LeCun, Y. and Huang, F.J. (2005) Loss Functions for Discriminative Training of Energy-Based Models. Proceedings of International Workshop on Artificial Intelligence and Statistics (AISTATS-05), Barbados, 6-8 January 2005, 206-213.

has been cited by the following article:

• TITLE: Fluctuation-Model-Based Discrete Probability Estimation for Small Samples

  AUTHORS: Takashi Isozaki

  KEYWORDS: Probability Estimation, Fluctuation Models, Helmholtz Free Energy, Canonical Distributions

  JOURNAL NAME: Open Journal of Statistics, Vol.5 No.5, August 20, 2015

  ABSTRACT: A robust method is proposed for estimating discrete probability functions for small samples. The proposed approach introduces and minimizes a parameterized objective function that is analogous to free energy functions in statistical physics. A key feature of the method is a model of the parameter that controls the trade-off between likelihood and robustness in response to the degree of fluctuation. The method thus does not require the value of the parameter to be manually selected. It is proved that the estimator approaches the maximum likelihood estimator at the asymptotic limit. The effectiveness of the method in terms of robustness is demonstrated by experimental studies on point estimation for probability distributions with various entropies.