1
|
|
|
<?php |
2
|
|
|
|
3
|
|
|
declare(strict_types=1); |
4
|
|
|
|
5
|
|
|
namespace Phpml\Helper\Optimizer; |
6
|
|
|
|
7
|
|
|
use Closure; |
8
|
|
|
use Phpml\Exception\InvalidArgumentException; |
9
|
|
|
use Phpml\Exception\InvalidOperationException; |
10
|
|
|
|
11
|
|
|
/** |
12
|
|
|
* Stochastic Gradient Descent optimization method |
13
|
|
|
* to find a solution for the equation A.ϴ = y where |
14
|
|
|
* A (samples) and y (targets) are known and ϴ is unknown. |
15
|
|
|
*/ |
16
|
|
|
class StochasticGD extends Optimizer |
17
|
|
|
{ |
18
|
|
|
/** |
19
|
|
|
* A (samples) |
20
|
|
|
* |
21
|
|
|
* @var array |
22
|
|
|
*/ |
23
|
|
|
protected $samples = []; |
24
|
|
|
|
25
|
|
|
/** |
26
|
|
|
* y (targets) |
27
|
|
|
* |
28
|
|
|
* @var array |
29
|
|
|
*/ |
30
|
|
|
protected $targets = []; |
31
|
|
|
|
32
|
|
|
/** |
33
|
|
|
* Callback function to get the gradient and cost value |
34
|
|
|
* for a specific set of theta (ϴ) and a pair of sample & target |
35
|
|
|
* |
36
|
|
|
* @var \Closure|null |
37
|
|
|
*/ |
38
|
|
|
protected $gradientCb; |
39
|
|
|
|
40
|
|
|
/** |
41
|
|
|
* Maximum number of iterations used to train the model |
42
|
|
|
* |
43
|
|
|
* @var int |
44
|
|
|
*/ |
45
|
|
|
protected $maxIterations = 1000; |
46
|
|
|
|
47
|
|
|
/** |
48
|
|
|
* Learning rate is used to control the speed of the optimization.<br> |
49
|
|
|
* |
50
|
|
|
* Larger values of lr may overshoot the optimum or even cause divergence |
51
|
|
|
* while small values slows down the convergence and increases the time |
52
|
|
|
* required for the training |
53
|
|
|
* |
54
|
|
|
* @var float |
55
|
|
|
*/ |
56
|
|
|
protected $learningRate = 0.001; |
57
|
|
|
|
58
|
|
|
/** |
59
|
|
|
* Minimum amount of change in the weights and error values |
60
|
|
|
* between iterations that needs to be obtained to continue the training |
61
|
|
|
* |
62
|
|
|
* @var float |
63
|
|
|
*/ |
64
|
|
|
protected $threshold = 1e-4; |
65
|
|
|
|
66
|
|
|
/** |
67
|
|
|
* Enable/Disable early stopping by checking the weight & cost values |
68
|
|
|
* to see whether they changed large enough to continue the optimization |
69
|
|
|
* |
70
|
|
|
* @var bool |
71
|
|
|
*/ |
72
|
|
|
protected $enableEarlyStop = true; |
73
|
|
|
|
74
|
|
|
/** |
75
|
|
|
* List of values obtained by evaluating the cost function at each iteration |
76
|
|
|
* of the algorithm |
77
|
|
|
* |
78
|
|
|
* @var array |
79
|
|
|
*/ |
80
|
|
|
protected $costValues = []; |
81
|
|
|
|
82
|
|
|
/** |
83
|
|
|
* Initializes the SGD optimizer for the given number of dimensions |
84
|
|
|
*/ |
85
|
|
|
public function __construct(int $dimensions) |
86
|
|
|
{ |
87
|
|
|
// Add one more dimension for the bias |
88
|
|
|
parent::__construct($dimensions + 1); |
89
|
|
|
|
90
|
|
|
$this->dimensions = $dimensions; |
91
|
|
|
} |
92
|
|
|
|
93
|
|
|
public function setTheta(array $theta): Optimizer |
94
|
|
|
{ |
95
|
|
|
if (count($theta) !== $this->dimensions + 1) { |
96
|
|
|
throw new InvalidArgumentException(sprintf('Number of values in the weights array should be %s', $this->dimensions + 1)); |
97
|
|
|
} |
98
|
|
|
|
99
|
|
|
$this->theta = $theta; |
100
|
|
|
|
101
|
|
|
return $this; |
102
|
|
|
} |
103
|
|
|
|
104
|
|
|
/** |
105
|
|
|
* Sets minimum value for the change in the theta values |
106
|
|
|
* between iterations to continue the iterations.<br> |
107
|
|
|
* |
108
|
|
|
* If change in the theta is less than given value then the |
109
|
|
|
* algorithm will stop training |
110
|
|
|
* |
111
|
|
|
* @return $this |
112
|
|
|
*/ |
113
|
|
|
public function setChangeThreshold(float $threshold = 1e-5) |
114
|
|
|
{ |
115
|
|
|
$this->threshold = $threshold; |
116
|
|
|
|
117
|
|
|
return $this; |
118
|
|
|
} |
119
|
|
|
|
120
|
|
|
/** |
121
|
|
|
* Enable/Disable early stopping by checking at each iteration |
122
|
|
|
* whether changes in theta or cost value are not large enough |
123
|
|
|
* |
124
|
|
|
* @return $this |
125
|
|
|
*/ |
126
|
|
|
public function setEarlyStop(bool $enable = true) |
127
|
|
|
{ |
128
|
|
|
$this->enableEarlyStop = $enable; |
129
|
|
|
|
130
|
|
|
return $this; |
131
|
|
|
} |
132
|
|
|
|
133
|
|
|
/** |
134
|
|
|
* @return $this |
135
|
|
|
*/ |
136
|
|
|
public function setLearningRate(float $learningRate) |
137
|
|
|
{ |
138
|
|
|
$this->learningRate = $learningRate; |
139
|
|
|
|
140
|
|
|
return $this; |
141
|
|
|
} |
142
|
|
|
|
143
|
|
|
/** |
144
|
|
|
* @return $this |
145
|
|
|
*/ |
146
|
|
|
public function setMaxIterations(int $maxIterations) |
147
|
|
|
{ |
148
|
|
|
$this->maxIterations = $maxIterations; |
149
|
|
|
|
150
|
|
|
return $this; |
151
|
|
|
} |
152
|
|
|
|
153
|
|
|
/** |
154
|
|
|
* Optimization procedure finds the unknow variables for the equation A.ϴ = y |
155
|
|
|
* for the given samples (A) and targets (y).<br> |
156
|
|
|
* |
157
|
|
|
* The cost function to minimize and the gradient of the function are to be |
158
|
|
|
* handled by the callback function provided as the third parameter of the method. |
159
|
|
|
*/ |
160
|
|
|
public function runOptimization(array $samples, array $targets, Closure $gradientCb): array |
161
|
|
|
{ |
162
|
|
|
$this->samples = $samples; |
163
|
|
|
$this->targets = $targets; |
164
|
|
|
$this->gradientCb = $gradientCb; |
165
|
|
|
|
166
|
|
|
$currIter = 0; |
167
|
|
|
$bestTheta = null; |
168
|
|
|
$bestScore = 0.0; |
169
|
|
|
$this->costValues = []; |
170
|
|
|
|
171
|
|
|
while ($this->maxIterations > $currIter++) { |
172
|
|
|
$theta = $this->theta; |
173
|
|
|
|
174
|
|
|
// Update the guess |
175
|
|
|
$cost = $this->updateTheta(); |
176
|
|
|
|
177
|
|
|
// Save the best theta in the "pocket" so that |
178
|
|
|
// any future set of theta worse than this will be disregarded |
179
|
|
|
if ($bestTheta === null || $cost <= $bestScore) { |
180
|
|
|
$bestTheta = $theta; |
181
|
|
|
$bestScore = $cost; |
182
|
|
|
} |
183
|
|
|
|
184
|
|
|
// Add the cost value for this iteration to the list |
185
|
|
|
$this->costValues[] = $cost; |
186
|
|
|
|
187
|
|
|
// Check for early stop |
188
|
|
|
if ($this->enableEarlyStop && $this->earlyStop($theta)) { |
189
|
|
|
break; |
190
|
|
|
} |
191
|
|
|
} |
192
|
|
|
|
193
|
|
|
$this->clear(); |
194
|
|
|
|
195
|
|
|
// Solution in the pocket is better than or equal to the last state |
196
|
|
|
// so, we use this solution |
197
|
|
|
return $this->theta = (array) $bestTheta; |
198
|
|
|
} |
199
|
|
|
|
200
|
|
|
/** |
201
|
|
|
* Returns the list of cost values for each iteration executed in |
202
|
|
|
* last run of the optimization |
203
|
|
|
*/ |
204
|
|
|
public function getCostValues(): array |
205
|
|
|
{ |
206
|
|
|
return $this->costValues; |
207
|
|
|
} |
208
|
|
|
|
209
|
|
|
protected function updateTheta(): float |
210
|
|
|
{ |
211
|
|
|
$jValue = 0.0; |
212
|
|
|
$theta = $this->theta; |
213
|
|
|
|
214
|
|
|
if ($this->gradientCb === null) { |
215
|
|
|
throw new InvalidOperationException('Gradient callback is not defined'); |
216
|
|
|
} |
217
|
|
|
|
218
|
|
|
foreach ($this->samples as $index => $sample) { |
219
|
|
|
$target = $this->targets[$index]; |
220
|
|
|
|
221
|
|
|
$result = ($this->gradientCb)($theta, $sample, $target); |
222
|
|
|
|
223
|
|
|
[$error, $gradient, $penalty] = array_pad($result, 3, 0); |
224
|
|
|
|
225
|
|
|
// Update bias |
226
|
|
|
$this->theta[0] -= $this->learningRate * $gradient; |
227
|
|
|
|
228
|
|
|
// Update other values |
229
|
|
|
for ($i = 1; $i <= $this->dimensions; ++$i) { |
230
|
|
|
$this->theta[$i] -= $this->learningRate * |
231
|
|
|
($gradient * $sample[$i - 1] + $penalty * $this->theta[$i]); |
232
|
|
|
} |
233
|
|
|
|
234
|
|
|
// Sum error rate |
235
|
|
|
$jValue += $error; |
236
|
|
|
} |
237
|
|
|
|
238
|
|
|
return $jValue / count($this->samples); |
239
|
|
|
} |
240
|
|
|
|
241
|
|
|
/** |
242
|
|
|
* Checks if the optimization is not effective enough and can be stopped |
243
|
|
|
* in case large enough changes in the solution do not happen |
244
|
|
|
*/ |
245
|
|
|
protected function earlyStop(array $oldTheta): bool |
246
|
|
|
{ |
247
|
|
|
// Check for early stop: No change larger than threshold (default 1e-5) |
248
|
|
|
$diff = array_map( |
249
|
|
|
function ($w1, $w2) { |
250
|
|
|
return abs($w1 - $w2) > $this->threshold ? 1 : 0; |
251
|
|
|
}, |
252
|
|
|
$oldTheta, |
253
|
|
|
$this->theta |
254
|
|
|
); |
255
|
|
|
|
256
|
|
|
if (array_sum($diff) == 0) { |
257
|
|
|
return true; |
258
|
|
|
} |
259
|
|
|
|
260
|
|
|
// Check if the last two cost values are almost the same |
261
|
|
|
$costs = array_slice($this->costValues, -2); |
262
|
|
|
if (count($costs) === 2 && abs($costs[1] - $costs[0]) < $this->threshold) { |
263
|
|
|
return true; |
264
|
|
|
} |
265
|
|
|
|
266
|
|
|
return false; |
267
|
|
|
} |
268
|
|
|
|
269
|
|
|
/** |
270
|
|
|
* Clears the optimizer internal vars after the optimization process. |
271
|
|
|
*/ |
272
|
|
|
protected function clear(): void |
273
|
|
|
{ |
274
|
|
|
$this->samples = []; |
275
|
|
|
$this->targets = []; |
276
|
|
|
$this->gradientCb = null; |
277
|
|
|
} |
278
|
|
|
} |
279
|
|
|
|