trueskill-tt/src/factor/margin.rs

use crate::{
    N_INF,
    factor::{Factor, VarId, VarStore},
    gaussian::Gaussian,
    pdf,
};

/// Gaussian observation factor on a diff variable.
///
/// Encodes the soft evidence `m_obs ~ N(diff, sigma²)`. The outgoing message
/// to `diff` is the constant `N(m_obs, sigma²)`, so this factor converges in a
/// single propagation: subsequent calls return a zero delta.
#[derive(Debug)]
pub struct MarginFactor {
    pub diff: VarId,
    pub m_obs: f64,
    pub sigma: f64,
    pub(crate) msg: Gaussian,
    pub(crate) evidence_cached: Option<f64>,
}

impl MarginFactor {
    #[must_use]
    pub fn new(diff: VarId, m_obs: f64, sigma: f64) -> Self {
        debug_assert!(sigma > 0.0, "score sigma must be positive");
        Self {
            diff,
            m_obs,
            sigma,
            msg: N_INF,
            evidence_cached: None,
        }
    }
}

impl MarginFactor {
    /// Propagate this factor's message, optionally damping the update in
    /// natural-parameter space. `alpha = 1.0` matches `Factor::propagate`
    /// 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;

        if self.evidence_cached.is_none() {
            self.evidence_cached = Some(cavity_evidence(cavity, self.m_obs, self.sigma));
        }

        let new_msg = Gaussian::from_ms(self.m_obs, self.sigma);
        let damped = self.msg.damp_natural(new_msg, alpha);
        let old_msg = self.msg;
        self.msg = damped;
        vars.set(self.diff, cavity * damped);

        old_msg.delta(damped)
    }
}

impl Factor for MarginFactor {
    fn propagate(&mut self, vars: &mut VarStore) -> (f64, f64) {
        self.propagate_with_alpha(vars, 1.0)
    }

    fn log_evidence(&self, _vars: &VarStore) -> f64 {
        self.evidence_cached.unwrap_or(1.0).ln()
    }
}

/// Density of the observed margin under the cavity, clamped to a positive
/// floor so a far-out observation cannot underflow to `0.0` and make
/// `log_evidence` `-inf`.
fn cavity_evidence(cavity: Gaussian, m_obs: f64, sigma: f64) -> f64 {
    let combined_sigma = (cavity.sigma().powi(2) + sigma.powi(2)).sqrt();

    pdf(m_obs, cavity.mu(), combined_sigma).max(f64::MIN_POSITIVE)
}

#[cfg(test)]
mod tests {
    use super::*;

    #[test]
    fn first_propagate_writes_tilted_marginal() {
        let mut vars = VarStore::new();
        let diff = vars.alloc(Gaussian::from_ms(0.0, 6.0));
        let mut f = MarginFactor::new(diff, 5.0, 1.0);

        f.propagate(&mut vars);

        let result = vars.get(diff);
        // pi = 1/36 + 1 ≈ 1.027778; tau = 0 + 5 = 5
        // mu = 5 / 1.027778 ≈ 4.864865; sigma = 1/sqrt(1.027778) ≈ 0.986394
        assert!((result.mu() - 4.864864864864865).abs() < 1e-12);
        assert!((result.sigma() - 0.986393923832144).abs() < 1e-12);
    }

    #[test]
    fn converges_in_one_step() {
        let mut vars = VarStore::new();
        let diff = vars.alloc(Gaussian::from_ms(0.0, 6.0));
        let mut f = MarginFactor::new(diff, 5.0, 1.0);

        f.propagate(&mut vars);
        let (dmu, dsig) = f.propagate(&mut vars);
        assert!(
            dmu < 1e-12,
            "expected ~0 delta on second propagate, got {dmu}"
        );
        assert!(dsig < 1e-12);
    }

    #[test]
    fn evidence_cached_on_first_propagate() {
        let mut vars = VarStore::new();
        let diff = vars.alloc(Gaussian::from_ms(0.0, 6.0));
        let mut f = MarginFactor::new(diff, 5.0, 1.0);
        assert!(f.evidence_cached.is_none());

        f.propagate(&mut vars);
        let z = f.evidence_cached.unwrap();
        // pdf(5, 0, sqrt(37)) ≈ 0.046783
        assert!((z - 0.04678300292616668).abs() < 1e-10);

        // Subsequent propagations don't change it.
        f.propagate(&mut vars);
        assert_eq!(f.evidence_cached.unwrap(), z);
    }

    #[test]
    fn log_evidence_matches_cached_ln() {
        let mut vars = VarStore::new();
        let diff = vars.alloc(Gaussian::from_ms(0.0, 6.0));
        let mut f = MarginFactor::new(diff, 5.0, 1.0);
        f.propagate(&mut vars);
        let logz = f.log_evidence(&vars);
        assert!((logz - (-3.062235327364623)).abs() < 1e-10);
    }

    #[test]
    fn propagate_with_alpha_one_matches_undamped_propagate() {
        let mut vars_a = VarStore::new();
        let diff_a = vars_a.alloc(Gaussian::from_ms(0.0, 6.0));
        let mut f_a = MarginFactor::new(diff_a, 5.0, 1.0);
        let delta_a = f_a.propagate(&mut vars_a);
        let result_a = vars_a.get(diff_a);

        let mut vars_b = VarStore::new();
        let diff_b = vars_b.alloc(Gaussian::from_ms(0.0, 6.0));
        let mut f_b = MarginFactor::new(diff_b, 5.0, 1.0);
        let delta_b = f_b.propagate_with_alpha(&mut vars_b, 1.0);
        let result_b = vars_b.get(diff_b);

        assert_eq!(result_a.pi(), result_b.pi());
        assert_eq!(result_a.tau(), result_b.tau());
        assert_eq!(delta_a, delta_b);
        assert_eq!(f_a.msg.pi(), f_b.msg.pi());
        assert_eq!(f_a.msg.tau(), f_b.msg.tau());
    }

    #[test]
    fn propagate_with_alpha_half_blends_msg_in_natural_params() {
        // Run undamped to capture (initial_msg, undamped_new_msg).
        let mut vars_full = VarStore::new();
        let diff_full = vars_full.alloc(Gaussian::from_ms(0.0, 6.0));
        let mut f_full = MarginFactor::new(diff_full, 5.0, 1.0);
        let initial_msg_pi = f_full.msg.pi();
        let initial_msg_tau = f_full.msg.tau();
        f_full.propagate(&mut vars_full);
        let undamped_msg_pi = f_full.msg.pi();
        let undamped_msg_tau = f_full.msg.tau();

        // Run damped at α = 0.5 from the same initial state.
        let mut vars_half = VarStore::new();
        let diff_half = vars_half.alloc(Gaussian::from_ms(0.0, 6.0));
        let mut f_half = MarginFactor::new(diff_half, 5.0, 1.0);
        f_half.propagate_with_alpha(&mut vars_half, 0.5);

        let expected_pi = 0.5 * undamped_msg_pi + 0.5 * initial_msg_pi;
        let expected_tau = 0.5 * undamped_msg_tau + 0.5 * initial_msg_tau;
        assert!((f_half.msg.pi() - expected_pi).abs() < 1e-12);
        assert!((f_half.msg.tau() - expected_tau).abs() < 1e-12);
    }
}