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
|
// Copyright (C) 2016 Davis E. King (davis@dlib.net)
// License: Boost Software License See LICENSE.txt for the full license.
#undef DLIB_ElASTIC_NET_ABSTRACT_Hh_
#ifdef DLIB_ElASTIC_NET_ABSTRACT_Hh_
#include "../matrix.h"
namespace dlib
{
// ----------------------------------------------------------------------------------------
class elastic_net
{
/*!
WHAT THIS OBJECT REPRESENTS
This object is a tool for solving the following optimization problem:
min_w: length_squared(X*w - Y) + ridge_lambda*length_squared(w)
such that: sum(abs(w)) <= lasso_budget
That is, it solves the elastic net optimization problem. This object also
has the special property that you can quickly obtain different solutions
for different settings of ridge_lambda, lasso_budget, and target Y values.
This is because a large amount of work is precomputed in the constructor.
The solver will also remember the previous solution and will use that to
warm start subsequent invocations. Therefore, you can efficiently get
solutions for a wide range of regularization parameters.
The particular algorithm used to solve it is described in the paper:
Zhou, Quan, et al. "A reduction of the elastic net to support vector
machines with an application to gpu computing." arXiv preprint
arXiv:1409.1976 (2014). APA
And for the SVM solver sub-component we use the algorithm from:
Hsieh, Cho-Jui, et al. "A dual coordinate descent method for large-scale
linear SVM." Proceedings of the 25th international conference on Machine
learning. ACM, 2008.
!*/
public:
template <typename EXP>
explicit elastic_net(
const matrix_exp<EXP>& XX
);
/*!
requires
- XX.size() != 0
- XX.nr() == XX.nc()
ensures
- #get_epsilon() == 1e-5
- #get_max_iterations() == 50000
- This object will not be verbose unless be_verbose() is called.
- #size() == XX.nc()
- #have_target_values() == false
- We interpret XX as trans(X)*X where X is as defined in the objective
function discussed above in WHAT THIS OBJECT REPRESENTS.
!*/
template <typename EXP1, typename EXP2>
elastic_net(
const matrix_exp<EXP1>& XX,
const matrix_exp<EXP2>& XY
);
/*!
requires
- XX.size() != 0
- XX.nr() == XX.nc()
- is_col_vector(XY)
- XX.nc() == Y.size()
ensures
- constructs this object by calling the elastic_net(XX) constructor and
then calling this->set_xy(XY).
- #have_target_values() == true
- We interpret XX as trans(X)*X where X is as defined in the objective
function discussed above in WHAT THIS OBJECT REPRESENTS. Similarly, XY
should be trans(X)*Y.
!*/
long size (
) const;
/*!
ensures
- returns the dimensionality of the data loaded into this object. That is,
how many elements are in the optimal w vector? This function returns
that number.
!*/
bool have_target_values (
) const;
/*!
ensures
- returns true if set_xy() has been called and false otherwise.
!*/
template <typename EXP>
void set_xy(
const matrix_exp<EXP>& XY
);
/*!
requires
- is_col_vector(Y)
- Y.size() == size()
ensures
- #have_target_values() == true
- Sets the target values of the regression. Note that we expect the given
matrix, XY, to be equal to trans(X)*Y, where X and Y have the definitions
discussed above in WHAT THIS OBJECT REPRESENTS.
!*/
void set_epsilon(
double eps
);
/*!
requires
- eps > 0
ensures
- #get_epsilon() == eps
!*/
double get_epsilon (
) const;
/*!
ensures
- returns the error epsilon that determines when the solver should stop.
Smaller values may result in a more accurate solution but take longer to
execute.
!*/
unsigned long get_max_iterations (
) const;
/*!
ensures
- returns the maximum number of iterations the optimizer is allowed to run
before it is required to stop and return a result.
!*/
void set_max_iterations (
unsigned long max_iter
);
/*!
ensures
- #get_max_iterations() == max_iter
!*/
void be_verbose (
);
/*!
ensures
- This object will print status messages to standard out so that a
user can observe the progress of the algorithm.
!*/
void be_quiet (
);
/*!
ensures
- this object will not print anything to standard out.
!*/
matrix<double,0,1> operator() (
double ridge_lambda,
double lasso_budget = std::numeric_limits<double>::infinity()
);
/*!
requires
- have_target_values() == true
- ridge_lambda > 0
- lasso_budget > 0
ensures
- Solves the optimization problem described in the WHAT THIS OBJECT
REPRESENTS section above and returns the optimal w.
- The returned vector has size() elements.
- if (lasso_budget == infinity) then
- The lasso constraint is ignored
!*/
};
// ----------------------------------------------------------------------------------------
}
#endif // DLIB_ElASTIC_NET_ABSTRACT_Hh_
|
