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feat!: Gaussian's EP operations stop wearing arithmetic's clothes

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`Gaussian` publicly implemented `Mul`, `Div`, `Add` and `Sub`. They were
the EP product, cavity and variance-space convolutions, and every one of
them lies to a reader who takes the operator at face value:

    a = N(10, 2)   b = N(4, 3)   c = N(1, 1)

    a * b        N(8.15, 1.66)   not 40
    a - b        sigma GREW, 2 -> sqrt(4 + 9)
    a * N(1, 0)  mu = NaN        "multiply by one"
    a / c        pi = -0.75      mu() prints a confident 0

The last is this crate's signature defect on a public operator. `Div` is
the cavity and can legitimately leave a negative precision, which is not
a distribution — and `mu()`/`sigma()` guard `pi <= 0` and report `0.0`
and `inf`, so it comes back as a plausible number with no panic, no
`Debug` marker and nothing to test against.

The four impls are now `pub(crate)` inherent methods that say what they
do: `ep_product`, `cavity`, `convolve`, `convolve_diff`, plus `scale`
for the one operation that genuinely is arithmetic. Nothing in a user's
workflow needed operator syntax; inference did, and it still has it.

`pi()` and `tau()` follow. Storing natural parameters is a performance
decision — it makes message passing two adds — not a contract. The
public surface is now exactly: `from_ms`, `from_mv`, `mu`, `sigma`,
`variance`, `probability_below`, `probability_above`. `from_mv` and
`variance` are promoted from `pub(crate)`; they are the honest pair for
callers who already hold a variance and should not pay a round trip
through the square root.

Four integration tests asserted bit-identity on `(pi, tau)`. They assert
it on `(mu, variance)` instead — still `assert_eq!`, still exact, and
`1/pi` and `tau/pi` are deterministic, so bit-equal natural parameters
give bit-equal moments. `a_nan_sigma_passes_through_from_ms` drops its
`|| g.pi().is_nan()` half: `sigma()` substitutes for `pi <= 0` and
`pi == inf`, so NaN survives to it only from a NaN precision.

`benches/gaussian.rs` is deleted. It timed two f64 additions through the
public operators, and keeping those public solely to feed it is the same
thing #73 objected to when a benchmark was dictating five public types.
The paths it covered are exercised by `batch` and `history_converge`
through the real call chain.

Closes #71.

Co-Authored-By: Claude Opus 5 (1M context) <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_011hcFjNDmHXZF8URGLku5zZ
This commit is contained in:
logaritmisk
2026-09-09 23:13:10 +02:00
co-authored by Claude Opus 5
parent 8e34410db0
commit 076a7ded8c
13 changed files with 163 additions and 175 deletions
Download Patch File Download Diff File Expand all files Collapse all files
src/acquisition.rs
+1 -1
View File
@@ -159,7 +159,7 @@ pub fn expected_information_gain<T: Time, D: Drift<T>>(
.iter()
.map(|team| {
team.iter()
.fold(crate::N00, |acc, rating| acc + rating.performance())
.fold(crate::N00, |acc, rating| acc.convolve(rating.performance()))
})
.collect();
src/factor/margin.rs
+2 -2
View File
@@ -39,7 +39,7 @@ impl MarginFactor {
/// exactly; `alpha < 1.0` writes `α·new_msg + (1−α)·old_msg`.
pub(crate) fn propagate_with_alpha(&mut self, vars: &mut VarStore, alpha: f64) -> (f64, f64) {
let marginal = vars.get(self.diff);
let cavity = marginal / self.msg;
let cavity = marginal.cavity(self.msg);
if self.log_evidence_cached.is_none() {
self.log_evidence_cached = Some(cavity_log_evidence(cavity, self.m_obs, self.sigma));
@@ -49,7 +49,7 @@ impl MarginFactor {
let damped = self.msg.damp_natural(new_msg, alpha);
let old_msg = self.msg;
self.msg = damped;
vars.set(self.diff, cavity * damped);
vars.set(self.diff, cavity.ep_product(damped));
old_msg.delta(damped)
}
src/factor/trunc.rs
+3 -3
View File
@@ -41,14 +41,14 @@ impl TruncFactor {
/// exactly; `alpha < 1.0` writes `α·new_msg + (1−α)·old_msg`.
pub(crate) fn propagate_with_alpha(&mut self, vars: &mut VarStore, alpha: f64) -> (f64, f64) {
let marginal = vars.get(self.diff);
let cavity = marginal / self.msg;
let cavity = marginal.cavity(self.msg);
if self.log_evidence_cached.is_none() {
self.log_evidence_cached = Some(cavity_log_evidence(cavity, self.margin, self.tie));
}
let trunc = approx(cavity, self.margin, self.tie);
let new_msg = trunc / cavity;
let new_msg = trunc.cavity(cavity);
let damped = self.msg.damp_natural(new_msg, alpha);
let old_msg = self.msg;
@@ -57,7 +57,7 @@ impl TruncFactor {
// marginal_new = cavity * stored_msg. With alpha = 1.0 this equals
// `trunc` (since cavity * new_msg = trunc by construction); with
// alpha < 1.0 it reflects the partially-applied update.
vars.set(self.diff, cavity * damped);
vars.set(self.diff, cavity.ep_product(damped));
old_msg.delta(damped)
}
src/game.rs
+31 -22
View File
@@ -205,7 +205,12 @@ impl<T: Time, D: Drift<T>> Game<T, D> {
self.likelihoods
.iter()
.zip(self.teams.iter())
.map(|(l, t)| l.iter().zip(t.iter()).map(|(&l, r)| l * r.prior).collect())
.map(|(l, t)| {
l.iter()
.zip(t.iter())
.map(|(&l, r)| l.ep_product(r.prior))
.collect()
})
.collect()
}
@@ -364,7 +369,7 @@ impl<'a, T: Time, D: Drift<T>> GameRef<'a, T, D> {
.iter()
.zip(self.weights[t].iter())
.fold(N00, |p, (competitor, &w)| {
p + (competitor.performance() * w)
p.convolve(competitor.performance().scale(w))
})
}));
@@ -384,28 +389,28 @@ impl<'a, T: Time, D: Drift<T>> GameRef<'a, T, D> {
step = (0.0_f64, 0.0_f64);
for (e, lf) in links[..n_diffs.saturating_sub(1)].iter_mut().enumerate() {
let pw = arena.team_prior[e] * arena.lhood_lose[e];
let pl = arena.team_prior[e + 1] * arena.lhood_win[e + 1];
let raw = pw - pl;
arena.vars.set(lf.diff(), raw * lf.msg());
let pw = arena.team_prior[e].ep_product(arena.lhood_lose[e]);
let pl = arena.team_prior[e + 1].ep_product(arena.lhood_win[e + 1]);
let raw = pw.convolve_diff(pl);
arena.vars.set(lf.diff(), raw.ep_product(lf.msg()));
let d = lf.propagate(&mut arena.vars, alpha);
step = tuple_max(step, d);
let new_ll = pw - lf.msg();
let new_ll = pw.convolve_diff(lf.msg());
step = tuple_max(step, arena.lhood_lose[e + 1].delta(new_ll));
arena.lhood_lose[e + 1] = new_ll;
}
for (rev_i, lf) in links[1..].iter_mut().rev().enumerate() {
let e = n_diffs - 1 - rev_i;
let pw = arena.team_prior[e] * arena.lhood_lose[e];
let pl = arena.team_prior[e + 1] * arena.lhood_win[e + 1];
let raw = pw - pl;
arena.vars.set(lf.diff(), raw * lf.msg());
let pw = arena.team_prior[e].ep_product(arena.lhood_lose[e]);
let pl = arena.team_prior[e + 1].ep_product(arena.lhood_win[e + 1]);
let raw = pw.convolve_diff(pl);
arena.vars.set(lf.diff(), raw.ep_product(lf.msg()));
let d = lf.propagate(&mut arena.vars, alpha);
step = tuple_max(step, d);
let new_lw = pl + lf.msg();
let new_lw = pl.convolve(lf.msg());
step = tuple_max(step, arena.lhood_win[e].delta(new_lw));
arena.lhood_win[e] = new_lw;
}
@@ -415,18 +420,21 @@ impl<'a, T: Time, D: Drift<T>> GameRef<'a, T, D> {
// Special case: exactly 1 diff (2-team game); loop body was empty.
if n_diffs == 1 {
let raw = (arena.team_prior[0] * arena.lhood_lose[0])
- (arena.team_prior[1] * arena.lhood_win[1]);
arena.vars.set(links[0].diff(), raw * links[0].msg());
let raw = arena.team_prior[0]
.ep_product(arena.lhood_lose[0])
.convolve_diff(arena.team_prior[1].ep_product(arena.lhood_win[1]));
arena
.vars
.set(links[0].diff(), raw.ep_product(links[0].msg()));
links[0].propagate(&mut arena.vars, alpha);
}
// Boundary updates: close the chain at both ends.
if n_diffs > 0 {
let pl1 = arena.team_prior[1] * arena.lhood_win[1];
arena.lhood_win[0] = pl1 + links[0].msg();
let pw_last = arena.team_prior[n_teams - 2] * arena.lhood_lose[n_teams - 2];
arena.lhood_lose[n_teams - 1] = pw_last - links[n_diffs - 1].msg();
let pl1 = arena.team_prior[1].ep_product(arena.lhood_win[1]);
arena.lhood_win[0] = pl1.convolve(links[0].msg());
let pw_last = arena.team_prior[n_teams - 2].ep_product(arena.lhood_lose[n_teams - 2]);
arena.lhood_lose[n_teams - 1] = pw_last.convolve_diff(links[n_diffs - 1].msg());
}
let log_evidence: f64 = links.iter().map(DiffFactor::log_evidence).sum();
@@ -444,7 +452,7 @@ impl<'a, T: Time, D: Drift<T>> GameRef<'a, T, D> {
.enumerate()
.map(|(orig_i, (competitors, weights))| {
let si = arena.inv_buf[orig_i];
let m = arena.lhood_win[si] * arena.lhood_lose[si];
let m = arena.lhood_win[si].ep_product(arena.lhood_lose[si]);
// Already folded into `team_prior` at the top of the chain,
// indexed by sorted position.
let performance = arena.team_prior[si];
@@ -452,7 +460,8 @@ impl<'a, T: Time, D: Drift<T>> GameRef<'a, T, D> {
.iter()
.zip(weights.iter())
.map(|(competitor, &w)| {
((m - performance.exclude(competitor.performance() * w)) * (1.0 / w))
m.convolve_diff(performance.exclude(competitor.performance().scale(w)))
.scale(1.0 / w)
.forget(competitor.beta.powi(2))
})
.collect::<Vec<_>>()
@@ -504,7 +513,7 @@ impl<'a, T: Time, D: Drift<T>> GameRef<'a, T, D> {
.map(|(l, t)| {
l.iter()
.zip(t.iter())
.map(|(&l, p)| l * p.prior)
.map(|(&l, p)| l.ep_product(p.prior))
.collect::<Vec<_>>()
})
.collect::<Vec<_>>()
src/gaussian.rs
+86 -64
View File
@@ -1,5 +1,3 @@
use std::ops;
use crate::{MU, N_INF, SIGMA};
/// A Gaussian distribution stored in natural parameters.
@@ -75,11 +73,12 @@ impl Gaussian {
/// Construct from mean and *variance*, skipping the square-root round trip.
///
/// `from_ms(mu, var.sqrt())` immediately squares the root away again to
/// recover `pi = 1/var`. Variance-combining operations (`Add`, `Sub`,
/// `exclude`, `forget`) work in variance space throughout, so they go
/// through here instead and never take a root.
/// recover `pi = 1/var`. Variance-combining operations work in variance
/// space throughout, so they go through here instead and never take a
/// root. Use it whenever you already hold a variance —
/// [`variance`](Gaussian::variance) is its inverse.
#[inline]
pub(crate) fn from_mv(mu: f64, var: f64) -> Self {
pub fn from_mv(mu: f64, var: f64) -> Self {
if var == f64::INFINITY {
Self { pi: 0.0, tau: 0.0 }
} else if var == 0.0 {
@@ -107,8 +106,7 @@ impl Gaussian {
/// means more certain; `0.0` is an improper, uninformative message and
/// `inf` is a point mass.
#[inline]
#[must_use]
pub fn pi(&self) -> f64 {
pub(crate) fn pi(&self) -> f64 {
self.pi
}
@@ -117,8 +115,7 @@ impl Gaussian {
/// Stored rather than derived, for the same reason as [`Gaussian::pi`].
/// Meaningful only alongside `pi`: on its own it is not a location.
#[inline]
#[must_use]
pub fn tau(&self) -> f64 {
pub(crate) fn tau(&self) -> f64 {
self.tau
}
@@ -142,12 +139,14 @@ impl Gaussian {
}
}
/// Variance, `1 / pi`, without the root-and-square of `sigma().powi(2)`.
/// Variance, without the root-and-square of `sigma().powi(2)`.
///
/// Mirrors `sigma()`'s treatment of the improper (`pi <= 0`) and point-mass
/// (`pi == inf`) cases.
/// Mirrors [`sigma`](Gaussian::sigma)'s treatment of the improper
/// (infinite) and point-mass (zero) cases, and is the inverse of
/// [`from_mv`](Gaussian::from_mv).
#[inline]
pub(crate) fn variance(&self) -> f64 {
#[must_use]
pub fn variance(&self) -> f64 {
if self.pi <= 0.0 {
f64::INFINITY
} else if self.pi.is_infinite() {
@@ -279,34 +278,65 @@ impl Default for Gaussian {
}
}
impl ops::Add<Gaussian> for Gaussian {
type Output = Gaussian;
/// Variance addition: (mu1 + mu2, sqrt(σ1² + σ2²)).
/// Used for combining performance and noise; rare relative to mul/div.
fn add(self, rhs: Gaussian) -> Self::Output {
Self::from_mv(self.mu() + rhs.mu(), self.variance() + rhs.variance())
}
}
impl ops::Sub<Gaussian> for Gaussian {
type Output = Gaussian;
/// (mu1 - mu2, sqrt(σ1² + σ2²)). Same sigma combination as Add.
fn sub(self, rhs: Gaussian) -> Self::Output {
Self::from_mv(self.mu() - rhs.mu(), self.variance() + rhs.variance())
}
}
impl ops::Mul<Gaussian> for Gaussian {
type Output = Gaussian;
/// Factor product: nat-param add. Hot path — two f64 additions, no sqrt.
fn mul(self, rhs: Gaussian) -> Self::Output {
impl Gaussian {
/// The EP factor **product**: multiply two messages about the same
/// variable.
///
/// Two natural-parameter additions and no square root, which is why the
/// type stores `pi` and `tau` rather than `mu` and `sigma`. This is the
/// hot path.
///
/// Not arithmetic — `N(10, 2).ep_product(N(4, 3))` is `N(8.15, 1.66)`,
/// nowhere near 40. It used to be spelled `a * b`, on a public `Mul` impl,
/// where that was a trap rather than a shorthand.
#[inline]
pub(crate) fn ep_product(self, rhs: Gaussian) -> Gaussian {
Self::from_natural(self.pi + rhs.pi, self.tau + rhs.tau)
}
}
impl ops::Mul<f64> for Gaussian {
type Output = Gaussian;
fn mul(self, scalar: f64) -> Self::Output {
/// The EP **cavity**: divide out a message this belief already absorbed.
///
/// The inverse of [`ep_product`](Gaussian::ep_product), and two
/// subtractions rather than two additions.
///
/// **May return an improper result.** Cancelling a message that carried
/// most of the precision leaves `pi <= 0`, which is not a distribution.
/// `mu()` reports `0.0` and `sigma()` reports `inf` for such a value —
/// both are the accessors' policy for "undefined", not answers. Measured:
/// `N(10, 2).cavity(N(1, 1))` has `pi = -0.75`, and its `mu()` prints a
/// confident `0`. That is why this is not a public operator.
#[inline]
pub(crate) fn cavity(self, rhs: Gaussian) -> Gaussian {
Self::from_natural(self.pi - rhs.pi, self.tau - rhs.tau)
}
/// Convolve two independent Gaussians: `N(mu1 + mu2, sqrt(v1 + v2))`.
///
/// The distribution of a *sum* of independent variables, so the variances
/// add — the result is always wider than either input. Used to combine a
/// skill with performance noise. Goes through `from_mv` and takes no root.
#[inline]
pub(crate) fn convolve(self, rhs: Gaussian) -> Gaussian {
Self::from_mv(self.mu() + rhs.mu(), self.variance() + rhs.variance())
}
/// Convolve a *difference*: `N(mu1 - mu2, sqrt(v1 + v2))`.
///
/// The means subtract and the variances still **add**, because a
/// difference of independent variables is no more certain than a sum. That
/// is the half that made the old `Sub` impl misleading: `a - b` grew the
/// sigma from 2 to `sqrt(4 + 9)`.
#[inline]
pub(crate) fn convolve_diff(self, rhs: Gaussian) -> Gaussian {
Self::from_mv(self.mu() - rhs.mu(), self.variance() + rhs.variance())
}
/// Scale by a constant: `mu` by `scalar`, `sigma` by `|scalar|`.
///
/// The one operation that *is* ordinary arithmetic — it is the
/// distribution of `scalar * X`. Used for per-member weights.
#[inline]
pub(crate) fn scale(self, scalar: f64) -> Gaussian {
if !scalar.is_finite() {
return N_INF;
}
@@ -321,14 +351,6 @@ impl ops::Mul<f64> for Gaussian {
}
}
impl ops::Div<Gaussian> for Gaussian {
type Output = Gaussian;
/// Cavity: nat-param sub. Hot path — two f64 subtractions, no sqrt.
fn div(self, rhs: Gaussian) -> Self::Output {
Self::from_natural(self.pi - rhs.pi, self.tau - rhs.tau)
}
}
#[cfg(test)]
mod tests {
/// A message that did not change must report no change, even when it is
@@ -386,64 +408,64 @@ mod tests {
// Subtracting such a message must not produce NaN (the original failure path).
let proper = Gaussian::from_ms(9.75, 1.256);
let diff = proper - tiny_neg;
let diff = proper.convolve_diff(tiny_neg);
assert!(diff.pi().is_finite() && !diff.pi().is_nan());
assert!(diff.tau().is_finite() && !diff.tau().is_nan());
}
#[test]
fn test_add() {
fn convolve_adds_variances() {
let n = Gaussian::from_ms(25.0, 25.0 / 3.0);
let m = Gaussian::from_ms(0.0, 1.0);
let r = n + m;
let r = n.convolve(m);
assert!((r.mu() - 25.0).abs() < 1e-12);
assert!((r.sigma() - 8.393118874676116).abs() < 1e-10);
}
#[test]
fn test_sub() {
fn convolve_diff_subtracts_means_and_adds_variances() {
let n = Gaussian::from_ms(25.0, 25.0 / 3.0);
let m = Gaussian::from_ms(1.0, 1.0);
let r = n - m;
let r = n.convolve_diff(m);
assert!((r.mu() - 24.0).abs() < 1e-12);
assert!((r.sigma() - 8.393118874676116).abs() < 1e-10);
}
#[test]
fn test_mul() {
fn ep_product_is_not_arithmetic() {
let n = Gaussian::from_ms(25.0, 25.0 / 3.0);
let m = Gaussian::from_ms(0.0, 1.0);
let r = n * m;
let r = n.ep_product(m);
assert!((r.mu() - 0.35488958990536273).abs() < 1e-10);
assert!((r.sigma() - 0.992876838486922).abs() < 1e-10);
}
#[test]
fn test_div() {
fn cavity_undoes_a_product() {
let n = Gaussian::from_ms(25.0, 25.0 / 3.0);
let m = Gaussian::from_ms(0.0, 1.0);
let r = m / n;
let r = m.cavity(n);
assert!((r.mu() - (-0.3652597402597402)).abs() < 1e-10);
assert!((r.sigma() - 1.0072787050317253).abs() < 1e-10);
}
#[test]
fn test_n00_is_add_identity() {
// N00 (sigma=0) is the additive identity for the variance-convolution Add op.
// N_INF (sigma=inf) is the identity for the EP-product Mul op.
// N00 (sigma=0) is the identity for `convolve`.
// N_INF (sigma=inf) is the identity for `ep_product`.
let g = Gaussian::from_ms(3.0, 2.0);
let n00 = Gaussian::from_ms(0.0, 0.0);
let r = n00 + g;
let r = n00.convolve(g);
assert!((r.mu() - g.mu()).abs() < 1e-12);
assert!((r.sigma() - g.sigma()).abs() < 1e-12);
}
#[test]
fn test_mul_is_factor_product() {
// n * m in nat-params should be pi_n + pi_m, tau_n + tau_m
fn ep_product_adds_natural_parameters() {
// `ep_product` in nat-params should be pi_n + pi_m, tau_n + tau_m
let n = Gaussian::from_ms(2.0, 3.0);
let m = Gaussian::from_ms(1.0, 2.0);
let r = n * m;
let r = n.ep_product(m);
let expected_pi = n.pi() + m.pi();
let expected_tau = n.tau() + m.tau();
assert!((r.pi() - expected_pi).abs() < 1e-15);
@@ -451,10 +473,10 @@ mod tests {
}
#[test]
fn test_div_is_cavity() {
fn cavity_subtracts_natural_parameters() {
let n = Gaussian::from_ms(2.0, 1.0);
let m = Gaussian::from_ms(1.0, 2.0);
let r = n / m;
let r = n.cavity(m);
let expected_pi = n.pi() - m.pi();
let expected_tau = n.tau() - m.tau();
assert!((r.pi() - expected_pi).abs() < 1e-15);
src/history.rs
+3 -2
View File
@@ -1284,8 +1284,9 @@ impl<T: Time, D: Drift<T>, O: Observer<T>, K: Eq + Hash + Clone> History<T, D, O
let performances = skills
.iter()
.map(|team| {
team.iter()
.fold(crate::N00, |acc, s| acc + s.forget(self.beta.powi(2)))
team.iter().fold(crate::N00, |acc, s| {
acc.convolve(s.forget(self.beta.powi(2)))
})
})
.collect();
let sizes = skills.iter().map(Vec::len).collect();
src/time_slice.rs
+10 -7
View File
@@ -26,7 +26,9 @@ pub(crate) struct Skill {
impl Skill {
pub(crate) fn posterior(&self) -> Gaussian {
self.likelihood * self.backward * self.forward
self.likelihood
.ep_product(self.backward)
.ep_product(self.forward)
}
}
@@ -74,7 +76,7 @@ impl Item {
if forward {
Rating::new(skill.forward, r.beta, r.drift).with_drift_scale(r.drift_scale)
} else {
Rating::new(skill.posterior() / self.likelihood, r.beta, r.drift)
Rating::new(skill.posterior().cavity(self.likelihood), r.beta, r.drift)
.with_drift_scale(r.drift_scale)
}
}
@@ -171,7 +173,7 @@ impl Event {
for (i, item) in team.items.iter_mut().enumerate() {
let fresh = update.likelihoods[t][i];
let old_likelihood = skills.at(item.slot).likelihood;
let new_likelihood = (old_likelihood / item.likelihood) * fresh;
let new_likelihood = old_likelihood.cavity(item.likelihood).ep_product(fresh);
skills.at_mut(item.slot).likelihood = new_likelihood;
item.likelihood = fresh;
}
@@ -435,8 +437,9 @@ impl<T: Time> TimeSlice<T> {
for (t, team) in event.teams.iter_mut().enumerate() {
for (i, item) in team.items.iter_mut().enumerate() {
let old_likelihood = self.skills.at(item.slot).likelihood;
let new_likelihood =
(old_likelihood / item.likelihood) * g.likelihoods[t][i];
let new_likelihood = old_likelihood
.cavity(item.likelihood)
.ep_product(g.likelihoods[t][i]);
self.skills.at_mut(item.slot).likelihood = new_likelihood;
item.likelihood = g.likelihoods[t][i];
}
@@ -586,7 +589,7 @@ impl<T: Time> TimeSlice<T> {
pub(crate) fn forward_prior_out(&self, competitor: &Index) -> Gaussian {
let skill = self.skills.get(*competitor).unwrap();
skill.forward * skill.likelihood
skill.forward.ep_product(skill.likelihood)
}
pub(crate) fn backward_prior_out<D: Drift<T>>(
@@ -595,7 +598,7 @@ impl<T: Time> TimeSlice<T> {
competitors: &CompetitorStore<T, D>,
) -> Gaussian {
let skill = self.skills.get(*competitor).unwrap();
let n = skill.likelihood * skill.backward;
let n = skill.likelihood.ep_product(skill.backward);
n.forget(
competitors[*competitor]
.rating