Mercurial > pylearn
annotate pylearn/algorithms/mcRBM.py @ 1524:9d21919e2332
autopep8
author | Frederic Bastien <nouiz@nouiz.org> |
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date | Fri, 02 Nov 2012 13:02:18 -0400 |
parents | 2a6a6f16416c |
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rev | line source |
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1 """ |
1500 | 2 This file implements the Mean & Covariance RBM discussed in |
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3 |
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4 Ranzato, M. and Hinton, G. E. (2010) |
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5 Modeling pixel means and covariances using factored third-order Boltzmann machines. |
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6 IEEE Conference on Computer Vision and Pattern Recognition. |
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7 |
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8 and performs one of the experiments on CIFAR-10 discussed in that paper. There are some minor |
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9 discrepancies between the paper and the accompanying code (train_mcRBM.py), and the |
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10 accompanying code has been taken to be correct in those cases because I couldn't get things to |
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11 work otherwise. |
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12 |
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13 |
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14 Math |
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15 ==== |
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16 |
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17 Energy of "covariance RBM" |
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18 |
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19 E = -0.5 \sum_f \sum_k P_{fk} h_k ( \sum_i C_{if} v_i )^2 |
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20 = -0.5 \sum_f (\sum_k P_{fk} h_k) ( \sum_i C_{if} v_i )^2 |
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21 "vector element f" "vector element f" |
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22 |
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23 In some parts of the paper, the P matrix is chosen to be a diagonal matrix with non-positive |
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24 diagonal entries, so it is helpful to see this as a simpler equation: |
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25 |
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26 E = \sum_f h_f ( \sum_i C_{if} v_i )^2 |
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27 |
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28 |
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29 |
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30 Version in paper |
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31 ---------------- |
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32 |
1500 | 33 Full Energy of the Mean and Covariance RBM, with |
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34 :math:`h_k = h_k^{(c)}`, |
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35 :math:`g_j = h_j^{(m)}`, |
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36 :math:`b_k = b_k^{(c)}`, |
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37 :math:`c_j = b_j^{(m)}`, |
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38 :math:`U_{if} = C_{if}`, |
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39 |
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40 E (v, h, g) = |
1500 | 41 - 0.5 \sum_f \sum_k P_{fk} h_k ( \sum_i (U_{if} v_i) / |U_{.f}|*|v| )^2 |
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42 - \sum_k b_k h_k |
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43 + 0.5 \sum_i v_i^2 |
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44 - \sum_j \sum_i W_{ij} g_j v_i |
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45 - \sum_j c_j g_j |
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46 |
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47 For the energy function to correspond to a probability distribution, P must be non-positive. P |
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48 is initialized to be a diagonal or a topological pooling matrix, and in our experience it can |
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49 be left as such because even in the paper it has a very low learning rate, and is only allowed |
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50 to be updated after the filters in U are learned (in effect). |
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51 |
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52 Version in published train_mcRBM code |
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53 ------------------------------------- |
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54 |
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55 The train_mcRBM file implements learning in a similar but technically different Energy function: |
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56 |
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57 E (v, h, g) = |
1500 | 58 - 0.5 \sum_f \sum_k P_{fk} h_k (\sum_i U_{if} v_i / sqrt(\sum_i v_i^2/I + 0.5))^2 |
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59 - \sum_k b_k h_k |
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60 + 0.5 \sum_i v_i^2 |
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61 - \sum_j \sum_i W_{ij} g_j v_i |
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62 - \sum_j c_j g_j |
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63 |
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64 There are two differences with respect to the paper: |
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65 |
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66 - 'v' is not normalized by its length, but rather it is normalized to have length close to |
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67 the square root of the number of its components. The variable called 'small' that |
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68 "avoids division by zero" is orders larger than machine precision, and is on the order of |
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69 the normalized sum-of-squares, so I've included it in the Energy function. |
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70 |
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71 - 'U' is also not normalized by its length. U is initialized to have columns that are |
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72 shorter than unit-length (approximately 0.2 with the 105 principle components in the |
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73 train_mcRBM data). During training, the columns of U are constrained manually to have |
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74 equal lengths (see the use of normVF), but Euclidean norm is allowed to change. During |
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75 learning it quickly converges towards 1 and then exceeds 1. It does not seem like this |
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76 column-wise normalization of U is justified by maximum-likelihood, I have no intuition |
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77 for why it is used. |
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78 |
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79 |
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80 Version in this code |
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81 -------------------- |
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82 |
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83 This file implements the same algorithm as the train_mcRBM code, except that the P matrix is |
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84 omitted for clarity, and replaced analytically with a negative identity matrix. |
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85 |
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86 E (v, h, g) = |
1500 | 87 + 0.5 \sum_k h_k (\sum_i U_{ik} v_i / sqrt(\sum_i v_i^2/I + 0.5))^2 |
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88 - \sum_k b_k h_k |
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89 + 0.5 \sum_i v_i^2 |
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90 - \sum_j \sum_i W_{ij} g_j v_i |
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91 - \sum_j c_j g_j |
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92 |
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93 E (v, h, g) = |
1500 | 94 - 0.5 \sum_f \sum_k P_{fk} h_k (\sum_i U_{if} v_i / sqrt(\sum_i v_i^2/I + 0.5))^2 |
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95 - \sum_k b_k h_k |
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96 + 0.5 \sum_i v_i^2 |
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97 - \sum_j \sum_i W_{ij} g_j v_i |
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98 - \sum_j c_j g_j |
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99 |
1500 | 100 |
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101 |
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102 Conventions in this file |
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103 ======================== |
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104 |
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105 This file contains some global functions, as well as a class (MeanCovRBM) that makes using them a little |
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106 more convenient. |
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107 |
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108 |
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109 Global functions like `free_energy` work on an mcRBM as parametrized in a particular way. |
1500 | 110 Suppose we have |
111 - I input dimensions, | |
112 - F squared filters, | |
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113 - J mean variables, and |
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114 - K covariance variables. |
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115 |
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116 The mcRBM is parametrized by 6 variables: |
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117 |
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118 - `P`, a matrix whose rows indicate covariance filter groups (F x K) |
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119 - `U`, a matrix whose rows are visible covariance directions (I x F) |
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120 - `W`, a matrix whose rows are visible mean directions (I x J) |
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121 - `b`, a vector of hidden covariance biases (K) |
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122 - `c`, a vector of hidden mean biases (J) |
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123 |
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124 Matrices are generally layed out and accessed according to a C-order convention. |
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125 |
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126 """ |
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127 |
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128 # |
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129 # WORKING NOTES |
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130 # THIS DERIVATION IS BASED ON THE ** PAPER ** ENERGY FUNCTION |
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131 # NOT THE ENERGY FUNCTION IN THE CODE!!! |
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132 # |
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133 # Free energy is the marginal energy of visible units |
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135 # Q(x) = exp(-E(x))/Z ==> -log(Q(x)) - log(Z) = E(x) |
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136 # |
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137 # |
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138 # E (v, h, g) = |
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139 # - 0.5 \sum_f \sum_k P_{fk} h_k ( \sum_i U_{if} v_i )^2 / |U_{*f}|^2 |v|^2 |
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140 # - \sum_k b_k h_k |
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141 # + 0.5 \sum_i v_i^2 |
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142 # - \sum_j \sum_i W_{ij} g_j v_i |
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143 # - \sum_j c_j g_j |
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144 # - \sum_i a_i v_i |
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145 # |
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146 # |
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147 # Derivation, in which partition functions are ignored. |
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148 # |
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149 # E(v) = -\log(Q(v)) |
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150 # = -\log( \sum_{h,g} Q(v,h,g)) |
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151 # = -\log( \sum_{h,g} exp(-E(v,h,g))) |
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152 # = -\log( \sum_{h,g} exp(- |
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153 # - 0.5 \sum_f \sum_k P_{fk} h_k ( \sum_i U_{if} v_i )^2 / (|U_{*f}| * |v|) |
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154 # - \sum_k b_k h_k |
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155 # + 0.5 \sum_i v_i^2 |
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156 # - \sum_j \sum_i W_{ij} g_j v_i |
1500 | 157 # - \sum_j c_j g_j |
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158 # - \sum_i a_i v_i )) |
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159 # |
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160 # Get rid of double negs in exp |
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161 # = -\log( \sum_{h} exp( |
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162 # + 0.5 \sum_f \sum_k P_{fk} h_k ( \sum_i U_{if} v_i )^2 / (|U_{*f}| * |v|) |
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163 # + \sum_k b_k h_k |
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164 # - 0.5 \sum_i v_i^2 |
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165 # ) * \sum_{g} exp( |
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166 # + \sum_j \sum_i W_{ij} g_j v_i |
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167 # + \sum_j c_j g_j)) |
1500 | 168 # - \sum_i a_i v_i |
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169 # |
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170 # Break up log |
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171 # = -\log( \sum_{h} exp( |
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172 # + 0.5 \sum_f \sum_k P_{fk} h_k ( \sum_i U_{if} v_i )^2 / (|U_{*f}|*|v|) |
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173 # + \sum_k b_k h_k |
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174 # )) |
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175 # -\log( \sum_{g} exp( |
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176 # + \sum_j \sum_i W_{ij} g_j v_i |
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177 # + \sum_j c_j g_j ))) |
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178 # + 0.5 \sum_i v_i^2 |
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180 # |
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181 # Use domain h is binary to turn log(sum(exp(sum...))) into sum(log(.. |
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182 # = -\log(\sum_{h} exp( |
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183 # + 0.5 \sum_f \sum_k P_{fk} h_k ( \sum_i U_{if} v_i )^2 / (|U_{*f}|* |v|) |
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184 # + \sum_k b_k h_k |
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185 # )) |
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186 # - \sum_{j} \log(1 + exp(\sum_i W_{ij} v_i + c_j )) |
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187 # + 0.5 \sum_i v_i^2 |
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189 # |
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190 # = - \sum_{k} \log(1 + exp(b_k + 0.5 \sum_f P_{fk}( \sum_i U_{if} v_i )^2 / (|U_{*f}|*|v|))) |
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191 # - \sum_{j} \log(1 + exp(\sum_i W_{ij} v_i + c_j )) |
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192 # + 0.5 \sum_i v_i^2 |
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194 # |
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195 # For negative-one-diagonal P this gives: |
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196 # |
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197 # = - \sum_{k} \log(1 + exp(b_k - 0.5 \sum_i (U_{ik} v_i )^2 / (|U_{*k}|*|v|))) |
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198 # - \sum_{j} \log(1 + exp(\sum_i W_{ij} v_i + c_j )) |
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199 # + 0.5 \sum_i v_i^2 |
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201 |
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202 import numpy as np |
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203 import numpy |
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204 |
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205 import theano |
1507 | 206 from theano import dot |
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207 from theano import tensor as TT |
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208 floatX = theano.config.floatX |
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209 |
1507 | 210 sharedX = lambda X, name : theano.shared(numpy.asarray(X, dtype=floatX), name=name) |
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211 |
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212 from pylearn.sampling.hmc import HMC_sampler |
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213 from pylearn.gd.sgd import sgd_updates |
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214 |
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215 ########################################### |
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216 # |
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217 # Candidates for factoring |
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218 # |
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219 ########################################### |
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220 |
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221 def l1(X): |
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222 """ |
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223 :param X: TensorType variable |
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224 |
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225 :rtype: TensorType scalar |
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226 |
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227 :returns: the sum of absolute values of the terms in X |
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228 |
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229 :math: \sum_i |X_i| |
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230 |
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231 Where i is an appropriately dimensioned index. |
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232 |
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233 """ |
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234 return abs(X).sum() |
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235 |
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236 def l2(X): |
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237 """ |
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238 :param X: TensorType variable |
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239 |
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240 :rtype: TensorType scalar |
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241 |
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242 :returns: the sum of absolute values of the terms in X |
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243 |
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244 :math: \sqrt{ \sum_i X_i^2 } |
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245 |
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246 Where i is an appropriately dimensioned index. |
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247 |
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248 """ |
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249 return TT.sqrt((X**2).sum()) |
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250 |
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251 def contrastive_cost(free_energy_fn, pos_v, neg_v): |
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252 """ |
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253 :param free_energy_fn: lambda (TensorType matrix MxN) -> TensorType vector of M free energies |
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254 :param pos_v: TensorType matrix MxN of M "positive phase" particles |
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255 :param neg_v: TensorType matrix MxN of M "negative phase" particles |
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256 |
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257 :returns: TensorType scalar that's the sum of the difference of free energies |
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258 |
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259 :math: \sum_i free_energy(pos_v[i]) - free_energy(neg_v[i]) |
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260 |
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261 """ |
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262 return (free_energy_fn(pos_v) - free_energy_fn(neg_v)).sum() |
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263 |
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264 def contrastive_grad(free_energy_fn, pos_v, neg_v, wrt, other_cost=0, consider_constant=[]): |
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265 """ |
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266 :param free_energy_fn: lambda (TensorType matrix MxN) -> TensorType vector of M free energies |
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267 :param pos_v: positive-phase sample of visible units |
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268 :param neg_v: negative-phase sample of visible units |
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269 :param wrt: TensorType variables with respect to which we want gradients (similar to the |
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270 'wrt' argument to tensor.grad) |
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271 :param other_cost: TensorType scalar (should be the sum over a minibatch, not mean) |
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272 |
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273 :returns: TensorType variables for the gradient on each of the 'wrt' arguments |
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274 |
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275 |
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276 :math: Cost = other_cost + \sum_i free_energy(pos_v[i]) - free_energy(neg_v[i]) |
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277 :math: d Cost / dW for W in `wrt` |
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278 |
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279 |
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280 This function is similar to tensor.grad - it returns the gradient[s] on a cost with respect |
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281 to one or more parameters. The difference between tensor.grad and this function is that |
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282 the negative phase term (`neg_v`) is considered constant, i.e. d `Cost` / d `neg_v` = 0. |
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283 This is desirable because `neg_v` might be the result of a sampling expression involving |
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284 some of the parameters, but the contrastive divergence algorithm does not call for |
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285 backpropagating through the sampling procedure. |
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286 |
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287 Warning - if other_cost depends on pos_v or neg_v and you *do* want to backpropagate from |
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288 the `other_cost` through those terms, then this function is inappropriate. In that case, |
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289 you should call tensor.grad separately for the other_cost and add the gradient expressions |
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290 you get from ``contrastive_grad(..., other_cost=0)`` |
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291 |
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292 """ |
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293 cost=contrastive_cost(free_energy_fn, pos_v, neg_v) |
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294 if other_cost: |
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295 cost = cost + other_cost |
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296 return theano.tensor.grad(cost, |
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297 wrt=wrt, |
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298 consider_constant=consider_constant+[neg_v]) |
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299 |
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300 ########################################### |
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301 # |
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302 # Expressions that are mcRBM-specific |
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303 # |
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304 ########################################### |
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305 |
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306 class mcRBM(object): |
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307 """Light-weight class that provides the math related to inference |
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308 |
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309 Attributes: |
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310 |
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311 - U - the covariance filters (theano shared variable) |
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312 - W - the mean filters (theano shared variable) |
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313 - a - the visible bias (theano shared variable) |
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314 - b - the covariance bias (theano shared variable) |
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315 - c - the mean bias (theano shared variable) |
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316 |
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317 """ |
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318 def __init__(self, U, W, a, b, c): |
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319 self.U = U |
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320 self.W = W |
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321 self.a = a |
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322 self.b = b |
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323 self.c = c |
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324 |
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325 def hidden_cov_units_preactivation_given_v(self, v, small=0.5): |
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326 """Return argument to the sigmoid that would give mean of covariance hid units |
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327 |
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328 See the math at the top of this file for what 'adjusted' means. |
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329 |
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330 return b - 0.5 * dot(adjusted(v), U)**2 |
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331 """ |
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332 unit_v = v / (TT.sqrt(TT.mean(v**2, axis=1)+small)).dimshuffle(0,'x') # adjust row norm |
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333 return self.b - 0.5 * dot(unit_v, self.U)**2 |
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334 |
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335 def free_energy_terms_given_v(self, v): |
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336 """Returns theano expression for the terms that are added to form the free energy of |
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337 visible vector `v` in an mcRBM. |
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338 |
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339 1. Free energy related to covariance hiddens |
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340 2. Free energy related to mean hiddens |
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341 3. Free energy related to L2-Norm of `v` |
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342 4. Free energy related to projection of `v` onto biases `a` |
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343 """ |
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344 t0 = -TT.sum(TT.nnet.softplus(self.hidden_cov_units_preactivation_given_v(v)),axis=1) |
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345 t1 = -TT.sum(TT.nnet.softplus(self.c + dot(v,self.W)), axis=1) |
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346 t2 = 0.5 * TT.sum(v**2, axis=1) |
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347 t3 = -TT.dot(v, self.a) |
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348 return [t0, t1, t2, t3] |
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349 |
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350 def free_energy_given_v(self, v): |
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351 """Returns theano expression for free energy of visible vector `v` in an mcRBM |
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352 """ |
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353 return TT.add(*self.free_energy_terms_given_v(v)) |
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354 |
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355 def expected_h_g_given_v(self, v): |
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356 """Returns tuple (`h`, `g`) of theano expression conditional expectations in an mcRBM. |
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357 |
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358 `h` is the conditional on the covariance units. |
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359 `g` is the conditional on the mean units. |
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361 """ |
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362 h = TT.nnet.sigmoid(self.hidden_cov_units_preactivation_given_v(v)) |
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363 g = TT.nnet.sigmoid(self.c + dot(v,self.W)) |
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364 return (h, g) |
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365 |
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366 def n_visible_units(self): |
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367 """Return the number of visible units of this RBM |
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368 |
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369 For an RBM made from shared variables, this will return an integer, |
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370 for a purely symbolic RBM this will return a theano expression. |
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372 """ |
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373 try: |
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374 return self.W.get_value(borrow=True, return_internal_type=True).shape[0] |
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375 except AttributeError: |
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376 return self.W.shape[0] |
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377 |
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378 def n_hidden_cov_units(self): |
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379 """Return the number of hidden units for the covariance in this RBM |
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380 |
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381 For an RBM made from shared variables, this will return an integer, |
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382 for a purely symbolic RBM this will return a theano expression. |
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384 """ |
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385 try: |
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386 return self.U.get_value(borrow=True, return_internal_type=True).shape[1] |
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387 except AttributeError: |
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388 return self.U.shape[1] |
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389 |
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390 def n_hidden_mean_units(self): |
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391 """Return the number of hidden units for the mean in this RBM |
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392 |
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393 For an RBM made from shared variables, this will return an integer, |
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394 for a purely symbolic RBM this will return a theano expression. |
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396 """ |
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397 try: |
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398 return self.W.get_value(borrow=True, return_internal_type=True).shape[1] |
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399 except AttributeError: |
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400 return self.W.shape[1] |
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401 |
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402 def CD1_sampler(self, v, n_particles, n_visible=None, rng=8923984): |
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403 """Return a symbolic negative-phase particle obtained by simulating the Hamiltonian |
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404 associated with the energy function. |
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405 """ |
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406 #TODO: why not expose all HMC arguments somehow? |
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407 if not hasattr(rng, 'randn'): |
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408 rng = np.random.RandomState(rng) |
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409 if n_visible is None: |
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410 n_visible = self.n_visible_units() |
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411 |
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412 # create a dummy hmc object because we want to use *some* of it |
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413 hmc = HMC_sampler.new_from_shared_positions( |
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414 shared_positions=v, # v is not shared, so some functionality will not work |
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415 energy_fn=self.free_energy_given_v, |
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416 seed=int(rng.randint(2**30)), |
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417 shared_positions_shape=(n_particles,n_visible), |
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418 compile_simulate=False) |
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419 updates = dict(hmc.updates()) |
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420 final_p = updates.pop(v) |
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421 return hmc, final_p, updates |
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422 |
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423 def sampler(self, n_particles, n_visible=None, rng=7823748): |
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424 """Return an `HMC_sampler` that will draw samples from the distribution over visible |
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425 units specified by this RBM. |
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426 |
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427 :param n_particles: this many parallel chains will be simulated. |
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428 :param rng: seed or numpy RandomState object to initialize particles, and to drive the simulation. |
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429 """ |
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430 #TODO: why not expose all HMC arguments somehow? |
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431 #TODO: Consider returning a sample kwargs for passing to HMC_sampler? |
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432 if not hasattr(rng, 'randn'): |
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433 rng = np.random.RandomState(rng) |
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434 if n_visible is None: |
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435 n_visible = self.n_visible_units() |
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436 rval = HMC_sampler.new_from_shared_positions( |
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437 shared_positions = sharedX( |
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438 rng.randn( |
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439 n_particles, |
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440 n_visible), |
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441 name='particles'), |
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442 energy_fn=self.free_energy_given_v, |
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443 seed=int(rng.randint(2**30))) |
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444 return rval |
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445 |
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446 if 0: |
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447 def as_feedforward_layer(self, v): |
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448 """Return a dictionary with keys: inputs, outputs and params |
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449 |
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450 The inputs is [v] |
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451 |
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452 The outputs is :math:`[E[h|v], E[g|v]]` where `h` is the covariance hidden units and `g` is |
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453 the mean hidden units. |
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454 |
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455 The params are ``[U, W, b, c]``, the model parameters that enter into the conditional |
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456 expectations. |
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457 |
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458 :TODO: add an optional parameter to return only one of the expections. |
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459 |
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460 """ |
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461 return dict( |
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462 inputs = [v], |
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463 outputs = list(self.expected_h_g_given_v(v)), |
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464 params = [self.U, self.W, self.b, self.c], |
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465 ) |
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466 |
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467 def params(self): |
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468 """Return the elements of [U,W,a,b,c] that are shared variables |
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469 |
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470 WRITEME : a *prescriptive* definition of this method suitable for mention in the API |
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471 doc. |
1500 | 472 |
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473 """ |
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474 return list(self._params) |
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475 |
967
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476 @classmethod |
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477 def alloc(cls, n_I, n_K, n_J, rng = 8923402190, |
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478 U_range=0.02, |
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479 W_range=0.05, |
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480 a_ival=0, |
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481 b_ival=2, |
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482 c_ival=-2): |
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483 """ |
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484 Return a MeanCovRBM instance with randomly-initialized shared variable parameters. |
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485 |
995
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486 :param n_I: input dimensionality |
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487 :param n_K: number of covariance hidden units |
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488 :param n_J: number of mean filters (linear) |
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489 :param rng: seed or numpy RandomState object to initialize parameters |
1500 | 490 |
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491 :note: |
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492 Constants for initial ranges and values taken from train_mcRBM.py. |
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493 """ |
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494 if not hasattr(rng, 'randn'): |
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495 rng = np.random.RandomState(rng) |
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496 |
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497 rval = cls( |
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498 U = sharedX(U_range * rng.randn(n_I, n_K),'U'), |
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499 W = sharedX(W_range * rng.randn(n_I, n_J),'W'), |
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500 a = sharedX(np.ones(n_I)*a_ival,'a'), |
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501 b = sharedX(np.ones(n_K)*b_ival,'b'), |
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502 c = sharedX(np.ones(n_J)*c_ival,'c'),) |
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503 rval._params = [rval.U, rval.W, rval.a, rval.b, rval.c] |
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504 return rval |
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505 |
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506 def topological_connectivity(out_shape=(12,12), window_shape=(3,3), window_stride=(2,2), dtype=None): |
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507 """Return numpy R x C matrix with connection weights from R inputs (filters) to C output (covariance) units. |
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508 """ |
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509 if window_stride[0] != window_stride[1]: |
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510 raise ValueError() |
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511 if out_shape[0] != out_shape[1]: |
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512 raise ValueError() |
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513 if window_shape[0] != window_shape[1]: |
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514 raise ValueError() |
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515 |
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516 if dtype is None: |
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517 dtype = theano.config.floatX |
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518 |
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519 ker = numpy.asarray([1., 2., 1.], dtype=dtype) |
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520 ker = numpy.outer(ker,ker) |
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521 ker /= ker.sum() |
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522 |
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523 in_shape = (window_stride[0] * out_shape[0], |
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524 window_stride[1] * out_shape[1]) |
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525 |
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526 tmp = numpy.zeros(in_shape, dtype=dtype) |
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527 rval = numpy.zeros(in_shape + out_shape, dtype=dtype) |
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528 A,B,C,D = rval.shape |
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529 |
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530 # for each output position (out_r, out_c) |
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531 for out_r in range(out_shape[0]): |
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532 for out_c in range(out_shape[1]): |
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533 # for each window position (win_r, win_c) |
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534 for win_r in range(window_shape[0]): |
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535 for win_c in range(window_shape[1]): |
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536 # add 1 to the corresponding input location |
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537 in_r = out_r * window_stride[0] + win_r - (window_shape[0]-1)//2 |
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538 in_c = out_c * window_stride[1] + win_c - (window_shape[1]-1)//2 |
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539 rval[(in_c+A)%A, (in_r+B)%B, out_r%C, out_c%D] = ker[win_r, win_c] |
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540 return rval.reshape((A*B,C*D)) |
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541 |
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542 class mcRBM_withP(mcRBM): |
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543 """Light-weight class that provides the math related to inference |
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544 |
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545 Attributes: |
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546 |
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547 - U - the covariance filters (theano shared variable) |
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548 - W - the mean filters (theano shared variable) |
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549 - a - the visible bias (theano shared variable) |
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550 - b - the covariance bias (theano shared variable) |
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551 - c - the mean bias (theano shared variable) |
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552 |
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553 """ |
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554 # PCA eigenvectors (E) [scaled by 1/sqrt(eigenvals)] has to be passed to model |
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555 # because v has to be divided by the number original dimensions |
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556 # not the number of pca dimensions in hidden_cov_units_preactivation_given_v() |
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557 def __init__(self, U, W, a, b, c, P, norm_doctoring): |
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558 self.P = P |
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559 self.norm_doctoring = norm_doctoring |
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560 super(mcRBM_withP, self).__init__(U,W,a,b,c) |
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561 |
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562 def hidden_cov_units_preactivation_given_v(self, v): |
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563 """Return argument to the sigmoid that would give mean of covariance hid units |
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564 |
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565 """ |
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566 slope, offset = self.norm_doctoring |
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567 norm_sq = TT.sum(v**2, axis=1) * slope + offset |
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568 unit_v = v / TT.sqrt(norm_sq).dimshuffle(0,'x') # adjust row norm |
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569 return self.b + 0.5 * dot(dot(unit_v, self.U)**2, self.P) |
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570 |
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571 def n_hidden_cov_units(self): |
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572 """Return the number of hidden units for the covariance in this RBM |
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573 |
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574 For an RBM made from shared variables, this will return an integer, |
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575 for a purely symbolic RBM this will return a theano expression. |
1500 | 576 |
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577 """ |
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578 try: |
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579 return self.P.get_value(borrow=True, return_internal_type=True).shape[1] |
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580 except AttributeError: |
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581 return self.P.shape[1] |
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582 |
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583 @classmethod |
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584 def alloc(cls, n_I, n_K, n_J, *args, **kwargs): |
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585 """ |
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586 Return a MeanCovRBM instance with randomly-initialized shared variable parameters. |
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587 |
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588 :param n_I: input dimensionality |
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589 :param n_K: number of covariance hidden units |
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590 :param n_J: number of mean filters (linear) |
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591 :param rng: seed or numpy RandomState object to initialize parameters |
1500 | 592 |
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593 :note: |
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594 Constants for initial ranges and values taken from train_mcRBM.py. |
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595 """ |
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596 return cls.alloc_with_P( |
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597 -numpy.eye((n_K, n_K)).astype(theano.config.floatX), |
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598 n_I, |
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599 n_J, |
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600 *args, **kwargs) |
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601 |
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602 @classmethod |
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603 def alloc_topo_P(cls, n_I, n_J, p_out_shape=(12,12), p_win_shape=(3,3), p_win_stride=(2,2), |
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604 **kwargs): |
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605 # the factor of 2 is for some degree of compatibility with Marc'Aurelio's code the 'w2' |
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606 # in his code is -0.5 * self.P |
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607 return cls.alloc_with_P( |
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608 -2*topological_connectivity(p_out_shape, p_win_shape, p_win_stride), |
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609 n_I=n_I, n_J=n_J, **kwargs) |
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610 |
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611 @classmethod |
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612 def alloc_with_P(cls, Pval, n_I, n_J, rng = 8923402190, |
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613 U_range=0.02, |
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614 W_range=0.05, |
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615 a_ival=0, |
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616 b_ival=2, |
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617 c_ival=-2, |
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618 norm_doctoring=(1.0/192, .5)): |
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619 n_F, n_K = Pval.shape |
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620 if not hasattr(rng, 'randn'): |
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621 rng = np.random.RandomState(rng) |
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622 rval = cls( |
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623 U = sharedX(U_range * rng.randn(n_I, n_F),'U'), |
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624 W = sharedX(W_range * rng.randn(n_I, n_J),'W'), |
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625 a = sharedX(np.ones(n_I)*a_ival,'a'), |
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626 b = sharedX(np.ones(n_K)*b_ival,'b'), |
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627 c = sharedX(np.ones(n_J)*c_ival,'c'), |
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628 P = sharedX(Pval, 'P'), |
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629 norm_doctoring=norm_doctoring) |
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630 rval._params = [rval.U, rval.W, rval.a, rval.b, rval.c, rval.P] |
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631 return rval |
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632 |
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633 class mcRBMTrainer(object): |
1500 | 634 """Light-weight class encapsulating math for mcRBM training |
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635 |
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636 Attributes: |
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637 - rbm - an mcRBM instance |
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638 - sampler - an HMC_sampler instance |
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639 - normVF - geometrically updated norm of U matrix columns (shared var) |
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640 - learn_rate - SGD learning rate [un-annealed] |
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641 - learn_rate_multipliers - the learning rates for each of the parameters of the rbm (in |
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642 order corresponding to what's returned by ``rbm.params()``) |
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643 - l1_penalty - float or TensorType scalar to modulate l1 penalty of rbm.U and rbm.W |
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644 - iter - number of cd_updates (shared var) - used to anneal the effective learn_rate |
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645 - lr_anneal_start - scalar or TensorType scalar - iter at which time to start decreasing |
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646 the learning rate proportional to 1/iter |
967
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647 |
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648 """ |
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649 # TODO: accept a GD algo as an argument? |
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650 @classmethod |
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651 def alloc_for_P(cls, rbm, visible_batch, batchsize, initial_lr_per_example=0.075, rng=234, |
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652 l1_penalty=0, |
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653 l1_penalty_start=0, |
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654 learn_rate_multipliers=None, |
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655 lr_anneal_start=2000, |
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656 p_training_start=4000, |
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657 p_training_lr=0.02, |
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658 persistent_chains=True |
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659 ): |
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660 if learn_rate_multipliers is None: |
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661 p_lr = sharedX(0.0, 'P_lr_multiplier') |
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662 learn_rate_multipliers = [2, .2, .02, .1, .02, p_lr] |
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663 else: |
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664 p_lr = None |
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665 rval = cls.alloc(rbm, visible_batch, batchsize, initial_lr_per_example, rng, l1_penalty, |
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666 l1_penalty_start, learn_rate_multipliers, lr_anneal_start, persistent_chains) |
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667 |
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668 rval.p_mask = sharedX((rbm.P.get_value(borrow=True)!=0).astype('float32'), 'p_mask') |
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669 |
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670 rval.p_lr = p_lr |
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671 rval.p_training_start=p_training_start |
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672 rval.p_training_lr=p_training_lr |
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673 return rval |
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674 |
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675 |
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676 @classmethod |
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677 def alloc(cls, rbm, visible_batch, batchsize, initial_lr_per_example=0.075, rng=234, |
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678 l1_penalty=0, |
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679 l1_penalty_start=0, |
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680 learn_rate_multipliers=[2, .2, .02, .1, .02], |
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681 lr_anneal_start=2000, |
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682 persistent_chains=True |
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683 ): |
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684 |
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685 """ |
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686 :param rbm: mcRBM instance to train |
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687 :param visible_batch: TensorType variable for training data |
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688 :param batchsize: the number of rows in visible_batch |
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689 :param initial_lr_per_example: the learning rate (may be annealed) |
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690 :param rng: seed or RandomState to initialze PCD sampler |
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691 :param l1_penalty: see class doc |
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692 :param learn_rate_multipliers: see class doc |
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693 :param lr_anneal_start: see class doc |
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694 """ |
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695 #TODO: :param lr_anneal_iter: the iteration at which 1/t annealing will begin |
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|
696 |
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697 #TODO: get batchsize from visible_batch?? |
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698 # allocates shared var for negative phase particles |
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|
699 |
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|
700 |
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701 # TODO: should normVF be initialized to match the size of rbm.U ? |
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|
702 |
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|
703 if (l1_penalty_start > 0) and (l1_penalty != 0.0): |
1287
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|
704 effective_l1_penalty = sharedX(0.0, 'effective_l1_penalty') |
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705 else: |
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706 effective_l1_penalty = l1_penalty |
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|
707 |
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|
708 if persistent_chains: |
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|
709 sampler = rbm.sampler(batchsize, rng=rng) |
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|
710 else: |
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|
711 sampler = None |
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|
712 |
1272
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|
713 return cls( |
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|
714 rbm=rbm, |
1284
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|
715 batchsize=batchsize, |
1272
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|
716 visible_batch=visible_batch, |
1284
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|
717 sampler=sampler, |
1272
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|
718 normVF=sharedX(1.0, 'normVF'), |
1284
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719 learn_rate=sharedX(initial_lr_per_example/batchsize, 'learn_rate'), |
1272
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720 iter=sharedX(0, 'iter'), |
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|
721 effective_l1_penalty=effective_l1_penalty, |
1272
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|
722 l1_penalty=l1_penalty, |
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|
723 l1_penalty_start=l1_penalty_start, |
1272
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|
724 learn_rate_multipliers=learn_rate_multipliers, |
1284
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|
725 lr_anneal_start=lr_anneal_start, |
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|
726 persistent_chains=persistent_chains,) |
1272
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|
727 |
1267
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|
728 def __init__(self, **kwargs): |
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refactoring mcRBM
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|
729 self.__dict__.update(kwargs) |
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|
730 |
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|
731 def normalize_U(self, new_U): |
1272
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|
732 """ |
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|
733 :param new_U: a proposed new value for rbm.U |
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|
734 |
1500 | 735 :returns: a pair of TensorType variables: |
1272
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|
736 a corrected new value for U, and a new value for self.normVF |
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|
737 |
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|
738 This is a weird normalization procedure, but the sample code for the paper has it, and |
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|
739 it seems to be important. |
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|
740 """ |
1267
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|
741 U_norms = TT.sqrt((new_U**2).sum(axis=0)) |
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|
742 new_normVF = .95 * self.normVF + .05 * TT.mean(U_norms) |
1272
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|
743 return (new_U * new_normVF / U_norms), new_normVF |
1267
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|
744 |
1284
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|
745 def contrastive_grads(self, neg_v = None): |
1272
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|
746 """Return the contrastive divergence gradients on the parameters of self.rbm """ |
1284
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|
747 if neg_v is None: |
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|
748 neg_v = self.sampler.positions |
1267
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refactoring mcRBM
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diff
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|
749 return contrastive_grad( |
1270
d38cb039c662
debugging mcRBM
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1267
diff
changeset
|
750 free_energy_fn=self.rbm.free_energy_given_v, |
1500 | 751 pos_v=self.visible_batch, |
1284
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|
752 neg_v=neg_v, |
1272
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|
753 wrt = self.rbm.params(), |
1284
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|
754 other_cost=(l1(self.rbm.U)+l1(self.rbm.W)) * self.effective_l1_penalty) |
967
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changeset
|
755 |
1272
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|
756 def cd_updates(self): |
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mcRBM working with whole learning algo in theano
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|
757 """ |
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|
758 Return a dictionary of shared variable updates that implements contrastive divergence |
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diff
changeset
|
759 learning by stochastic gradient descent with an annealed learning rate. |
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changeset
|
760 """ |
967
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adding algorithms/mcRBM, but it is not done yet
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changeset
|
761 |
1284
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|
762 ups = {} |
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|
763 |
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|
764 if self.persistent_chains: |
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changeset
|
765 grads = self.contrastive_grads() |
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changeset
|
766 ups.update(dict(self.sampler.updates())) |
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|
767 else: |
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changeset
|
768 cd1_sampler, final_p, cd1_updates = self.rbm.CD1_sampler(self.visible_batch, |
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|
769 self.batchsize) |
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changeset
|
770 self._last_cd1_sampler = cd1_sampler # hacked in here for the unit test |
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changeset
|
771 #ignore the cd1_sampler |
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changeset
|
772 grads = self.contrastive_grads(neg_v = final_p) |
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changeset
|
773 ups.update(dict(cd1_updates)) |
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changeset
|
774 |
1267
075c193afd1b
refactoring mcRBM
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diff
changeset
|
775 |
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diff
changeset
|
776 # contrastive divergence updates |
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refactoring mcRBM
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diff
changeset
|
777 # TODO: sgd_updates is a particular optization algo (others are possible) |
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refactoring mcRBM
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diff
changeset
|
778 # parametrize so that algo is plugin |
075c193afd1b
refactoring mcRBM
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diff
changeset
|
779 # the normalization normVF might be sgd-specific though... |
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diff
changeset
|
780 |
075c193afd1b
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changeset
|
781 # TODO: when sgd has an annealing schedule, this should |
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refactoring mcRBM
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diff
changeset
|
782 # go through that mechanism. |
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changeset
|
783 |
075c193afd1b
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changeset
|
784 lr = TT.clip( |
1500 | 785 self.learn_rate * TT.cast(self.lr_anneal_start / (self.iter+1), floatX), |
1267
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refactoring mcRBM
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diff
changeset
|
786 0.0, #min |
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changeset
|
787 self.learn_rate) #max |
967
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diff
changeset
|
788 |
1284
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changeset
|
789 ups.update(dict(sgd_updates( |
1272
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changeset
|
790 self.rbm.params(), |
1267
075c193afd1b
refactoring mcRBM
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diff
changeset
|
791 grads, |
1284
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changeset
|
792 stepsizes=[a*lr for a in self.learn_rate_multipliers]))) |
1272
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changeset
|
793 |
ba25c6e4f55d
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changeset
|
794 ups[self.iter] = self.iter + 1 |
979
2a53384d9742
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parents:
978
diff
changeset
|
795 |
1267
075c193afd1b
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diff
changeset
|
796 |
075c193afd1b
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James Bergstra <bergstrj@iro.umontreal.ca>
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diff
changeset
|
797 # add trainer updates (replace CD update of U) |
1272
ba25c6e4f55d
mcRBM working with whole learning algo in theano
James Bergstra <bergstrj@iro.umontreal.ca>
parents:
1270
diff
changeset
|
798 ups[self.rbm.U], ups[self.normVF] = self.normalize_U(ups[self.rbm.U]) |
1267
075c193afd1b
refactoring mcRBM
James Bergstra <bergstrj@iro.umontreal.ca>
parents:
1000
diff
changeset
|
799 |
1284
1817485d586d
mcRBM - many changes incl. adding support for pooling matrix
James Bergstra <bergstrj@iro.umontreal.ca>
parents:
1275
diff
changeset
|
800 #l1_updates: |
1817485d586d
mcRBM - many changes incl. adding support for pooling matrix
James Bergstra <bergstrj@iro.umontreal.ca>
parents:
1275
diff
changeset
|
801 if (self.l1_penalty_start > 0) and (self.l1_penalty != 0.0): |
1817485d586d
mcRBM - many changes incl. adding support for pooling matrix
James Bergstra <bergstrj@iro.umontreal.ca>
parents:
1275
diff
changeset
|
802 ups[self.effective_l1_penalty] = TT.switch( |
1817485d586d
mcRBM - many changes incl. adding support for pooling matrix
James Bergstra <bergstrj@iro.umontreal.ca>
parents:
1275
diff
changeset
|
803 self.iter >= self.l1_penalty_start, |
1817485d586d
mcRBM - many changes incl. adding support for pooling matrix
James Bergstra <bergstrj@iro.umontreal.ca>
parents:
1275
diff
changeset
|
804 self.l1_penalty, |
1817485d586d
mcRBM - many changes incl. adding support for pooling matrix
James Bergstra <bergstrj@iro.umontreal.ca>
parents:
1275
diff
changeset
|
805 0.0) |
1817485d586d
mcRBM - many changes incl. adding support for pooling matrix
James Bergstra <bergstrj@iro.umontreal.ca>
parents:
1275
diff
changeset
|
806 |
1817485d586d
mcRBM - many changes incl. adding support for pooling matrix
James Bergstra <bergstrj@iro.umontreal.ca>
parents:
1275
diff
changeset
|
807 if getattr(self,'p_lr', None): |
1817485d586d
mcRBM - many changes incl. adding support for pooling matrix
James Bergstra <bergstrj@iro.umontreal.ca>
parents:
1275
diff
changeset
|
808 ups[self.p_lr] = TT.switch(self.iter > self.p_training_start, |
1817485d586d
mcRBM - many changes incl. adding support for pooling matrix
James Bergstra <bergstrj@iro.umontreal.ca>
parents:
1275
diff
changeset
|
809 self.p_training_lr, |
1817485d586d
mcRBM - many changes incl. adding support for pooling matrix
James Bergstra <bergstrj@iro.umontreal.ca>
parents:
1275
diff
changeset
|
810 0) |
1322
cdda4f98c2a2
mcRBM - added mask for updates to P matrix
James Bergstra <bergstrj@iro.umontreal.ca>
parents:
1287
diff
changeset
|
811 new_P = ups[self.rbm.P] * self.p_mask |
cdda4f98c2a2
mcRBM - added mask for updates to P matrix
James Bergstra <bergstrj@iro.umontreal.ca>
parents:
1287
diff
changeset
|
812 no_pos_P = TT.switch(new_P<0, new_P, 0) |
cdda4f98c2a2
mcRBM - added mask for updates to P matrix
James Bergstra <bergstrj@iro.umontreal.ca>
parents:
1287
diff
changeset
|
813 ups[self.rbm.P] = - no_pos_P / no_pos_P.sum(axis=0) #normalize to that columns sum 1 |
1284
1817485d586d
mcRBM - many changes incl. adding support for pooling matrix
James Bergstra <bergstrj@iro.umontreal.ca>
parents:
1275
diff
changeset
|
814 |
1267
075c193afd1b
refactoring mcRBM
James Bergstra <bergstrj@iro.umontreal.ca>
parents:
1000
diff
changeset
|
815 return ups |