|
1
|
|
|
<?php |
|
2
|
|
|
|
|
3
|
|
|
declare(strict_types=1); |
|
4
|
|
|
|
|
5
|
|
|
namespace Phpml\Helper\Optimizer; |
|
6
|
|
|
|
|
7
|
|
|
/** |
|
8
|
|
|
* Batch version of Gradient Descent to optimize the weights |
|
9
|
|
|
* of a classifier given samples, targets and the objective function to minimize |
|
10
|
|
|
*/ |
|
11
|
|
|
class GD extends StochasticGD |
|
12
|
|
|
{ |
|
13
|
|
|
/** |
|
14
|
|
|
* Number of samples given |
|
15
|
|
|
* |
|
16
|
|
|
* @var int |
|
17
|
|
|
*/ |
|
18
|
|
|
protected $sampleCount; |
|
19
|
|
|
|
|
20
|
|
|
/** |
|
21
|
|
|
* @param array $samples |
|
22
|
|
|
* @param array $targets |
|
23
|
|
|
* @param \Closure $gradientCb |
|
24
|
|
|
* |
|
25
|
|
|
* @return array |
|
26
|
|
|
*/ |
|
27
|
|
|
public function runOptimization(array $samples, array $targets, \Closure $gradientCb) |
|
28
|
|
|
{ |
|
29
|
|
|
$this->samples = $samples; |
|
30
|
|
|
$this->targets = $targets; |
|
31
|
|
|
$this->gradientCb = $gradientCb; |
|
32
|
|
|
$this->sampleCount = count($this->samples); |
|
33
|
|
|
|
|
34
|
|
|
// Batch learning is executed: |
|
35
|
|
|
$currIter = 0; |
|
36
|
|
|
$this->costValues = []; |
|
37
|
|
|
while ($this->maxIterations > $currIter++) { |
|
38
|
|
|
$theta = $this->theta; |
|
39
|
|
|
|
|
40
|
|
|
// Calculate update terms for each sample |
|
41
|
|
|
list($errors, $updates, $totalPenalty) = $this->gradient($theta); |
|
42
|
|
|
|
|
43
|
|
|
$this->updateWeightsWithUpdates($updates, $totalPenalty); |
|
44
|
|
|
|
|
45
|
|
|
$this->costValues[] = array_sum($errors)/$this->sampleCount; |
|
46
|
|
|
|
|
47
|
|
|
if ($this->earlyStop($theta)) { |
|
48
|
|
|
break; |
|
49
|
|
|
} |
|
50
|
|
|
} |
|
51
|
|
|
|
|
52
|
|
|
return $this->theta; |
|
53
|
|
|
} |
|
54
|
|
|
|
|
55
|
|
|
/** |
|
56
|
|
|
* Calculates gradient, cost function and penalty term for each sample |
|
57
|
|
|
* then returns them as an array of values |
|
58
|
|
|
* |
|
59
|
|
|
* @param array $theta |
|
60
|
|
|
* |
|
61
|
|
|
* @return array |
|
62
|
|
|
*/ |
|
63
|
|
|
protected function gradient(array $theta) |
|
64
|
|
|
{ |
|
65
|
|
|
$costs = []; |
|
66
|
|
|
$gradient= []; |
|
67
|
|
|
$totalPenalty = 0; |
|
68
|
|
|
|
|
69
|
|
|
foreach ($this->samples as $index => $sample) { |
|
70
|
|
|
$target = $this->targets[$index]; |
|
71
|
|
|
|
|
72
|
|
|
$result = ($this->gradientCb)($theta, $sample, $target); |
|
73
|
|
|
list($cost, $grad, $penalty) = array_pad($result, 3, 0); |
|
74
|
|
|
|
|
75
|
|
|
$costs[] = $cost; |
|
76
|
|
|
$gradient[]= $grad; |
|
77
|
|
|
$totalPenalty += $penalty; |
|
78
|
|
|
} |
|
79
|
|
|
|
|
80
|
|
|
$totalPenalty /= $this->sampleCount; |
|
81
|
|
|
|
|
82
|
|
|
return [$costs, $gradient, $totalPenalty]; |
|
83
|
|
|
} |
|
84
|
|
|
|
|
85
|
|
|
/** |
|
86
|
|
|
* @param array $updates |
|
87
|
|
|
* @param float $penalty |
|
88
|
|
|
*/ |
|
89
|
|
|
protected function updateWeightsWithUpdates(array $updates, float $penalty) |
|
90
|
|
|
{ |
|
91
|
|
|
// Updates all weights at once |
|
92
|
|
|
for ($i=0; $i <= $this->dimensions; $i++) { |
|
93
|
|
|
if ($i == 0) { |
|
94
|
|
|
$this->theta[0] -= $this->learningRate * array_sum($updates); |
|
95
|
|
|
} else { |
|
96
|
|
|
$col = array_column($this->samples, $i - 1); |
|
97
|
|
|
|
|
98
|
|
|
$error = 0; |
|
99
|
|
|
foreach ($col as $index => $val) { |
|
100
|
|
|
$error += $val * $updates[$index]; |
|
101
|
|
|
} |
|
102
|
|
|
|
|
103
|
|
|
$this->theta[$i] -= $this->learningRate * |
|
104
|
|
|
($error + $penalty * $this->theta[$i]); |
|
105
|
|
|
} |
|
106
|
|
|
} |
|
107
|
|
|
} |
|
108
|
|
|
} |
|
109
|
|
|
|
php-ai /
php-ml
