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annotate doc/v2_planning/API_formulas.txt @ 1377:0665274b14af

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Minor fixes for better Sphinx doc output
author Olivier Delalleau <delallea@iro>
date Thu, 18 Nov 2010 14:14:48 -0500
parents 42ddbefd1e03
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42ddbefd1e03 made the API_formulas.txt and removed duplicate stuff from the formulas.txt file
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1 .. _v2planning_formulas:
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3 Math formulas API
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4 =================
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5
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6 Why we need a formulas API
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7 --------------------------
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8
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9 Their is a few reasons why having a library of mathematical formula for theano is a good reason:
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10
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11 * Some formula have some special thing needed for the gpu.
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12 * Sometimes we need to cast to floatX...
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13 * Some formula have numerical stability problem.
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14 * Some formula gradiant have numerical stability problem. (Happen more frequently then the previous ones)
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15 * If theano don't always do some stability optimization, we could do it manually in the formulas
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16 * Some formula as complex to implement and take many try to do correctly.
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17 * Can mimic the hierarchy of other library to ease the migration to theano
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19 Having a library help in that we solve those problem only once.
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20
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21 What is a formula
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22 -----------------
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23
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24 We define formulas as something that don't have a state. They are implemented as
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25 python function that take theano variable as input and they output theano
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26 variable. If you want state, look at what the others commities will do.
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27
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28 Formulas documentation
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29 ----------------------
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31 We must respect what the coding commitee have set for the docstring of the file and of the function.
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32
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33 * A latex mathematical description of the formulas(for picture representation in generated documentation)
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34 * Tags(for searching):
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35 * a list of lower level fct used
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36 * category(name of the submodule itself)
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37 * Tell if we did some work to make it more numerical stable. Do theano do the optimization needed?
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38 * Tell if the grad is numericaly stable? Do theano do the optimization needed?
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39 * Tell if work/don't/unknow on gpu.
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40 * Tell alternate name
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41 * Tell the domaine, range of the input/output(range should use the english notation of including or excluding)
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42
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43 Proposed hierarchy
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44 ------------------
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46 Here is the proposed hierarchy for formulas:
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47
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48 * pylearn.formulas.costs: generic / common cost functions, e.g. various cross-entropies, squared error,
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49 abs. error, various sparsity penalties (L1, Student)
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50 * pylearn.formulas.regularization: formulas for regularization
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51 * pylearn.formulas.linear: formulas for linear classifier, linear regression, factor analysis, PCA
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52 * pylearn.formulas.nnet: formulas for building layers of various kinds, various activation functions,
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53 layers which could be plugged with various costs & penalties, and stacked
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54 * pylearn.formulas.ae: formulas for auto-encoders and denoising auto-encoder variants
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55 * pylearn.formulas.noise: formulas for corruption processes
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56 * pylearn.formulas.rbm: energies, free energies, conditional distributions, Gibbs sampling
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57 * pylearn.formulas.trees: formulas for decision trees
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58 * pylearn.formulas.boosting: formulas for boosting variants
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59 * pylearn.formulas.maths for other math formulas
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60 * pylearn.formulas.scipy.stats: example to implement the same interface as existing lib
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61
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62 etc.
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63
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64 Example
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65 -------
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66 .. code-block:: python
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67
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68 """
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69 This script defines a few often used cost functions.
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70 """
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71 import theano
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72 import theano.tensor as T
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73 from tags import tags
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74
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75 @tags('cost','binary','cross-entropy')
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76 def binary_crossentropy(output, target):
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77 """ Compute the crossentropy of binary output wrt binary target.
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78
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79 .. math::
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80 L_{CE} \equiv t\log(o) + (1-t)\log(1-o)
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81
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82 :type output: Theano variable
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83 :param output: Binary output or prediction :math:`\in[0,1]`
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84 :type target: Theano variable
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85 :param target: Binary target usually :math:`\in\{0,1\}`
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86 """
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87 return -(target * tensor.log(output) + (1.0 - target) * tensor.log(1.0 - output))
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88
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89
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90 TODO
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91 ----
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92 * define a list of search tag to start with
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93 * Add to the html page a list of the tag and a list of each fct associated to them.
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94 * move existing formulas to pylearn as examples and add other basics ones.
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95 * theano.tensor.nnet will probably be copied to pylearn.formulas.nnet and depricated.
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96