gamlss-spline 0.2.1

Spline bases, penalties, and metadata for GAMLSS modeling
Documentation 
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147

use gamlss_core::{Link, PredictorBlock, Softplus};

use crate::SplineError;
use crate::ispline::ISplineBasis;

/// Direction of a hard-monotone I-spline predictor.
#[derive(Debug, Clone, Copy, PartialEq, Eq)]
pub enum MonotoneDirection {
    /// Nondecreasing predictor.
    Increasing,
    /// Nonincreasing predictor.
    Decreasing,
}

impl MonotoneDirection {
    fn sign(self) -> f64 {
        match self {
            Self::Increasing => 1.0,
            Self::Decreasing => -1.0,
        }
    }
}

/// Hard-monotone I-spline predictor using softplus-constrained increments.
#[derive(Debug, Clone, PartialEq)]
pub struct MonotoneISplineDesign {
    x: Vec<f64>,
    basis: ISplineBasis,
    direction: MonotoneDirection,
}

impl MonotoneISplineDesign {
    /// Creates a monotone I-spline predictor.
    pub fn new(
        x: &[f64],
        basis: ISplineBasis,
        direction: MonotoneDirection,
    ) -> Result<Self, SplineError> {
        if x.iter().any(|value| !value.is_finite()) {
            return Err(SplineError::NonFiniteValue);
        }
        Ok(Self {
            x: x.to_vec(),
            basis,
            direction,
        })
    }

    /// Returns the basis metadata.
    #[must_use]
    pub fn basis(&self) -> &ISplineBasis {
        &self.basis
    }

    /// Input coordinates.
    #[must_use]
    pub fn x(&self) -> &[f64] {
        &self.x
    }

    /// Number of positive increments.
    #[must_use]
    pub fn n_increments(&self) -> usize {
        self.basis.n_basis()
    }

    /// Monotonicity direction.
    #[must_use]
    pub fn direction(&self) -> MonotoneDirection {
        self.direction
    }

    /// Predictor derivative with respect to `x`.
    #[must_use]
    pub fn eta_derivative_row(&self, row: usize, beta: &[f64]) -> f64 {
        debug_assert!(row < self.x.len());
        debug_assert_eq!(beta.len(), self.nparams());

        let sign = self.direction.sign();
        self.basis
            .evaluate_derivative(self.x[row])
            .iter()
            .zip(&beta[1..])
            .map(|(basis, beta)| sign * Softplus::inverse(*beta) * basis)
            .sum()
    }

    fn add_row_gradient(&self, row: usize, score: f64, beta: &[f64], grad: &mut [f64]) {
        let sign = self.direction.sign();
        grad[0] += score;
        for (index, basis) in self.basis.evaluate(self.x[row]).into_iter().enumerate() {
            grad[index + 1] += score * sign * basis * Softplus::derivative_inverse(beta[index + 1]);
        }
    }
}

impl PredictorBlock for MonotoneISplineDesign {
    fn nrows(&self) -> usize {
        self.x.len()
    }

    fn nparams(&self) -> usize {
        1 + self.basis.n_basis()
    }

    fn eta_row(&self, row: usize, beta: &[f64]) -> f64 {
        debug_assert!(row < self.x.len());
        debug_assert_eq!(beta.len(), self.nparams());

        let sign = self.direction.sign();
        beta[0]
            + self
                .basis
                .evaluate(self.x[row])
                .iter()
                .zip(&beta[1..])
                .map(|(basis, beta)| sign * Softplus::inverse(*beta) * basis)
                .sum::<f64>()
    }

    fn add_gradient(&self, scores: &[f64], beta: &[f64], grad: &mut [f64]) {
        debug_assert_eq!(scores.len(), self.x.len());
        debug_assert_eq!(beta.len(), self.nparams());
        debug_assert_eq!(grad.len(), self.nparams());

        for (row, score) in scores.iter().copied().enumerate() {
            self.add_row_gradient(row, score, beta, grad);
        }
    }

    fn add_weighted_gradient(
        &self,
        scores: &[f64],
        multiplier: &[f64],
        beta: &[f64],
        grad: &mut [f64],
    ) {
        debug_assert_eq!(scores.len(), self.x.len());
        debug_assert_eq!(multiplier.len(), self.x.len());
        debug_assert_eq!(beta.len(), self.nparams());
        debug_assert_eq!(grad.len(), self.nparams());

        for (row, (&score, &multiplier)) in scores.iter().zip(multiplier).enumerate() {
            self.add_row_gradient(row, score * multiplier, beta, grad);
        }
    }
}