In Win-Vector LLC Data Science Consulting.

Paper abstract bibtex

Paper abstract bibtex

As our colleague so aptly demonstrated ( http://www.win-vector.com/blog/2011/09/the-simpler- derivation-of-logistic-regression/ ) there is one derivation of Logistic Regression that is particularly beautiful. It is not as general as that found in Agresti[Agresti, 1990] (which deals with generalized linear models in their full generality), but gets to the important balance equations very quickly. We will pursue this further to re-derive multi-category logistic regression in both its standard (sigmoid) phrasing and also in its equivalent maximum entropy clothing. It is well known that logistic regression and maximum entropy modeling are equivalent (for example see [Klein and Manning, 2003])- but we will show that the simpler derivation already given is a very good way to demonstrate the equivalence (and points out that logistic regression is actually special- not just one of many equivalent GLMs).

@incollection{mountEquivalenceLogisticRegression2011, title = {The Equivalence of Logistic Regression and Maximum Entropymodels}, author = {Mount, John}, date = {2011-09}, publisher = {{Win-Vector LLC Data Science Consulting}}, url = {https://scholar.google.com/scholar?cluster=8900605637623791351}, abstract = {As our colleague so aptly demonstrated ( http://www.win-vector.com/blog/2011/09/the-simpler- derivation-of-logistic-regression/ ) there is one derivation of Logistic Regression that is particularly beautiful. It is not as general as that found in Agresti[Agresti, 1990] (which deals with generalized linear models in their full generality), but gets to the important balance equations very quickly. We will pursue this further to re-derive multi-category logistic regression in both its standard (sigmoid) phrasing and also in its equivalent maximum entropy clothing. It is well known that logistic regression and maximum entropy modeling are equivalent (for example see [Klein and Manning, 2003])- but we will show that the simpler derivation already given is a very good way to demonstrate the equivalence (and points out that logistic regression is actually special- not just one of many equivalent GLMs).}, keywords = {*imported-from-citeulike-INRMM,~INRMM-MiD:c-12013393,entropy,mathematics,regression,statistics} }

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