gp.hpp 17.6 KB
Newer Older
1
2
#ifndef LIMBO_MODEL_GP_HPP
#define LIMBO_MODEL_GP_HPP
3
4

#include <cassert>
5
#include <iostream>
6
#include <limits>
7
#include <vector>
8

9
#include <Eigen/Cholesky>
10
11
12
#include <Eigen/Core>
#include <Eigen/LU>

13
#include <limbo/model/gp/no_lf_opt.hpp>
14

15
namespace limbo {
16
    namespace model {
Jean-Baptiste Mouret's avatar
Jean-Baptiste Mouret committed
17
18
19
20
21
        /// @ingroup model
        /// A classic Gaussian process.
        /// It is parametrized by:
        /// - a mean function
        /// - [optionnal] an optimizer for the hyper-parameters
22
        template <typename Params, typename KernelFunction, typename MeanFunction, class HyperParamsOptimizer = gp::NoLFOpt<Params>>
23
        class GP {
24
        public:
25
            /// useful because the model might be created before knowing anything about the process
26
            GP() : _dim_in(-1), _dim_out(-1) {}
27
28
29

            /// useful because the model might be created  before having samples
            GP(int dim_in, int dim_out)
30
                : _dim_in(dim_in), _dim_out(dim_out), _kernel_function(dim_in), _mean_function(dim_out) {}
31

32
            /// Compute the GP from samples, observation, noise. [optional: blacklisted samples]. This call needs to be explicit!
33
            void compute(const std::vector<Eigen::VectorXd>& samples,
Antoine Cully's avatar
Antoine Cully committed
34
35
36
37
                const std::vector<Eigen::VectorXd>& observations,
                const Eigen::VectorXd& noises,
                const std::vector<Eigen::VectorXd>& bl_samples = std::vector<Eigen::VectorXd>(),
                const Eigen::VectorXd& noises_bl = Eigen::VectorXd())
38
39
40
41
            {
                assert(samples.size() != 0);
                assert(observations.size() != 0);
                assert(samples.size() == observations.size());
Konstantinos Chatzilygeroudis's avatar
Konstantinos Chatzilygeroudis committed
42
                assert(bl_samples.size() == (unsigned int)noises_bl.size());
43

44
45
                _dim_in = samples[0].size();
                _kernel_function = KernelFunction(_dim_in); // the cost of building a functor should be relatively low
46

47
48
                _dim_out = observations[0].size();
                _mean_function = MeanFunction(_dim_out); // the cost of building a functor should be relatively low
49

50
51
52
53
54
55
56
                _samples = samples;

                _observations.resize(observations.size(), _dim_out);
                for (int i = 0; i < _observations.rows(); ++i)
                    _observations.row(i) = observations[i];

                _mean_observation = _observations.colwise().mean();
57

Antoine Cully's avatar
Antoine Cully committed
58
59
                _noises = noises;
                _noises_bl = noises_bl;
60

61
62
63
                _bl_samples = bl_samples;

                this->_compute_obs_mean();
64
                this->_compute_full_kernel();
65

66
67
                if (!_bl_samples.empty())
                    this->_compute_bl_kernel();
68
            }
69

70
            /// Do not forget to call this if you use hyper-prameters optimization!!
Konstantinos Chatzilygeroudis's avatar
Konstantinos Chatzilygeroudis committed
71
72
            void optimize_hyperparams()
            {
73
74
                HyperParamsOptimizer()(*this);
            }
75

76
77
            /// add sample and update the GP. This code uses an incremental implementation of the Cholesky
            /// decomposition. It is therefore much faster than a call to compute()
78
79
80
81
82
83
            void add_sample(const Eigen::VectorXd& sample, const Eigen::VectorXd& observation, double noise)
            {
                if (_samples.empty()) {
                    if (_bl_samples.empty()) {
                        _dim_in = sample.size();
                        _kernel_function = KernelFunction(_dim_in); // the cost of building a functor should be relatively low
Konstantinos Chatzilygeroudis's avatar
Konstantinos Chatzilygeroudis committed
84
85
                    }
                    else {
86
87
88
89
90
                        assert(sample.size() == _dim_in);
                    }

                    _dim_out = observation.size();
                    _mean_function = MeanFunction(_dim_out); // the cost of building a functor should be relatively low
Konstantinos Chatzilygeroudis's avatar
Konstantinos Chatzilygeroudis committed
91
92
                }
                else {
93
94
                    assert(sample.size() == _dim_in);
                    assert(observation.size() == _dim_out);
95
96
                }

97
98
99
100
101
102
103
                _samples.push_back(sample);

                _observations.conservativeResize(_observations.rows() + 1, _dim_out);
                _observations.bottomRows<1>() = observation.transpose();

                _mean_observation = _observations.colwise().mean();

Antoine Cully's avatar
Antoine Cully committed
104
105
106
                _noises.conservativeResize(_noises.size() + 1);
                _noises[_noises.size() - 1] = noise;
                //_noise = noise;
107
108

                this->_compute_obs_mean();
109
                this->_compute_incremental_kernel();
110
111
112

                if (!_bl_samples.empty())
                    this->_compute_bl_kernel();
113
114
            }

115
            /// add blacklisted sample and update the GP
116
117
118
119
120
            void add_bl_sample(const Eigen::VectorXd& bl_sample, double noise)
            {
                if (_samples.empty() && _bl_samples.empty()) {
                    _dim_in = bl_sample.size();
                    _kernel_function = KernelFunction(_dim_in); // the cost of building a functor should be relatively low
Konstantinos Chatzilygeroudis's avatar
Konstantinos Chatzilygeroudis committed
121
122
                }
                else {
123
124
125
126
                    assert(bl_sample.size() == _dim_in);
                }

                _bl_samples.push_back(bl_sample);
Antoine Cully's avatar
Antoine Cully committed
127
128
129
130

                _noises_bl.conservativeResize(_noises_bl.size() + 1);
                _noises_bl[_noises_bl.size() - 1] = noise;
                //_noise = noise;
131
132
133
134
135
136

                if (!_samples.empty()) {
                    this->_compute_bl_kernel();
                }
            }

137
            /**
138
             \\rst
139
             return :math:`\mu`, :math:`\sigma^2` (unormalized). If there is no sample, return the value according to the mean function. Using this method instead of separate calls to mu() and sigma() is more efficient because some computations are shared between mu() and sigma().
140
141
             \\endrst
	  		*/
142
143
144
145
            std::tuple<Eigen::VectorXd, double> query(const Eigen::VectorXd& v) const
            {
                if (_samples.size() == 0 && _bl_samples.size() == 0)
                    return std::make_tuple(_mean_function(v, *this),
146
                        _kernel_function(v, v));
147
148
149
150
151
152
153
154
155
156

                if (_samples.size() == 0)
                    return std::make_tuple(_mean_function(v, *this),
                        _sigma(v, _compute_k_bl(v, _compute_k(v))));

                Eigen::VectorXd k = _compute_k(v);
                return std::make_tuple(_mu(v, k), _sigma(v, _compute_k_bl(v, k)));
            }

            /**
157
             \\rst
158
             return :math:`\mu` (unormalized). If there is no sample, return the value according to the mean function.
159
160
             \\endrst
	  		*/
161
162
163
164
165
166
167
168
            Eigen::VectorXd mu(const Eigen::VectorXd& v) const
            {
                if (_samples.size() == 0)
                    return _mean_function(v, *this);
                return _mu(v, _compute_k(v));
            }

            /**
169
             \\rst
170
             return :math:`\sigma^2` (unormalized). If there is no sample, return the max :math:`\sigma^2`.
171
172
             \\endrst
	  		*/
173
174
175
            double sigma(const Eigen::VectorXd& v) const
            {
                if (_samples.size() == 0 && _bl_samples.size() == 0)
176
                    return _kernel_function(v, v);
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
                return _sigma(v, _compute_k_bl(v, _compute_k(v)));
            }

            /// return the number of dimensions of the input
            int dim_in() const
            {
                assert(_dim_in != -1); // need to compute first !
                return _dim_in;
            }

            /// return the number of dimensions of the output
            int dim_out() const
            {
                assert(_dim_out != -1); // need to compute first !
                return _dim_out;
            }

            const KernelFunction& kernel_function() const { return _kernel_function; }

196
            KernelFunction& kernel_function() { return _kernel_function; }
197
198
199
200
201

            const MeanFunction& mean_function() const { return _mean_function; }

            MeanFunction& mean_function() { return _mean_function; }

Jean-Baptiste Mouret's avatar
Jean-Baptiste Mouret committed
202
            /// return the maximum observation (only call this if the output of the GP is of dimension 1)
203
204
205
206
207
208
            Eigen::VectorXd max_observation() const
            {
                if (_observations.cols() > 1)
                    std::cout << "WARNING max_observation with multi dimensional "
                                 "observations doesn't make sense"
                              << std::endl;
209
                return Eigen::VectorXd(_observations.maxCoeff());
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
            }

            /// return the mean observation (only call this if the output of the GP is of dimension 1)
            Eigen::VectorXd mean_observation() const
            {
                // TO-DO: Check if _dim_out is correct?!
                return _samples.size() > 0 ? _mean_observation
                                           : Eigen::VectorXd::Zero(_dim_out);
            }

            const Eigen::MatrixXd& mean_vector() const { return _mean_vector; }

            const Eigen::MatrixXd& obs_mean() const { return _obs_mean; }

            /// return the number of samples used to compute the GP
            int nb_samples() const { return _samples.size(); }

            /** return the number of blacklisted samples used to compute the GP
228
	     \\rst
229
	     For the blacklist concept, see the Limbo-specific concept guide.
230
	     \\endrst
231
	     */
232
233
            int nb_bl_samples() const { return _bl_samples.size(); }

234
            ///  recomputes the GP
Jean-Baptiste Mouret's avatar
Jean-Baptiste Mouret committed
235
            void recompute(bool update_obs_mean = true)
236
            {
237
238
239
                assert(!_samples.empty());

                if (update_obs_mean)
240
                    this->_compute_obs_mean();
241

242
                this->_compute_full_kernel();
243
244
245

                if (!_bl_samples.empty())
                    this->_compute_bl_kernel();
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
            }

            /// return the likelihood (do not compute it!)
            double get_lik() const { return _lik; }

            /// set the likelihood (you need to compute it from outside!)
            void set_lik(const double& lik) { _lik = lik; }

            /// LLT matrix (from Cholesky decomposition)
            //const Eigen::LLT<Eigen::MatrixXd>& llt() const { return _llt; }
            const Eigen::MatrixXd& matrixL() const { return _matrixL; }

            const Eigen::MatrixXd& alpha() const { return _alpha; }

            /// return the list of samples that have been tested so far
            const std::vector<Eigen::VectorXd>& samples() const { return _samples; }

        protected:
            int _dim_in;
            int _dim_out;

            KernelFunction _kernel_function;
            MeanFunction _mean_function;

            std::vector<Eigen::VectorXd> _samples;
            Eigen::MatrixXd _observations;
            std::vector<Eigen::VectorXd> _bl_samples; // black listed samples
            Eigen::MatrixXd _mean_vector;
            Eigen::MatrixXd _obs_mean;

Antoine Cully's avatar
Antoine Cully committed
276
277
278
279
            //double _noise;
            Eigen::VectorXd _noises;
            Eigen::VectorXd _noises_bl;

280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
            Eigen::MatrixXd _alpha;
            Eigen::VectorXd _mean_observation;

            Eigen::MatrixXd _kernel;

            // Eigen::MatrixXd _inverted_kernel;

            Eigen::MatrixXd _matrixL;
            Eigen::MatrixXd _inv_bl_kernel;

            double _lik;

            void _compute_obs_mean()
            {
                _mean_vector.resize(_samples.size(), _dim_out);
                for (int i = 0; i < _mean_vector.rows(); i++)
                    _mean_vector.row(i) = _mean_function(_samples[i], *this);
                _obs_mean = _observations - _mean_vector;
            }

300
            void _compute_full_kernel()
301
            {
302
303
304
305
306
307
                size_t n = _samples.size();
                _kernel.resize(n, n);

                // O(n^2) [should be negligible]
                for (size_t i = 0; i < n; i++)
                    for (size_t j = 0; j <= i; ++j)
Antoine Cully's avatar
Antoine Cully committed
308
                        _kernel(i, j) = _kernel_function(_samples[i], _samples[j]) + ((i == j) ? _noises[i] : 0); // noise only on the diagonal
309
310
311
312
313
314
315
316

                for (size_t i = 0; i < n; i++)
                    for (size_t j = 0; j < i; ++j)
                        _kernel(j, i) = _kernel(i, j);

                // O(n^3)
                _matrixL = Eigen::LLT<Eigen::MatrixXd>(_kernel).matrixL();

317
                this->_compute_alpha();
318
319
320
            }

            void _compute_incremental_kernel()
321
            {
322
                // Incremental LLT
323
                // This part of the code is inpired from the Bayesopt Library (cholesky_add_row function).
324
325
                // However, the mathematical fundations can be easily retrieved by detailling the equations of the
                // extended L matrix that produces the desired kernel.
326

327
328
                size_t n = _samples.size();
                _kernel.conservativeResize(n, n);
329

330
                for (size_t i = 0; i < n; ++i) {
Antoine Cully's avatar
Antoine Cully committed
331
                    _kernel(i, n - 1) = _kernel_function(_samples[i], _samples[n - 1]) + ((i == n - 1) ? _noises[i] : 0); // noise only on the diagonal
332
                    _kernel(n - 1, i) = _kernel(i, n - 1);
333
334
                }

335
336
337
338
339
340
                _matrixL.conservativeResizeLike(Eigen::MatrixXd::Zero(n, n));

                double L_j;
                for (size_t j = 0; j < n - 1; ++j) {
                    L_j = _kernel(n - 1, j) - (_matrixL.block(j, 0, 1, j) * _matrixL.block(n - 1, 0, 1, j).transpose())(0, 0);
                    _matrixL(n - 1, j) = (L_j) / _matrixL(j, j);
341
342
                }

343
344
                L_j = _kernel(n - 1, n - 1) - (_matrixL.block(n - 1, 0, 1, n - 1) * _matrixL.block(n - 1, 0, 1, n - 1).transpose())(0, 0);
                _matrixL(n - 1, n - 1) = sqrt(L_j);
Antoine Cully's avatar
Antoine Cully committed
345

346
                this->_compute_alpha();
347
348
            }

349
            void _compute_alpha()
350
            {
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
                // alpha = K^{-1} * this->_obs_mean;
                _alpha = _matrixL.template triangularView<Eigen::Lower>().solve(_obs_mean);
                _matrixL.template triangularView<Eigen::Lower>().adjoint().solveInPlace(_alpha); //can probably be improved by avoiding to generate the view twice
            }

            void _compute_bl_kernel()
            {
                Eigen::MatrixXd A1 = Eigen::MatrixXd::Identity(this->_samples.size(), this->_samples.size());
                _matrixL.template triangularView<Eigen::Lower>().solveInPlace(A1);
                _matrixL.template triangularView<Eigen::Lower>().transpose().solveInPlace(A1);

                _inv_bl_kernel.resize(_samples.size() + _bl_samples.size(),
                    _samples.size() + _bl_samples.size());

                Eigen::MatrixXd B(_samples.size(), _bl_samples.size());
                for (size_t i = 0; i < _samples.size(); i++)
                    for (size_t j = 0; j < _bl_samples.size(); ++j)
                        B(i, j) = _kernel_function(_samples[i], _bl_samples[j]);

                Eigen::MatrixXd D(_bl_samples.size(), _bl_samples.size());
                for (size_t i = 0; i < _bl_samples.size(); i++)
                    for (size_t j = 0; j < _bl_samples.size(); ++j)
Antoine Cully's avatar
Antoine Cully committed
373
                        D(i, j) = _kernel_function(_bl_samples[i], _bl_samples[j]) + ((i == j) ? _noises_bl[i] : 0);
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388

                Eigen::MatrixXd comA = (D - B.transpose() * A1 * B);
                Eigen::LLT<Eigen::MatrixXd> llt_bl(comA);
                Eigen::MatrixXd comA1 = Eigen::MatrixXd::Identity(_bl_samples.size(), _bl_samples.size());
                llt_bl.matrixL().solveInPlace(comA1);
                llt_bl.matrixL().transpose().solveInPlace(comA1);

                // fill the matrix block wise
                _inv_bl_kernel.block(0, 0, _samples.size(), _samples.size()) = A1 + A1 * B * comA1 * B.transpose() * A1;
                _inv_bl_kernel.block(0, _samples.size(), _samples.size(),
                    _bl_samples.size())
                    = -A1 * B * comA1;
                _inv_bl_kernel.block(_samples.size(), 0, _bl_samples.size(),
                    _samples.size())
                    = _inv_bl_kernel.block(0, _samples.size(), _samples.size(),
Konstantinos Chatzilygeroudis's avatar
Konstantinos Chatzilygeroudis committed
389
                                         _bl_samples.size())
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
                          .transpose();
                _inv_bl_kernel.block(_samples.size(), _samples.size(), _bl_samples.size(),
                    _bl_samples.size())
                    = comA1;
            }

            Eigen::VectorXd _mu(const Eigen::VectorXd& v, const Eigen::VectorXd& k) const
            {
                return (k.transpose() * _alpha) + _mean_function(v, *this).transpose();
            }

            double _sigma(const Eigen::VectorXd& v, const Eigen::VectorXd& k) const
            {
                double res;
                if (_bl_samples.size() == 0) {
                    Eigen::VectorXd z = _matrixL.triangularView<Eigen::Lower>().solve(k);
                    res = _kernel_function(v, v) - z.dot(z);
                }
                else {
                    res = _kernel_function(v, v) - k.transpose() * _inv_bl_kernel * k;
                }

                return (res <= std::numeric_limits<double>::epsilon()) ? 0 : res;
            }

            Eigen::VectorXd _compute_k(const Eigen::VectorXd& v) const
            {
                Eigen::VectorXd k(_samples.size());
                for (int i = 0; i < k.size(); i++)
                    k[i] = _kernel_function(_samples[i], v);
                return k;
            }

            Eigen::VectorXd _compute_k_bl(const Eigen::VectorXd& v,
                const Eigen::VectorXd& k) const
            {
                if (_bl_samples.size() == 0) {
                    return k;
                }

                Eigen::VectorXd k_bl(_samples.size() + _bl_samples.size());

                k_bl.head(_samples.size()) = k;
                for (size_t i = 0; i < _bl_samples.size(); i++)
                    k_bl[i + this->_samples.size()] = this->_kernel_function(_bl_samples[i], v);
                return k_bl;
            }
        };
    }
}
440

441
#endif