compute 0.2.3

A crate for statistical computing.
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
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217

use super::Optimizer;
use crate::prelude::Vector;
use approx_eq::rel_diff;
use reverse::*;

/// Implements the Adam optimizer. See [Kingma and Ba 2014](https://arxiv.org/abs/1412.6980) for
/// details about the algorithm.
///
/// # Examples
///
/// ```rust
/// // optimize the [Rosenbrock function](https://en.wikipedia.org/wiki/Rosenbrock_function)
/// // with fixed parameters `a = 1` and `b = 100`.
/// // the minimum value is at (1, 1), which is what we will try to recover
///
/// use compute::optimize::*;
/// use approx_eq::assert_approx_eq;
/// use reverse::Var;
///
/// fn rosenbrock<'a>(p: &[Var<'a>], d: &[&[f64]]) -> Var<'a> {
///     assert_eq!(p.len(), 2);
///     assert_eq!(d.len(), 1);
///     assert_eq!(d[0].len(), 2);
///
///     let (x, y) = (p[0], p[1]);
///     let (a, b) = (d[0][0], d[0][1]);
///
///     (a - x).powi(2) + b * (y - x.powi(2)).powi(2)
/// }
///
/// let init = [0., 0.];
/// let optim = Adam::with_stepsize(5e-4);
/// let popt = optim.optimize(rosenbrock, &init, &[&[1., 100.]], 10000);
///
/// assert_approx_eq!(popt[0], 1.);
/// assert_approx_eq!(popt[1], 1.);
/// ```
#[derive(Debug, Clone)]
pub struct Adam {
    stepsize: f64, // step size
    beta1: f64,    // exponential decay rate for first moment
    beta2: f64,    // exponential decay rate for second moment
    epsilon: f64,  // small number to prevent division by zero
    tape: Tape,    // tape for gradients
}

impl Adam {
    /// Create a new Adam optimizer.
    /// stepsize: step size
    /// beta1: exponential decay rate for first moment
    /// beta2: exponential decay rate for second moment
    /// epsilon: small number to prevent division by zero
    pub fn new(stepsize: f64, beta1: f64, beta2: f64, epsilon: f64) -> Self {
        assert!(beta1 > 0., "beta1 must be positive");
        assert!(beta2 > 0., "beta2 must be positive");
        Adam {
            stepsize,
            beta1,
            beta2,
            epsilon,
            tape: Tape::new(),
        }
    }
    pub fn set_stepsize(&mut self, stepsize: f64) {
        self.stepsize = stepsize;
    }
    pub fn with_stepsize(stepsize: f64) -> Self {
        let mut adam = Self::default();
        adam.set_stepsize(stepsize);
        adam
    }
}

impl Default for Adam {
    /// Uses the defaults recommended by Kingma and Ba 2014
    fn default() -> Self {
        Self::new(0.001, 0.9, 0.999, 1e-8)
    }
}

impl Optimizer for Adam {
    type Output = Vector;
    /// Run the optimization algorithm, given a vector of parameters to optimize and a function which calculates the residuals.
    fn optimize<F>(
        &self,
        f: F,
        parameters: &[f64],
        data: &[&[f64]],
        maxsteps: usize,
    ) -> Self::Output
    where
        F: for<'a> Fn(&[Var<'a>], &[&[f64]]) -> Var<'a>,
    {
        self.tape.clear();
        let mut params = parameters
            .iter()
            .map(|&x| self.tape.add_var(x))
            .collect::<Vec<_>>();
        let param_len = params.len();

        let mut t: usize = 0;
        let mut m = Vector::zeros(param_len);
        let mut v = Vector::zeros(param_len);
        let mut converged = false;

        while t < maxsteps && !converged {
            t += 1;

            let prev_params = params.clone();

            let res = f(&params, data);

            eprintln!("t = {:?}, res = {}", t, res.val());

            let grad = res.grad().wrt(&params);

            for p in 0..param_len {
                m[p] = self.beta1 * m[p] + (1. - self.beta1) * grad[p]; // biased first moment estimate
                v[p] = self.beta2 * v[p] + (1. - self.beta2) * grad[p] * grad[p]; // biased second moment estimate
                let mhat = m[p] / (1. - self.beta1.powi(t as i32)); // bias-corrected first moment estimate
                let vhat = v[p] / (1. - self.beta2.powi(t as i32)); // bias-corrected second moment estimate
                params[p] = params[p] - self.stepsize * mhat / (vhat.sqrt() + self.epsilon);
            }

            if crate::statistics::max(
                &(0..param_len)
                    .map(|i| rel_diff(params[i].val(), prev_params[i].val()))
                    .collect::<Vec<_>>(),
            ) < f64::EPSILON
            {
                converged = true;
            }

            // clear gradients and intermediate variables
            self.tape.clear();
            params = params
                .iter()
                .map(|&x| self.tape.add_var(x.val()))
                .collect::<Vec<_>>();
        }

        Vector::new(params.iter().map(|x| x.val()).collect::<Vec<_>>())
    }
}

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

    #[test]
    fn test_adam_slr() {
        let x = vec![
            0., 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.,
        ];
        // actual coefficients
        let coeffs = vec![5., -2.5];
        let y = [
            5., 2.5, 0., -2.5, -5., -7.5, -10., -12.5, -15., -17.5, -20., -22.5, -25., -27.5, -30.,
            -32.5, -35., -37.5, -40., -42.5, -45., -47.5, -50., -52.5, -55., -57.5, -60., -62.5,
            -65., -67.5, -70., -72.5, -75., -77.5, -80., -82.5, -85., -87.5, -90., -92.5, -95.,
            -97.5, -100., -102.5, -105., -107.5, -110., -112.5, -115., -117.5, -120., -122.5,
            -125., -127.5, -130., -132.5, -135., -137.5, -140., -142.5, -145., -147.5, -150.,
            -152.5, -155., -157.5, -160., -162.5, -165., -167.5, -170., -172.5, -175., -177.5,
            -180., -182.5, -185., -187.5, -190., -192.5, -195., -197.5, -200., -202.5, -205.,
            -207.5, -210., -212.5, -215., -217.5, -220., -222.5, -225., -227.5, -230., -232.5,
            -235., -237.5, -240., -242.5,
        ];

        fn fn_resid<'a>(params: &[Var<'a>], data: &[&[f64]]) -> Var<'a> {
            let (x, y) = (data[0], data[1]);
            x.iter()
                .zip(y)
                .map(|(&xv, &yv)| ((params[0] + xv * params[1]) - yv).powi(2))
                .sum()
        }

        let mut optim = Adam::default();
        optim.set_stepsize(0.1);
        let est_params = optim.optimize(fn_resid, &[1., 1.], &[&x, &y], 5000);

        for i in 0..2 {
            assert_approx_eq!(est_params[i], coeffs[i], 0.01);
        }
    }

    #[test]
    // #[ignore]
    fn test_adam_rosenbrock() {
        // optimize the [Rosenbrock function](https://en.wikipedia.org/wiki/Rosenbrock_function)
        // with fixed parameters `a = 1` and `b = 100`.
        // the minimum value is at (1, 1), which is what we will try to recover

        fn rosenbrock<'a>(p: &[Var<'a>], d: &[&[f64]]) -> Var<'a> {
            assert_eq!(p.len(), 2);
            assert_eq!(d.len(), 1);
            assert_eq!(d[0].len(), 2);

            let (x, y) = (p[0], p[1]);
            let (a, b) = (d[0][0], d[0][1]);

            (a - x).powi(2) + b * (y - x.powi(2)).powi(2)
        }

        let init = [0., 0.];
        let optim = Adam::with_stepsize(5e-4);
        let popt = optim.optimize(rosenbrock, &init, &[&[1., 100.]], 10000);

        assert_approx_eq!(popt[0], 1.);
        assert_approx_eq!(popt[1], 1.);
    }
}