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How biased are maximum entropy models?
Jakob H Macke · Iain Murray · Peter E Latham

Mon Dec 12 10:00 AM -- 02:59 PM (PST) @ None #None

Maximum entropy models have become popular statistical models in neuroscience and other areas in biology, and can be useful tools for obtaining estimates of mu- tual information in biological systems. However, maximum entropy models fit to small data sets can be subject to sampling bias; i.e. the true entropy of the data can be severely underestimated. Here we study the sampling properties of estimates of the entropy obtained from maximum entropy models. We show that if the data is generated by a distribution that lies in the model class, the bias is equal to the number of parameters divided by twice the number of observations. However, in practice, the true distribution is usually outside the model class, and we show here that this misspecification can lead to much larger bias. We provide a perturba- tive approximation of the maximally expected bias when the true model is out of model class, and we illustrate our results using numerical simulations of an Ising model; i.e. the second-order maximum entropy distribution on binary data.

Author Information

Jakob H Macke (University of Tübingen & MPI IS Tübingen)
Iain Murray (University of Edinburgh)

Iain Murray is a SICSA Lecturer in Machine Learning at the University of Edinburgh. Iain was introduced to machine learning by David MacKay and Zoubin Ghahramani, both previous NIPS tutorial speakers. He obtained his PhD in 2007 from the Gatsby Computational Neuroscience Unit at UCL. His thesis on Monte Carlo methods received an honourable mention for the ISBA Savage Award. He was a commonwealth fellow in Machine Learning at the University of Toronto, before moving to Edinburgh in 2010. Iain's research interests include building flexible probabilistic models of data, and probabilistic inference from indirect and uncertain observations. Iain is passionate about teaching. He has lectured at several Summer schools, is listed in the top 15 authors on videolectures.net, and was awarded the EUSA Van Heyningen Award for Teaching in Science and Engineering in 2015.

Peter E Latham (Gatsby Unit, UCL)

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