irithyll_core/loss/
squared.rs

1//! Squared error loss for regression.
2//!
3//! L(y, f) = 0.5 * (f - y)^2
4//!
5//! The default choice for regression tasks. Gradient is simply the residual,
6//! and the hessian is a constant 1.0, making Newton steps equivalent to
7//! gradient steps.
8
9use super::Loss;
10
11/// Mean squared error loss (L2 loss, scaled by 0.5).
12///
13/// Optimal for regression when the noise is Gaussian.
14/// Sensitive to outliers -- consider [`HuberLoss`](super::huber::HuberLoss)
15/// for heavy-tailed distributions.
16#[derive(Debug, Clone, Copy)]
17pub struct SquaredLoss;
18
19impl Loss for SquaredLoss {
20    #[inline]
21    fn n_outputs(&self) -> usize {
22        1
23    }
24
25    #[inline]
26    fn gradient(&self, target: f64, prediction: f64) -> f64 {
27        prediction - target
28    }
29
30    #[inline]
31    fn hessian(&self, _target: f64, _prediction: f64) -> f64 {
32        1.0
33    }
34
35    #[inline]
36    fn loss(&self, target: f64, prediction: f64) -> f64 {
37        let r = prediction - target;
38        0.5 * r * r
39    }
40
41    #[inline]
42    fn predict_transform(&self, raw: f64) -> f64 {
43        raw
44    }
45
46    fn initial_prediction(&self, targets: &[f64]) -> f64 {
47        if targets.is_empty() {
48            return 0.0;
49        }
50        let sum: f64 = targets.iter().sum();
51        sum / targets.len() as f64
52    }
53
54    fn loss_type(&self) -> Option<super::LossType> {
55        Some(super::LossType::Squared)
56    }
57}
58
59#[cfg(test)]
60mod tests {
61    use super::*;
62
63    const EPS: f64 = 1e-12;
64
65    #[test]
66    fn test_n_outputs() {
67        assert_eq!(SquaredLoss.n_outputs(), 1);
68    }
69
70    #[test]
71    fn test_gradient_at_known_points() {
72        let loss = SquaredLoss;
73        assert!((loss.gradient(3.0, 3.0)).abs() < EPS);
74        assert!((loss.gradient(1.0, 4.0) - 3.0).abs() < EPS);
75        assert!((loss.gradient(5.0, 2.0) - (-3.0)).abs() < EPS);
76    }
77
78    #[test]
79    fn test_hessian_is_constant() {
80        let loss = SquaredLoss;
81        assert!((loss.hessian(0.0, 0.0) - 1.0).abs() < EPS);
82        assert!((loss.hessian(100.0, -50.0) - 1.0).abs() < EPS);
83        assert!((loss.hessian(-7.0, 42.0) - 1.0).abs() < EPS);
84    }
85
86    #[test]
87    fn test_loss_value() {
88        let loss = SquaredLoss;
89        assert!((loss.loss(1.0, 3.0) - 2.0).abs() < EPS);
90        assert!((loss.loss(5.0, 5.0)).abs() < EPS);
91        assert!((loss.loss(0.0, 1.0) - 0.5).abs() < EPS);
92    }
93
94    #[test]
95    fn test_predict_transform_is_identity() {
96        let loss = SquaredLoss;
97        assert!((loss.predict_transform(42.0) - 42.0).abs() < EPS);
98        assert!((loss.predict_transform(-3.25) - (-3.25)).abs() < EPS);
99    }
100
101    #[test]
102    fn test_initial_prediction_is_mean() {
103        let loss = SquaredLoss;
104        let targets = [1.0, 2.0, 3.0, 4.0, 5.0];
105        assert!((loss.initial_prediction(&targets) - 3.0).abs() < EPS);
106
107        let single = [7.0];
108        assert!((loss.initial_prediction(&single) - 7.0).abs() < EPS);
109    }
110
111    #[test]
112    fn test_initial_prediction_empty() {
113        let loss = SquaredLoss;
114        assert!((loss.initial_prediction(&[])).abs() < EPS);
115    }
116
117    #[test]
118    fn test_gradient_is_derivative_of_loss() {
119        let loss = SquaredLoss;
120        let target = 2.5;
121        let pred = 4.0;
122        let h = 1e-6;
123        let numerical = (loss.loss(target, pred + h) - loss.loss(target, pred - h)) / (2.0 * h);
124        let analytical = loss.gradient(target, pred);
125        assert!((numerical - analytical).abs() < 1e-5);
126    }
127}
irithyll_core/loss/squared.rs

irithyll_core/loss/
squared.rs
