Changeset 448
- Timestamp:
- 07/21/07 23:07:35 (1 year ago)
- Files:
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- trunk/learn/scikits/learn/machine/em/Changelog (modified) (1 diff)
- trunk/learn/scikits/learn/machine/em/README (modified) (2 diffs)
- trunk/learn/scikits/learn/machine/em/doc (modified) (1 prop)
- trunk/learn/scikits/learn/machine/em/doc/Makefile (modified) (1 diff)
- trunk/learn/scikits/learn/machine/em/doc/index.txt (modified) (13 diffs)
- trunk/learn/scikits/learn/machine/em/doc/tutorial.pdf (modified) (64 diffs)
- trunk/learn/scikits/learn/machine/em/examples/basic_example1.py (modified) (1 diff)
- trunk/learn/scikits/learn/machine/em/examples/basic_example2.py (modified) (1 diff)
- trunk/learn/scikits/learn/machine/em/examples/basic_example3.py (modified) (1 diff)
- trunk/learn/scikits/learn/machine/em/examples/discriminant_analysis.py (modified) (3 diffs)
- trunk/learn/scikits/learn/machine/em/examples/pdfestimation.py (modified) (3 diffs)
- trunk/learn/scikits/learn/machine/em/examples/pdfestimation1d.py (modified) (3 diffs)
- trunk/learn/scikits/learn/machine/em/examples/plotexamples.py (modified) (3 diffs)
- trunk/learn/scikits/learn/machine/em/examples/regularized_example.py (modified) (2 diffs)
- trunk/learn/scikits/learn/machine/em/tests/test_densities.py (modified) (9 diffs)
- trunk/learn/scikits/learn/machine/em/tests/test_examples.py (modified) (1 diff)
- trunk/learn/scikits/learn/machine/em/tests/test_gauss_mix.py (modified) (2 diffs)
- trunk/learn/scikits/learn/machine/em/tests/test_gmm_em.py (modified) (2 diffs)
- trunk/learn/scikits/learn/machine/pyem (added)
- trunk/learn/scikits/learn/machine/pyem/__init__.py (added)
- trunk/learn/scikits/learn/machine/setup.py (modified) (1 diff)
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trunk/learn/scikits/learn/machine/em/Changelog
r447 r448 1 pyem (0.5.7dev) Sun, 22 Jul 2007 11:05:58 +0900 2 3 * pyem is now part of the scikits.learn package 4 * Renamed to em 5 1 6 pyem (0.5.7dev) Mon, 28 May 2007 11:31:08 +0900 2 7 trunk/learn/scikits/learn/machine/em/README
r447 r448 1 Last Change: S at Jun 0912:00 PM 2007 J1 Last Change: Sun Jul 22 12:00 PM 2007 J 2 2 3 pyem is a python module build upon numpy and scipy 4 (see http://www.scipy.org/) for learning mixtures models 5 using Expectation Maximization. For now, only Gaussian 6 Mixture Models are implemented. Included features: 3 em is a python module build upon numpy and scipy (see http://www.scipy.org/) 4 for learning mixtures models using Expectation Maximization. For now, only 5 Gaussian Mixture Models are implemented. Included features: 7 6 8 7 * computation of Gaussian pdf for multi-variate Gaussian … … 11 10 * Confidence ellipsoides with probability at arbitrary level 12 11 * Classic EM for Gaussian Mixture Models 13 * K-mean based and random initialization for EM available12 * Experimental regularized (MAP) EM trunk/learn/scikits/learn/machine/em/doc
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*.pyc
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trunk/learn/scikits/learn/machine/em/doc/Makefile
r363 r448 1 # Last Change: Mon Jul 02 09:00 PM 2007 J1 # Last Change: Sun Jul 22 11:00 AM 2007 J 2 2 3 3 # This makefile is used to build the pdf from the rest file and inlined code 4 4 # from python examples 5 5 6 py2tex = PYTHONPATH=/home/david/local/lib/python2.4/site-packagespygmentize -l python -f tex6 py2tex = pygmentize -l python -f tex 7 7 rst2tex = PYTHONPATH=/home/david/local/lib/python2.4/site-packages rst2newlatex.py \ 8 8 --stylesheet-path base.tex --user-stylesheet user.tex trunk/learn/scikits/learn/machine/em/doc/index.txt
r363 r448 1 1 .. 2 2 restindex 3 page-title: Pyem4 crumb: Pyem5 link-title: Pyem3 page-title: Em 4 crumb: Em 5 link-title: Em 6 6 encoding: utf-8 7 7 output-encoding: None 8 tags: python, pyem,Expectation Maximization,EM,online EM,recursive EM8 tags: python,em,Expectation Maximization,EM,online EM,recursive EM 9 9 file: basic_example1.py 10 10 file: basic_example2.py … … 14 14 /restindex 15 15 16 .. Last Change: Mon Jul 02 09:00 PM 2007 J16 .. Last Change: Sun Jul 22 11:00 AM 2007 J 17 17 18 18 =================================================== 19 PyEM, a python package for Gaussian mixture models19 em, a python package for Gaussian mixture models 20 20 =================================================== 21 21 22 22 .. contents:: Tables of contents 23 23 24 PyEM is a package which enables to create Gaussian Mixture Models24 EM is a package which enables to create Gaussian Mixture Models 25 25 (diagonal and full covariance matrices supported), to sample them, 26 26 and to estimate them from data using Expectation Maximization algorithm. … … 30 30 online EM (ie recursive EM) and variational Bayes implementation. 31 31 32 PyEM is implemented in python, and uses the excellent numpy and scipy32 EM is implemented in python, and uses the excellent numpy and scipy 33 33 packages. Numpy is a python packages which gives python a fast 34 34 multi-dimensional array capabilities (ala matlab and the likes); scipy … … 41 41 42 42 .. _scipy: http://www.scipy.org 43 44 Pyem depends on several packages to work: 43 .. _scikits: https://projects.scipy.org/scipy/scikits/ 44 45 The toolbox depends on several packages to work: 45 46 46 47 - numpy 47 - matplotlib (if you wish to use the plotting facilities of pyem) 48 - scipy 49 - setuptools 50 - matplotlib (if you wish to use the plotting facilities: this is not mandatory) 48 51 49 52 Those packages are likely to be already installed in a typical numpy/scipy environment. 50 53 51 Since september 2006, pyem is included in the sandbox of `scipy`_. The sandbox52 contains packages which are pending for approval in main scipy; that means it 53 is not installed by default, and that you need to install scipy from sources. 54 For the most up-to-date version of pyem, you need to download scipy from 55 s ubversion, which contains the development branch of scipy.56 57 To install pyem, you just need to edit (or create if it does not exist) 58 the file Lib/sandbox/enabled_packages.txt in scipy sources, and 59 add one line with the name of the package (eg pyem). 60 After, you just need to install scipy normally as explained 61 `here <http://www.scipy.org/Installing_SciPy>`_. 62 63 You can (and should) also test pyem installation using the following:54 Since July 2007, the toolbox is included in the learn scikits (`scikits`_). 55 There is no official release yet, but you can get the package through svn with 56 the following command: 57 58 svn co http://svn.scipy.org/svn/scikits/trunk scikits.dev 59 60 Of course, you can also use a graphical tool such as TortoiseSVN on windows if 61 you do not feel confortable with the command line. Then, you can install it 62 with the following command in the scikits.dev directory: 63 64 python setup.py install 65 66 You can (and should) also test em installation using the following: 64 67 65 68 .. raw:: html … … 67 70 {+mycoloring} 68 71 69 from sci py.sandbox import pyem70 pyem.test()72 from scikits.learn.machine import em 73 em.test() 71 74 {-mycoloring} 72 75 … … 74 77 ============ 75 78 76 Once you are inside a python interpreter, you can import pyem77 using thefollwing command:79 Once you are inside a python interpreter, you can import the package using the 80 follwing command: 78 81 79 82 .. raw:: html 80 83 81 84 {+mycoloring} 82 83 from scipy.sandbox import pyem 85 from scikits.learn.machine import em 84 86 {-mycoloring} 85 87 … … 88 90 ----------------------------------------- 89 91 90 Importing pyem gives access to 3 classes: GM (for Gausssian Mixture), GMM91 (Gaussian Mixture Model) and EM (for Expectation Maximization). The first92 class GM can be used to create an artificial Gaussian Model, samples it, 93 or plot it. The following example show how to create 94 a 2 dimension Gaussian Model with 3 components, sample it and plot 95 its confidence ellipsoids withmatplotlib:96 97 .. raw:: html 98 99 {mycolorize;input/softwares/ pyem/basic_example1.py}92 Importing the package gives access to 3 classes: GM (for Gausssian Mixture), 93 GMM (Gaussian Mixture Model) and EM (for Expectation Maximization). The first 94 class GM can be used to create an artificial Gaussian Model, samples it, or 95 plot it. The following example show how to create a 2 dimension Gaussian Model 96 with 3 components, sample it and plot its confidence ellipsoids with 97 matplotlib: 98 99 .. raw:: html 100 101 {mycolorize;input/softwares/em/basic_example1.py} 100 102 101 103 .. raw:: latex … … 121 123 122 124 If you want to learn a Gaussian mixture from data with EM, you need to use two 123 classes from pyem: GMM and EM. You first create a GMM object from a GM124 instance; then you can give the GMM object as a parameter to the EM class to 125 compute iterations of EM; once the EM has finished the computation, the GM 126 instance ofGMM contains the computed parameters.127 128 .. raw:: html 129 130 {mycolorize;input/softwares/ pyem/basic_example2.py}125 classes from em: GMM and EM. You first create a GMM object from a GM instance; 126 then you can give the GMM object as a parameter to the EM class to compute 127 iterations of EM; once the EM has finished the computation, the GM instance of 128 GMM contains the computed parameters. 129 130 .. raw:: html 131 132 {mycolorize;input/softwares/em/basic_example2.py} 131 133 132 134 .. raw:: latex … … 147 149 ------------------------------------------------------- 148 150 149 The GMM class is also able to compute the bayesian information criterion 150 (BIC), which can be used to assess the number of clusters into the data. 151 It was first suggested by Schwarz (see bibliography), who gave a Bayesian 152 argument for adopting the BIC. The BIC is derived from an approximation 153 of the integrated likelihood of the model, based on regularity assumptions. 154 The following code generates an artificial mixture of 4 clusters, runs 155 EM with models of 1 to 6 clusters, and prints which number of clusters 156 is the most likely from the BIC: 157 158 .. raw:: html 159 160 {mycolorize;input/softwares/pyem/basic_example3.py} 151 The GMM class is also able to compute the bayesian information criterion (BIC), 152 which can be used to assess the number of clusters into the data. It was first 153 suggested by Schwarz (see bibliography), who gave a Bayesian argument for 154 adopting the BIC. The BIC is derived from an approximation of the integrated 155 likelihood of the model, based on regularity assumptions. The following code 156 generates an artificial mixture of 4 clusters, runs EM with models of 1 to 6 157 clusters, and prints which number of clusters is the most likely from the BIC: 158 159 .. raw:: html 160 161 {mycolorize;input/softwares/em/basic_example3.py} 161 162 162 163 .. raw:: latex … … 170 171 :height: 400 171 172 172 The above example also shows that you can control the plotting 173 parameters by using returned handles from plot methods. This can be 174 useful for complexdrawing.173 The above example also shows that you can control the plotting parameters by 174 using returned handles from plot methods. This can be useful for complex 175 drawing. 175 176 176 177 Examples … … 202 203 TODO (this is fundamentally the same than pdf estimation, though) 203 204 204 Using PyEM for supervised learning 205 ---------------------------------- 205 supervised learning (e.g discriminative analysis) 206 ------------------------------------------------- 206 207 207 208 The following example shows how to do classification using discriminative … … 228 229 ==================== 229 230 230 Pyem is implemented in python (100% of the code has a python implementation), 231 but thanks to the Moore Law, it is reasonably fast so that it can be used for 232 other problems than toys problem. On my computer (linux on bi xeon 3.2 Ghz, 2Gb 233 RAM), running 10 iterations of EM algorithm on 100 000 samples of dimension 15, 234 for a diagonal model with 30 components, takes around 1 minute and 15 seconds: 235 this makes the implementation usable for moderately complex problems such as 236 speaker recognition using MFCC. If this is too slow, there is a C 237 implementation for Gaussian densities which can be enabled by commenting out 238 one line in pyem/gmm_em.py, which should gives a speed up of a factor 2 at 239 least; this has not been tested much, though, so beware. 240 241 Also, increasing the number of components and/or dimension is much more 242 expensive than increasing the number of samples: a 5 dimension model of 100 243 components will be much slower to estimate with 500 samples than a 5 dimension 244 10 components with 5000 samples. This is because loops on dimension/components 245 are in python, whereas loops on samples are in C (through numpy). I don't 231 The package is implemented in python (100% of the code has a python 232 implementation, so that it can be used for educational purpose too), but thanks 233 to the Moore Law, it is reasonably fast so that it can be used for other 234 problems than toys problem. On my computer (linux on bi xeon 3.2 Ghz, 2Gb RAM), 235 running 10 iterations of EM algorithm on 100 000 samples of dimension 15, for a 236 diagonal model with 30 components, takes around 1 minute and 15 seconds: this 237 makes the implementation usable for moderately complex problems such as speaker 238 recognition using MFCC. If this is too slow, there is a C implementation for 239 Gaussian densities which can be enabled by commenting out one line in the file 240 gmm_em.py, which should gives a speed up of a factor 2 at least; this has not 241 been tested much, though, so beware. 242 243 Also, increasing the number of components or dimension is much more expensive 244 than increasing the number of samples: a 5 dimension model of 100 components 245 will be much slower to estimate with 500 samples than a 5 dimension 10 246 components with 5000 samples. This is because loops on dimension or components 247 are in python, whereas loops on samples are in C (through numpy). I don't 246 248 think there is an easy fix to this problem. 247 249 248 Full covariances will be slow, because you cannot avoid nested loop 249 in python this case without insane amount of memory. A C implementation 250 may be implemented, but this is not my top priority; most of the time, you 251 should avoid full covariance models anyway.250 Full covariances will be slow, because you cannot avoid nested loop in python 251 this case without insane amount of memory. A C implementation may be 252 implemented, but this is not my top priority; most of the time, you should 253 avoid full covariance models if possible. 252 254 253 255 TODO … … 267 269 268 270 - add other models (mixtures of multinomial: easy, simple HMM: easy, other ?) 269 - add bayes prior using MCMC (hard, use PyMC MCfor sampling ?)271 - add bayes prior using MCMC (hard, use PyMC for sampling ?) 270 272 271 273 Bibliography trunk/learn/scikits/learn/machine/em/doc/tutorial.pdf
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