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Simplify trueskill calculations
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Actually improves the accuracy slightly, compared to the other trueskill libraries like ts-trueskill.
And by slightly it means ~0.0000000000007 difference instead of ~0.0000000000009
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@atomflunder
atomflunder committed Oct 10, 2024
1 parent 5256e1b commit 6bba1cc
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Showing 2 changed files with 30 additions and 78 deletions.
16 changes: 8 additions & 8 deletions src/trueskill/factor_graph.rs
View file
Original file line number Diff line number Diff line change
Expand Up @@ -230,17 +230,17 @@ impl SumFactor {
pub struct TruncateFactor {
id: usize,
variable: Rc<RefCell<Variable>>,
v_func: Box<dyn Fn(f64, f64) -> f64>,
w_func: Box<dyn Fn(f64, f64) -> f64>,
v_func: Box<dyn Fn(f64, f64, f64) -> f64>,
w_func: Box<dyn Fn(f64, f64, f64) -> f64>,
draw_margin: f64,
}

impl TruncateFactor {
pub fn new(
id: usize,
variable: Rc<RefCell<Variable>>,
v_func: Box<dyn Fn(f64, f64) -> f64>,
w_func: Box<dyn Fn(f64, f64) -> f64>,
v_func: Box<dyn Fn(f64, f64, f64) -> f64>,
w_func: Box<dyn Fn(f64, f64, f64) -> f64>,
draw_margin: f64,
) -> Self {
variable.borrow_mut().messages.entry(id).or_default();
Expand All @@ -260,10 +260,10 @@ impl TruncateFactor {
variable.gaussian / variable.messages[&self.id]
};
let pi_sqrt = div.pi.sqrt();
let arg_1 = div.tau / pi_sqrt;
let arg_2 = self.draw_margin * pi_sqrt;
let v = (self.v_func)(arg_1, arg_2);
let w = (self.w_func)(arg_1, arg_2);
let arg_1 = div.tau;
let arg_2 = self.draw_margin * div.pi;
let v = (self.v_func)(arg_1, arg_2, pi_sqrt);
let w = (self.w_func)(arg_1, arg_2, pi_sqrt);
let denom = 1.0 - w;

let pi = div.pi / denom;
Expand Down
92 changes: 22 additions & 70 deletions src/trueskill/mod.rs
View file
Original file line number Diff line number Diff line change
Expand Up @@ -1809,54 +1809,6 @@ fn build_trunc_layer(
beta: f64,
starting_id: usize,
) -> Vec<TruncateFactor> {
fn v_w(diff: f64, draw_margin: f64) -> f64 {
let x = diff - draw_margin;
let denom = cdf(x, 0.0, 1.0);

if denom == 0.0 {
-x
} else {
pdf(x, 0.0, 1.0) / denom
}
}

fn v_d(diff: f64, draw_margin: f64) -> f64 {
let abs_diff = diff.abs();
let a = draw_margin - abs_diff;
let b = -draw_margin - abs_diff;
let denom = cdf(a, 0.0, 1.0) - cdf(b, 0.0, 1.0);
let numer = pdf(b, 0.0, 1.0) - pdf(a, 0.0, 1.0);

let lhs = if denom == 0.0 { a } else { numer / denom };
let rhs = if diff < 0.0 { -1.0 } else { 1.0 };

lhs * rhs
}

fn w_w(diff: f64, draw_margin: f64) -> f64 {
let x = diff - draw_margin;
let v = v_w(diff, draw_margin);
let w = v * (v + x);
if 0.0 < w && w < 1.0 {
return w;
}

panic!("floating point error");
}

#[allow(clippy::suboptimal_flops)]
fn w_d(diff: f64, draw_margin: f64) -> f64 {
let abs_diff = diff.abs();
let a = draw_margin - abs_diff;
let b = -draw_margin - abs_diff;
let denom = cdf(a, 0.0, 1.0) - cdf(b, 0.0, 1.0);

assert!(!(denom == 0.0), "floating point error");

let v = v_d(abs_diff, draw_margin);
v.mul_add(v, (a * pdf(a, 0.0, 1.0) - b * pdf(b, 0.0, 1.0)) / denom)
}

let mut v = Vec::with_capacity(team_diff_vars.len());
let mut i = starting_id;
for (x, team_diff_var) in team_diff_vars.iter().enumerate() {
Expand All @@ -1865,14 +1817,14 @@ fn build_trunc_layer(
.map(|v| v.0.len() as f64)
.sum();
let draw_margin = draw_margin(draw_probability, beta, size);
let v_func: Box<dyn Fn(f64, f64) -> f64>;
let w_func: Box<dyn Fn(f64, f64) -> f64>;
let v_func: Box<dyn Fn(f64, f64, f64) -> f64>;
let w_func: Box<dyn Fn(f64, f64, f64) -> f64>;
if sorted_teams_and_ranks[x].1 == sorted_teams_and_ranks[x + 1].1 {
v_func = Box::new(v_d);
w_func = Box::new(w_d);
v_func = Box::new(v_draw);
w_func = Box::new(w_draw);
} else {
v_func = Box::new(v_w);
w_func = Box::new(w_w);
v_func = Box::new(v_non_draw);
w_func = Box::new(w_non_draw);
};

v.push(TruncateFactor::new(
Expand Down Expand Up @@ -2668,26 +2620,26 @@ mod tests {
let results = trueskill_multi_team(&teams_and_ranks, &TrueSkillConfig::new());

assert!((results[0][0].rating - 40.876_849_177_315_655).abs() < f64::EPSILON);
assert!((results[0][1].rating - 45.493_394_092_398_44).abs() < f64::EPSILON);
assert!((results[0][1].rating - 45.493_394_092_398_45).abs() < f64::EPSILON);

assert!((results[1][0].rating - 19.608_650_920_845_236).abs() < f64::EPSILON);
assert!((results[1][0].rating - 19.608_650_920_845_23).abs() < f64::EPSILON);
assert!((results[1][1].rating - 18.712_463_514_890_54).abs() < f64::EPSILON);
assert!((results[1][2].rating - 29.353_112_227_810_637).abs() < f64::EPSILON);
assert!((results[1][3].rating - 9.872_175_198_037_164).abs() < f64::EPSILON);

assert!((results[2][0].rating - 48.829_832_201_455_32).abs() < f64::EPSILON);
assert!((results[2][1].rating - 29.812_500_188_903_005).abs() < f64::EPSILON);
assert!((results[2][0].rating - 48.829_832_201_455_31).abs() < f64::EPSILON);
assert!((results[2][1].rating - 29.812_500_188_902_998).abs() < f64::EPSILON);

assert!((results[0][0].uncertainty - 3.839_527_589_355_37).abs() < f64::EPSILON);
assert!((results[0][0].uncertainty - 3.839_527_589_355_369_8).abs() < f64::EPSILON);
assert!((results[0][1].uncertainty - 2.933_671_613_522_051).abs() < f64::EPSILON);

assert!((results[1][0].uncertainty - 6.396_044_310_523_897).abs() < f64::EPSILON);
assert!((results[1][0].uncertainty - 6.396_044_310_523_896).abs() < f64::EPSILON);
assert!((results[1][1].uncertainty - 5.624_556_429_622_889).abs() < f64::EPSILON);
assert!((results[1][2].uncertainty - 7.673_456_361_986_594).abs() < f64::EPSILON);
assert!((results[1][2].uncertainty - 7.673_456_361_986_593).abs() < f64::EPSILON);
assert!((results[1][3].uncertainty - 3.891_408_425_994_520_3).abs() < f64::EPSILON);

assert!((results[2][0].uncertainty - 4.590_018_525_151_38).abs() < f64::EPSILON);
assert!((results[2][1].uncertainty - 1.976_314_792_712_798_2).abs() < f64::EPSILON);
assert!((results[2][0].uncertainty - 4.590_018_525_151_379).abs() < f64::EPSILON);
assert!((results[2][1].uncertainty - 1.976_314_792_712_798).abs() < f64::EPSILON);
}

#[test]
Expand All @@ -2714,7 +2666,7 @@ mod tests {

let results = trueskill_multi_team(teams_and_ranks, &TrueSkillConfig::new());

assert!((results[0][0].rating - 41.720_925_460_665).abs() < f64::EPSILON);
assert!((results[0][0].rating - 41.720_925_460_665_01).abs() < f64::EPSILON);
assert!((results[1][0].rating - 20.997_268_045_415_94).abs() < f64::EPSILON);
assert!((results[2][0].rating - 41.771_076_420_914_83).abs() < f64::EPSILON);

Expand Down Expand Up @@ -2753,15 +2705,15 @@ mod tests {

let results = trueskill_multi_team(teams_and_ranks, &TrueSkillConfig::new());

assert!((results[0][0].rating - 46.844_398_641_974_195).abs() < f64::EPSILON);
assert!((results[0][0].rating - 46.844_398_641_974_97).abs() < f64::EPSILON);
assert!((results[1][0].rating - -21.0).abs() < f64::EPSILON);
assert!((results[2][0].rating - 121.973_594_228_967_41).abs() < f64::EPSILON);
assert!((results[3][0].rating - 3.577_783_039_440_541_7).abs() < f64::EPSILON);
assert!((results[2][0].rating - 121.973_594_228_967_43).abs() < f64::EPSILON);
assert!((results[3][0].rating - 3.577_783_039_440_43).abs() < f64::EPSILON);

assert!((results[0][0].uncertainty - 4.453_979_220_473_841).abs() < f64::EPSILON);
assert!((results[0][0].uncertainty - 4.453_979_220_477_661).abs() < f64::EPSILON);
assert!((results[1][0].uncertainty - 1.871_855_882_391_709_3).abs() < f64::EPSILON);
assert!((results[2][0].uncertainty - 0.083_922_196_135_183_51).abs() < f64::EPSILON);
assert!((results[3][0].uncertainty - 1.197_926_990_096_083_4).abs() < f64::EPSILON);
assert!((results[2][0].uncertainty - 0.083_922_196_135_183_55).abs() < f64::EPSILON);
assert!((results[3][0].uncertainty - 1.197_926_990_096_302_3).abs() < f64::EPSILON);
}

#[test]
Expand Down

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