
/ (d.sigma().powi(2) - sigma_trunc.powi(2)),
|
||||
)
|
||||
};
|
||||
|
||||
let mut res = Vec::new();
|
||||
|
||||
for i in 0..t.len() {
|
||||
let mut team = Vec::new();
|
||||
|
||||
for j in 0..self.teams[o[i]].len() {
|
||||
//
|
||||
let mu = if d.sigma() == sigma_trunc {
|
||||
0.0
|
||||
} else {
|
||||
self.teams[o[i]][j].prior.mu()
|
||||
+ (delta_div - d.mu()) * (-1.0f64).powi(if i == 1 { 1 } else { 0 })
|
||||
};
|
||||
|
||||
let sigma_analitico = (theta_div_pow2 + d.sigma().powi(2)
|
||||
- self.teams[o[i]][j].prior.sigma().powi(2))
|
||||
.sqrt();
|
||||
|
||||
team.push(Gaussian::new(mu, sigma_analitico));
|
||||
}
|
||||
|
||||
res.push(team);
|
||||
}
|
||||
|
||||
if o[0] >= o[1] {
|
||||
res.swap(0, 1);
|
||||
}
|
||||
|
||||
res
|
||||
}
|
||||
|
||||
fn likelihood_teams(&mut self) -> Vec<Gaussian> {
|
||||
let (o, mut t, mut d, tie, margin) = self.graphical_model();
|
||||
|
||||
let mut step = (f64::INFINITY, f64::INFINITY);
|
||||
let mut i = 0;
|
||||
|
||||
while ((step.0 > 1e-6) || (step.1 > 1e-6)) && i < 10 {
|
||||
step = (0.0, 0.0);
|
||||
|
||||
for e in 0..d.len() - 1 {
|
||||
d[e].prior = t[e].posterior_win() - t[e + 1].posterior_lose();
|
||||
|
||||
if i == 0 {
|
||||
let mu = d[e].prior.mu();
|
||||
let sigma = d[e].prior.sigma();
|
||||
|
||||
if tie[e] {
|
||||
self.evidence *=
|
||||
utils::cdf(margin[e], mu, sigma) - utils::cdf(-margin[e], mu, sigma)
|
||||
} else {
|
||||
self.evidence *= 1.0 - utils::cdf(margin[e], mu, sigma);
|
||||
}
|
||||
}
|
||||
|
||||
d[e].likelihood = utils::approx(d[e].prior, margin[e], tie[e]) / d[e].prior;
|
||||
|
||||
let likelihood_lose = t[e].posterior_win() - d[e].likelihood;
|
||||
let delta = t[e + 1].likelihood_lose.delta(likelihood_lose);
|
||||
|
||||
step = (
|
||||
if step.0 > delta.0 { step.0 } else { delta.0 },
|
||||
if step.1 > delta.1 { step.1 } else { delta.1 },
|
||||
);
|
||||
|
||||
t[e + 1].likelihood_lose = likelihood_lose;
|
||||
}
|
||||
|
||||
for e in (1..d.len()).rev() {
|
||||
d[e].prior = t[e].posterior_win() - t[e + 1].posterior_lose();
|
||||
|
||||
if i == 0 && e == d.len() - 1 {
|
||||
self.partial_evidence(&d, &margin, &tie, e);
|
||||
}
|
||||
|
||||
d[e].likelihood = utils::approx(d[e].prior, margin[e], tie[e]) / d[e].prior;
|
||||
|
||||
let likelihood_win = t[e + 1].posterior_lose() + d[e].likelihood;
|
||||
let delta = t[e].likelihood_win.delta(likelihood_win);
|
||||
|
||||
step = (
|
||||
if step.0 > delta.0 { step.0 } else { delta.0 },
|
||||
if step.1 > delta.1 { step.1 } else { delta.1 },
|
||||
);
|
||||
|
||||
t[e].likelihood_win = likelihood_win;
|
||||
}
|
||||
|
||||
i += 1;
|
||||
}
|
||||
|
||||
if d.len() == 1 {
|
||||
self.partial_evidence(&d, &margin, &tie, 0);
|
||||
|
||||
d[0].prior = t[0].posterior_win() - t[1].posterior_lose();
|
||||
d[0].likelihood = utils::approx(d[0].prior, margin[0], tie[0]) / d[0].prior;
|
||||
}
|
||||
|
||||
let t_e = t.len();
|
||||
let d_e = d.len();
|
||||
|
||||
t[0].likelihood_win = t[1].posterior_lose() + d[0].likelihood;
|
||||
t[t_e - 1].likelihood_lose = t[t_e - 2].posterior_win() - d[d_e - 1].likelihood;
|
||||
|
||||
(0..t.len())
|
||||
.map(|e| t[o[e]].likelihood())
|
||||
.collect::<Vec<_>>()
|
||||
}
|
||||
|
||||
fn compute_likelihoods(&mut self) {
|
||||
if self.teams.len() > 2 {
|
||||
let m_t_ft = self.likelihood_teams();
|
||||
|
||||
self.likelihoods = (0..self.teams.len())
|
||||
.map(|e| {
|
||||
(0..self.teams[e].len())
|
||||
.map(|i| m_t_ft[e] - self.performance(e).exclude(self.teams[e][i].prior))
|
||||
.collect::<Vec<_>>()
|
||||
})
|
||||
.collect::<Vec<_>>();
|
||||
} else {
|
||||
self.likelihoods = self.likelihood_analitico();
|
||||
}
|
||||
}
|
||||
|
||||
pub fn posteriors(&self) -> Vec<Vec<Gaussian>> {
|
||||
(0..self.teams.len())
|
||||
.map(|e| {
|
||||
(0..self.teams[e].len())
|
||||
.map(|i| self.likelihoods[e][i] * self.teams[e][i].prior)
|
||||
.collect::<Vec<_>>()
|
||||
})
|
||||
.collect::<Vec<_>>()
|
||||
}
|
||||
}
|
||||
|
||||
fn sortperm(xs: &[u16]) -> Vec<usize> {
|
||||
let mut x = xs.iter().enumerate().collect::<Vec<_>>();
|
||||
x.sort_unstable_by_key(|(_, x)| Reverse(*x));
|
||||
x.into_iter().map(|(i, _)| i).collect()
|
||||
}
|
||||
|
||||
#[cfg(test)]
|
||||
mod tests {
|
||||
use crate::{Gaussian, Player, GAMMA, N_INF};
|
||||
|
||||
use super::*;
|
||||
|
||||
#[test]
|
||||
fn test_sortperm() {
|
||||
assert_eq!(sortperm(&[0, 1, 2, 0]), vec![2, 1, 0, 3]);
|
||||
}
|
||||
|
||||
#[test]
|
||||
fn test_1vs1() {
|
||||
let t_a = Player::new(
|
||||
Gaussian::new(25.0, 25.0 / 3.0),
|
||||
25.0 / 6.0,
|
||||
25.0 / 300.0,
|
||||
N_INF,
|
||||
);
|
||||
|
||||
let t_b = Player::new(
|
||||
Gaussian::new(25.0, 25.0 / 3.0),
|
||||
25.0 / 6.0,
|
||||
25.0 / 300.0,
|
||||
N_INF,
|
||||
);
|
||||
|
||||
let g = Game::new(vec![vec![t_a], vec![t_b]], vec![0, 1], 0.0);
|
||||
let p = g.posteriors();
|
||||
|
||||
let a = p[0][0];
|
||||
let b = p[1][0];
|
||||
|
||||
assert_eq!(a.mu(), 20.79477925612302);
|
||||
assert_eq!(b.mu(), 29.205220743876975);
|
||||
assert_eq!(a.sigma(), 7.194481422570443);
|
||||
|
||||
let t_a = Player::new(Gaussian::new(29.0, 1.0), 25.0 / 6.0, GAMMA, N_INF);
|
||||
let t_b = Player::new(Gaussian::new(25.0, 25.0 / 3.0), 25.0 / 6.0, GAMMA, N_INF);
|
||||
|
||||
let g = Game::new(vec![vec![t_a], vec![t_b]], vec![0, 1], 0.0);
|
||||
let p = g.posteriors();
|
||||
|
||||
let a = p[0][0];
|
||||
let b = p[1][0];
|
||||
|
||||
assert_eq!(a.mu(), 28.896475351225412);
|
||||
assert_eq!(a.sigma(), 0.9966043313004235);
|
||||
assert_eq!(b.mu(), 32.18921172045737);
|
||||
assert_eq!(b.sigma(), 6.062063735879715);
|
||||
|
||||
let t_a = Player::new(Gaussian::new(1.139, 0.531), 1.0, 0.2125, N_INF);
|
||||
let t_b = Player::new(Gaussian::new(15.568, 0.51), 1.0, 0.2125, N_INF);
|
||||
|
||||
let g = Game::new(vec![vec![t_a], vec![t_b]], vec![0, 1], 0.0);
|
||||
|
||||
assert_eq!(g.likelihoods[0][0].sigma(), f64::INFINITY);
|
||||
assert_eq!(g.likelihoods[1][0].sigma(), f64::INFINITY);
|
||||
assert_eq!(g.likelihoods[0][0].mu(), 0.0);
|
||||
}
|
||||
|
||||
#[test]
|
||||
fn test_1vs1vs1() {
|
||||
let t_a = Player::new(
|
||||
Gaussian::new(25.0, 25.0 / 3.0),
|
||||
25.0 / 6.0,
|
||||
25.0 / 300.0,
|
||||
N_INF,
|
||||
);
|
||||
let t_b = Player::new(
|
||||
Gaussian::new(25.0, 25.0 / 3.0),
|
||||
25.0 / 6.0,
|
||||
25.0 / 300.0,
|
||||
N_INF,
|
||||
);
|
||||
let t_c = Player::new(
|
||||
Gaussian::new(25.0, 25.0 / 3.0),
|
||||
25.0 / 6.0,
|
||||
25.0 / 300.0,
|
||||
N_INF,
|
||||
);
|
||||
|
||||
let g = Game::new(vec![vec![t_a], vec![t_b], vec![t_c]], vec![1, 2, 0], 0.0);
|
||||
let p = g.posteriors();
|
||||
|
||||
let a = p[0][0];
|
||||
let b = p[1][0];
|
||||
let c = p[2][0];
|
||||
|
||||
assert_eq!(a.mu(), 25.00000000000592);
|
||||
assert_eq!(a.sigma(), 6.238469796269066);
|
||||
assert_eq!(b.mu(), 31.31135822129149);
|
||||
assert_eq!(b.sigma(), 6.69881865477675);
|
||||
assert_eq!(c.mu(), 18.688641778702593);
|
||||
assert_eq!(c.sigma(), 6.698818654778007);
|
||||
|
||||
let t_a = Player::new(
|
||||
Gaussian::new(25.0, 25.0 / 3.0),
|
||||
25.0 / 6.0,
|
||||
25.0 / 300.0,
|
||||
N_INF,
|
||||
);
|
||||
let t_b = Player::new(
|
||||
Gaussian::new(25.0, 25.0 / 3.0),
|
||||
25.0 / 6.0,
|
||||
25.0 / 300.0,
|
||||
N_INF,
|
||||
);
|
||||
let t_c = Player::new(
|
||||
Gaussian::new(25.0, 25.0 / 3.0),
|
||||
25.0 / 6.0,
|
||||
25.0 / 300.0,
|
||||
N_INF,
|
||||
);
|
||||
|
||||
let g = Game::new(vec![vec![t_a], vec![t_b], vec![t_c]], vec![2, 1, 0], 0.0);
|
||||
let p = g.posteriors();
|
||||
|
||||
let a = p[0][0];
|
||||
let b = p[1][0];
|
||||
let c = p[2][0];
|
||||
|
||||
assert_eq!(a.mu(), 31.31135822129149);
|
||||
assert_eq!(a.sigma(), 6.69881865477675);
|
||||
assert_eq!(b.mu(), 25.00000000000592);
|
||||
assert_eq!(b.sigma(), 6.238469796269066);
|
||||
assert_eq!(c.mu(), 18.688641778702593);
|
||||
assert_eq!(c.sigma(), 6.698818654778007);
|
||||
|
||||
let t_a = Player::new(
|
||||
Gaussian::new(25.0, 25.0 / 3.0),
|
||||
25.0 / 6.0,
|
||||
25.0 / 300.0,
|
||||
N_INF,
|
||||
);
|
||||
let t_b = Player::new(
|
||||
Gaussian::new(25.0, 25.0 / 3.0),
|
||||
25.0 / 6.0,
|
||||
25.0 / 300.0,
|
||||
N_INF,
|
||||
);
|
||||
let t_c = Player::new(
|
||||
Gaussian::new(25.0, 25.0 / 3.0),
|
||||
25.0 / 6.0,
|
||||
25.0 / 300.0,
|
||||
N_INF,
|
||||
);
|
||||
|
||||
let g = Game::new(vec![vec![t_a], vec![t_b], vec![t_c]], vec![1, 2, 0], 0.5);
|
||||
let p = g.posteriors();
|
||||
|
||||
let a = p[0][0];
|
||||
let b = p[1][0];
|
||||
let c = p[2][0];
|
||||
|
||||
assert_eq!(a.mu(), 24.999999999511545);
|
||||
assert_eq!(a.sigma(), 6.092561128305945);
|
||||
assert_eq!(b.mu(), 33.37931495595287);
|
||||
assert_eq!(b.sigma(), 6.483575782278924);
|
||||
assert_eq!(c.mu(), 16.62068504453558);
|
||||
assert_eq!(c.sigma(), 6.483575782198122);
|
||||
}
|
||||
|
||||
#[test]
|
||||
fn test_1vs1_draw() {
|
||||
let t_a = Player::new(
|
||||
Gaussian::new(25.0, 25.0 / 3.0),
|
||||
25.0 / 6.0,
|
||||
25.0 / 300.0,
|
||||
N_INF,
|
||||
);
|
||||
|
||||
let t_b = Player::new(
|
||||
Gaussian::new(25.0, 25.0 / 3.0),
|
||||
25.0 / 6.0,
|
||||
25.0 / 300.0,
|
||||
N_INF,
|
||||
);
|
||||
|
||||
let g = Game::new(vec![vec![t_a], vec![t_b]], vec![0, 0], 0.25);
|
||||
let p = g.posteriors();
|
||||
|
||||
let a = p[0][0];
|
||||
let b = p[1][0];
|
||||
|
||||
assert_eq!(a.mu(), 25.0);
|
||||
assert_eq!(a.sigma(), 6.469480769842277);
|
||||
assert_eq!(b.mu(), 25.0);
|
||||
assert_eq!(b.sigma(), 6.469480769842277);
|
||||
|
||||
let t_a = Player::new(Gaussian::new(25.0, 3.0), 25.0 / 6.0, 25.0 / 300.0, N_INF);
|
||||
|
||||
let t_b = Player::new(Gaussian::new(29.0, 2.0), 25.0 / 6.0, 25.0 / 300.0, N_INF);
|
||||
|
||||
let g = Game::new(vec![vec![t_a], vec![t_b]], vec![0, 0], 0.25);
|
||||
let p = g.posteriors();
|
||||
|
||||
let a = p[0][0];
|
||||
let b = p[1][0];
|
||||
|
||||
assert_eq!(a.mu(), 25.736001810566616);
|
||||
assert_eq!(a.sigma(), 2.709956162204711);
|
||||
assert_eq!(b.mu(), 28.67288808419261);
|
||||
assert_eq!(b.sigma(), 1.9164711604544398);
|
||||
}
|
||||
|
||||
#[test]
|
||||
fn test_1vs1vs1_draw() {
|
||||
let t_a = Player::new(
|
||||
Gaussian::new(25.0, 25.0 / 3.0),
|
||||
25.0 / 6.0,
|
||||
25.0 / 300.0,
|
||||
N_INF,
|
||||
);
|
||||
let t_b = Player::new(
|
||||
Gaussian::new(25.0, 25.0 / 3.0),
|
||||
25.0 / 6.0,
|
||||
25.0 / 300.0,
|
||||
N_INF,
|
||||
);
|
||||
let t_c = Player::new(
|
||||
Gaussian::new(25.0, 25.0 / 3.0),
|
||||
25.0 / 6.0,
|
||||
25.0 / 300.0,
|
||||
N_INF,
|
||||
);
|
||||
|
||||
let g = Game::new(vec![vec![t_a], vec![t_b], vec![t_c]], vec![0, 0, 0], 0.25);
|
||||
let p = g.posteriors();
|
||||
|
||||
let a = p[0][0];
|
||||
let b = p[1][0];
|
||||
let c = p[2][0];
|
||||
|
||||
assert_eq!(a.mu(), 24.999999999999996);
|
||||
assert_eq!(a.sigma(), 5.729068664890827);
|
||||
assert_eq!(b.mu(), 25.000000000000004);
|
||||
assert_eq!(b.sigma(), 5.707423522433266);
|
||||
assert_eq!(c.mu(), 24.999999999999996);
|
||||
assert_eq!(c.sigma(), 5.729068664890825);
|
||||
|
||||
let t_a = Player::new(Gaussian::new(25.0, 3.0), 25.0 / 6.0, 25.0 / 300.0, N_INF);
|
||||
let t_b = Player::new(Gaussian::new(25.0, 3.0), 25.0 / 6.0, 25.0 / 300.0, N_INF);
|
||||
let t_c = Player::new(Gaussian::new(29.0, 2.0), 25.0 / 6.0, 25.0 / 300.0, N_INF);
|
||||
|
||||
let g = Game::new(vec![vec![t_a], vec![t_b], vec![t_c]], vec![0, 0, 0], 0.25);
|
||||
let p = g.posteriors();
|
||||
|
||||
let a = p[0][0];
|
||||
let b = p[1][0];
|
||||
let c = p[2][0];
|
||||
|
||||
assert_eq!(a.mu(), 25.48850755025261);
|
||||
assert_eq!(a.sigma(), 2.638208444298423);
|
||||
assert_eq!(b.mu(), 25.51067170990121);
|
||||
assert_eq!(b.sigma(), 2.6287517663583633);
|
||||
assert_eq!(c.mu(), 28.555920328820523);
|
||||
assert_eq!(c.sigma(), 1.8856891308577184);
|
||||
}
|
||||
}
|
||||
Reference in New Issue
Block a user