1 | // $Id: Perceptron.cc 3709 2017-11-08 22:49:06Z peter $ |
---|
2 | |
---|
3 | /* |
---|
4 | Copyright (C) 2017 Peter Johansson |
---|
5 | |
---|
6 | This file is part of the yat library, http://dev.thep.lu.se/yat |
---|
7 | |
---|
8 | The yat library is free software; you can redistribute it and/or |
---|
9 | modify it under the terms of the GNU General Public License as |
---|
10 | published by the Free Software Foundation; either version 3 of the |
---|
11 | License, or (at your option) any later version. |
---|
12 | |
---|
13 | The yat library is distributed in the hope that it will be useful, |
---|
14 | but WITHOUT ANY WARRANTY; without even the implied warranty of |
---|
15 | MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU |
---|
16 | General Public License for more details. |
---|
17 | |
---|
18 | You should have received a copy of the GNU General Public License |
---|
19 | along with yat. If not, see <http://www.gnu.org/licenses/>. |
---|
20 | */ |
---|
21 | |
---|
22 | #include <config.h> |
---|
23 | |
---|
24 | #include "Perceptron.h" |
---|
25 | |
---|
26 | #include "Target.h" |
---|
27 | |
---|
28 | #include "yat/utility/DiagonalMatrix.h" |
---|
29 | #include "yat/utility/Matrix.h" |
---|
30 | #include "yat/utility/Vector.h" |
---|
31 | |
---|
32 | #include <gsl/gsl_cdf.h> |
---|
33 | |
---|
34 | #include <cassert> |
---|
35 | #include <cmath> |
---|
36 | #include <cmath> |
---|
37 | |
---|
38 | namespace theplu { |
---|
39 | namespace yat { |
---|
40 | namespace classifier { |
---|
41 | |
---|
42 | const utility::Matrix& Perceptron::covariance(void) const |
---|
43 | { |
---|
44 | return covariance_; |
---|
45 | } |
---|
46 | |
---|
47 | |
---|
48 | double Perceptron::margin(size_t i, double alpha) const |
---|
49 | { |
---|
50 | return gsl_cdf_ugaussian_Qinv(alpha/2) * std::sqrt(covariance_(i, i)); |
---|
51 | } |
---|
52 | |
---|
53 | |
---|
54 | double Perceptron::oddsratio(size_t i) const |
---|
55 | { |
---|
56 | return std::exp(weight_(i)); |
---|
57 | } |
---|
58 | |
---|
59 | |
---|
60 | double Perceptron::oddsratio_lower_CI(size_t i, double alpha) const |
---|
61 | { |
---|
62 | return std::exp(weight_(i) - margin(i, alpha)); |
---|
63 | } |
---|
64 | |
---|
65 | |
---|
66 | double Perceptron::oddsratio_upper_CI(size_t i, double alpha) const |
---|
67 | { |
---|
68 | return std::exp(weight_(i) + margin(i, alpha)); |
---|
69 | } |
---|
70 | |
---|
71 | |
---|
72 | double Perceptron::p_value(size_t i) const |
---|
73 | { |
---|
74 | double z = weight_(i) / std::sqrt(covariance_(i, i)); |
---|
75 | return 2*gsl_cdf_ugaussian_Q(std::abs(z)); |
---|
76 | } |
---|
77 | |
---|
78 | |
---|
79 | double Perceptron::predict(const utility::VectorBase& x) const |
---|
80 | { |
---|
81 | assert(x.size() == weight_.size()); |
---|
82 | const double f = weight_ * x; |
---|
83 | return 1.0 / (1 + std::exp(-f)); |
---|
84 | } |
---|
85 | |
---|
86 | |
---|
87 | void Perceptron::train(const utility::Matrix& X, const Target& target) |
---|
88 | { |
---|
89 | size_t n = X.rows(); |
---|
90 | size_t p = X.columns(); |
---|
91 | |
---|
92 | assert(target.size() == n); |
---|
93 | weight_.resize(p); |
---|
94 | covariance_.resize(p, p); |
---|
95 | |
---|
96 | // weight vector is updated as |
---|
97 | // w = (X'SX)^-1 X' (SXw + y - mu) |
---|
98 | // X is n x p |
---|
99 | // mu is vector of (trained) expected values (see predict(1)) |
---|
100 | utility::Vector mu(n); |
---|
101 | // S is diagonal n x n with S_ii = mu_i (1 - mu_i) |
---|
102 | utility::DiagonalMatrix S(n, n); |
---|
103 | // y is binary vector |
---|
104 | utility::Vector y(n); |
---|
105 | for (size_t i=0; i<n; ++i) |
---|
106 | if (target.binary(i)) |
---|
107 | y(i) = 1.0; |
---|
108 | |
---|
109 | size_t max_epochs = 100; |
---|
110 | double sum_squared = 1.0; // some (relatively) large number |
---|
111 | for (size_t epoch=0; sum_squared > 1e-8 && epoch < max_epochs; ++epoch) { |
---|
112 | for (size_t i=0; i<mu.size(); ++i) { |
---|
113 | mu(i) = predict(X.row_const_view(i)); |
---|
114 | S(i) = mu(i) * (1.0 - mu(i)); |
---|
115 | } |
---|
116 | |
---|
117 | // w = (X'SX)^-1 X' (SXw + y - mu) |
---|
118 | assert(X.rows() == S.rows()); |
---|
119 | assert(S.columns() == X.rows()); |
---|
120 | utility::inverse_svd(transpose(X)*S*X, covariance_); |
---|
121 | |
---|
122 | assert(y.size() == mu.size()); |
---|
123 | utility::Vector delta = covariance_ * (transpose(X) * (y - mu)); |
---|
124 | weight_ += delta; |
---|
125 | sum_squared = delta * delta; |
---|
126 | } |
---|
127 | } |
---|
128 | |
---|
129 | |
---|
130 | const utility::Vector& Perceptron::weight(void) const |
---|
131 | { |
---|
132 | return weight_; |
---|
133 | } |
---|
134 | |
---|
135 | |
---|
136 | }}} |
---|