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