opendp 0.4.0

A library of differential privacy algorithms for the statistical analysis of sensitive private data.
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
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255

use std::f64::consts::SQRT_2;

use num::{Float, One, Zero};
use statrs::function::erf::erf_inv;

use crate::error::Fallible;
use crate::traits::InfCast;
use std::fmt::Debug;

pub fn laplacian_scale_to_accuracy<T: Float + Zero + One + Debug>(scale: T, alpha: T) -> Fallible<T> {
    if scale.is_sign_negative() {
        return fallible!(InvalidDistance, "scale may not be negative")
    }
    if alpha <= T::zero() || T::one() < alpha {
        return fallible!(InvalidDistance, "alpha ({:?}) must be in (0, 1]")
    }
    Ok(scale * alpha.recip().ln())
}

pub fn accuracy_to_laplacian_scale<T: Float + Zero + One + Debug>(accuracy: T, alpha: T) -> Fallible<T> {
    if accuracy.is_sign_negative() {
        return fallible!(InvalidDistance, "accuracy may not be negative")
    }
    if alpha <= T::zero() || T::one() <= alpha {
        return fallible!(InvalidDistance, "alpha ({:?}) must be in (0, 1)")
    }
    Ok(accuracy / alpha.recip().ln())
}

pub fn gaussian_scale_to_accuracy<T>(scale: T, alpha: T) -> Fallible<T>
    where f64: InfCast<T>, T: InfCast<f64> {
    let scale = f64::inf_cast(scale)?;
    let alpha = f64::inf_cast(alpha)?;
    if scale.is_sign_negative() {
        return fallible!(InvalidDistance, "scale may not be negative")
    }
    if alpha <= 0. || 1. < alpha {
        return fallible!(InvalidDistance, "alpha ({:?}) must be in (0, 1]")
    }
    T::inf_cast(scale * SQRT_2 * erf_inv(1. - alpha))
}

pub fn accuracy_to_gaussian_scale<T>(accuracy: T, alpha: T) -> Fallible<T>
    where f64: InfCast<T>, T: InfCast<f64> {
    let accuracy = f64::inf_cast(accuracy)?;
    let alpha = f64::inf_cast(alpha)?;
    if accuracy.is_sign_negative() {
        return fallible!(InvalidDistance, "accuracy may not be negative")
    }
    if alpha <= 0. || 1. <= alpha {
        return fallible!(InvalidDistance, "alpha ({:?}) must be in (0, 1)")
    }
    T::inf_cast(accuracy / SQRT_2 / erf_inv(1. - alpha))
}


#[cfg(test)]
pub mod test {
    use std::fmt::Debug;
    use std::ops::{Mul, Sub};

    use super::*;
    use crate::meas::{make_base_laplace, make_base_gaussian, make_base_geometric};
    use crate::error::ExplainUnwrap;
    use crate::dom::AllDomain;

    fn print_statement<T: Copy + Debug + One + From<i8> + Sub<Output=T> + Mul<Output=T>>(dist: &str, scale: T, accuracy: T, alpha: T) {
        let _100 = T::from(100);
        println!("When the {dist} scale is {scale:?}, the DP estimate differs from the true value \
                    by no more than {accuracy:?} at a level-alpha of {alpha:?}, \
                    or with (1 - {alpha:?})100% = {perc:.2?}% confidence.",
                 dist = dist, scale = scale,
                 accuracy = accuracy, alpha = alpha, perc = (T::one() - alpha) * _100);
    }

    #[test]
    fn test_laplacian_scale_to_accuracy() -> Fallible<()> {
        macro_rules! check_laplacian_scale_to_accuracy {(scale=$scale:literal, alpha=$alpha:literal) =>
            (print_statement("laplacian", $scale, laplacian_scale_to_accuracy($scale, $alpha)?, $alpha))
        }
        check_laplacian_scale_to_accuracy!(scale=1., alpha=0.05);
        check_laplacian_scale_to_accuracy!(scale=2., alpha=0.05);
        check_laplacian_scale_to_accuracy!(scale=0., alpha=0.55);
        Ok(())
    }

    #[test]
    pub fn test_accuracy_to_laplacian_scale() -> Fallible<()> {
        macro_rules! check_accuracy_to_laplacian_scale {(accuracy=$accuracy:literal, alpha=$alpha:literal) =>
            (print_statement("laplacian", accuracy_to_laplacian_scale($accuracy, $alpha)?, $accuracy, $alpha))
        }
        check_accuracy_to_laplacian_scale!(accuracy=1., alpha=0.05);
        check_accuracy_to_laplacian_scale!(accuracy=2., alpha=0.05);
        check_accuracy_to_laplacian_scale!(accuracy=0.01, alpha=0.1);
        Ok(())
    }

    #[test]
    pub fn test_gaussian_scale_to_accuracy() -> Fallible<()> {
        macro_rules! check_gaussian_scale_to_accuracy {(scale=$scale:literal, alpha=$alpha:literal) =>
            (print_statement("gaussian", $scale, gaussian_scale_to_accuracy($scale, $alpha)?, $alpha))
        }

        check_gaussian_scale_to_accuracy!(scale=1., alpha=0.05);
        check_gaussian_scale_to_accuracy!(scale=2., alpha=0.10);
        check_gaussian_scale_to_accuracy!(scale=3., alpha=0.55);
        Ok(())
    }

    #[test]
    pub fn test_accuracy_to_gaussian_scale() -> Fallible<()> {
        macro_rules! check_accuracy_to_gaussian_scale {(accuracy=$accuracy:literal, alpha=$alpha:literal) =>
            (print_statement("gaussian", accuracy_to_gaussian_scale($accuracy, $alpha)?, $accuracy, $alpha))
        }
        check_accuracy_to_gaussian_scale!(accuracy=1., alpha=0.05);
        check_accuracy_to_gaussian_scale!(accuracy=2., alpha=0.05);
        check_accuracy_to_gaussian_scale!(accuracy=1.2, alpha=0.1);
        Ok(())
    }


    #[test]
    fn test_relative_laplacian_scale_to_accuracy() -> Fallible<()> {
        // fix the scale.
        // you get a tighter accuracy interval when you require greater statistical significance
        // a higher confidence accuracy interval is wider than a lower confidence accuracy interval
        assert!(laplacian_scale_to_accuracy(1., 0.05)? // 95% confidence
            > laplacian_scale_to_accuracy(1., 0.06)?); // 94% confidence

        // fix the alpha/statistical significance.
        // you get a tighter accuracy interval when there is less noise
        // a less noisy sample produces a tighter/smaller accuracy interval
        assert!(laplacian_scale_to_accuracy(2., 0.05)? // 95% confidence
            > laplacian_scale_to_accuracy(1., 0.05)?); // 95% confidence

        Ok(())
    }

    #[test]
    pub fn test_relative_accuracy_to_laplacian_scale() -> Fallible<()> {
        // fix the size of the accuracy interval.
        // if I want more confidence in the result, then I should have less noise
        // you get a larger noise scale when you require greater statistical significance
        // a higher confidence laplace scale is smaller than a lower confidence laplace scale
        assert!(accuracy_to_laplacian_scale(1., 0.05)? // 95% confidence
            < accuracy_to_laplacian_scale(1., 0.06)?); // 94% confidence

        // fix alpha/statistical significance.
        // you get a larger noise scale when there is a wider accuracy interval
        assert!(accuracy_to_laplacian_scale(2., 0.05)? // 95% confidence
            > accuracy_to_laplacian_scale(1., 0.05)?); // 95% confidence

        Ok(())
    }

    #[test]
    pub fn test_relative_gaussian_scale_to_accuracy() -> Fallible<()> {
        // fix the scale.
        // you get a tighter accuracy interval when you require greater statistical significance
        // a higher confidence accuracy interval is wider than a lower confidence accuracy interval
        assert!(gaussian_scale_to_accuracy(1., 0.05)? // 95% confidence
            > gaussian_scale_to_accuracy(1., 0.06)?); // 94% confidence

        // fix the alpha/statistical significance.
        // you get a tighter accuracy interval when there is less noise
        // a less noisy sample produces a tighter/smaller accuracy interval
        assert!(gaussian_scale_to_accuracy(2., 0.05)? // 95% confidence
            > gaussian_scale_to_accuracy(1., 0.05)?); // 95% confidence

        Ok(())
    }

    #[test]
    pub fn test_relative_accuracy_to_gaussian_scale() -> Fallible<()> {
        // fix the size of the accuracy interval.
        // if I want more confidence in the result, then I should have less noise
        // you get a larger noise scale when you require greater statistical significance
        // a higher confidence noise scale is smaller than a lower confidence noise scale
        assert!(accuracy_to_gaussian_scale(1., 0.05)? // 95% confidence
            < accuracy_to_gaussian_scale(1., 0.06)?); // 94% confidence

        // fix alpha/statistical significance.
        // you get a larger noise scale when there is a wider accuracy interval
        assert!(accuracy_to_gaussian_scale(2., 0.05)? // 95% confidence
            > accuracy_to_gaussian_scale(1., 0.05)?); // 95% confidence
        Ok(())
    }

    #[test]
    pub fn test_empirical_laplace_accuracy() -> Fallible<()> {
        let accuracy = 1.0;
        let theoretical_alpha = 0.05;
        let scale = accuracy_to_laplacian_scale(accuracy, theoretical_alpha)?;
        let base_laplace = make_base_laplace::<AllDomain<f64>>(scale)?;
        let n = 50_000;
        let empirical_alpha = (0..n)
            .filter(|_| base_laplace.invoke(&0.0).unwrap_test().abs() > accuracy)
            .count() as f64 / n as f64;

        println!("Laplacian significance levels/alpha");
        println!("Theoretical: {:?}", theoretical_alpha);
        println!("Empirical:   {:?}", empirical_alpha);
        assert!((empirical_alpha - theoretical_alpha).abs() < 1e-2);
        Ok(())
    }

    #[test]
    pub fn test_empirical_gaussian_accuracy() -> Fallible<()> {
        let accuracy = 1.0;
        let theoretical_alpha = 0.05;
        let scale = accuracy_to_gaussian_scale(accuracy, theoretical_alpha)?;
        let base_gaussian = make_base_gaussian::<AllDomain<f64>>(scale)?;
        let n = 50_000;
        let empirical_alpha = (0..n)
            .filter(|_| base_gaussian.invoke(&0.0).unwrap_test().abs() > accuracy)
            .count() as f64 / n as f64;

        println!("Gaussian significance levels/alpha");
        println!("Theoretical: {:?}", theoretical_alpha);
        println!("Empirical:   {:?}", empirical_alpha);
        assert!((empirical_alpha - theoretical_alpha).abs() < 1e-2);
        Ok(())
    }

    #[test]
    pub fn test_empirical_geometric_accuracy() -> Fallible<()> {
        let accuracy = 25;
        let theoretical_alpha = 0.05;
        let scale = accuracy_to_laplacian_scale(accuracy as f64, theoretical_alpha)?;
        println!("scale: {}", scale);
        let base_geometric = make_base_geometric::<AllDomain<i8>, f64>(scale, None)?;
        let n = 50_000;
        let empirical_alpha = (0..n)
            .filter(|_| base_geometric.invoke(&0).unwrap_test().abs() >= accuracy)
            .count() as f64 / n as f64;

        println!("Geometric significance levels/alpha");
        println!("Theoretical: {:?}", theoretical_alpha);
        println!("Empirical:   {:?}", empirical_alpha);
        assert!((empirical_alpha - theoretical_alpha).abs() < 1e-2);
        Ok(())
    }

    #[test]
    pub fn test_roundtrip() -> Fallible<()> {
        let accuracy = 1.;
        let alpha = 0.05;
        let accuracy_2 = gaussian_scale_to_accuracy(accuracy_to_gaussian_scale(accuracy, alpha)?, alpha)?;
        assert!((accuracy - accuracy_2).abs() < 1e-8);

        let accuracy_2 = laplacian_scale_to_accuracy(accuracy_to_laplacian_scale(accuracy, alpha)?, alpha)?;
        assert!((accuracy - accuracy_2).abs() < 1e-8);
        Ok(())
    }
}