Density Estimation Based on Moments Maximum Entropy Density Estimation Let X be a continuous variable with probability density function f(x). Then Shanon's entropy is defined by H = f logf q q q dq f ? f (11) where f1 q dqf f ? A maximum entropy density function can be obtained by maximizing the Shanon's Estimation of Entropy and Mutual Information 1195 tion and is interested in estimating the underlying density. It is clear that there exists no maximum likelihood estimator of the density in the space of smooth functions (the object that formally maximizes the likelihood, a sum The density of the maximum entropy distribution for this class is constant on each of the intervals [a j-1,a j). The uniform distribution on the finite set {x 1,,x n} (which assigns a probability of 1/n to each of these values) is the maximum entropy distribution among all discrete distributions supported on this set. Maximum entropy density estimation with generalized regularization and an application to species distribution modeling M Dud?k, SJ Phillips, RE Schapire Journal of Machine Learning Research 8, 1217-1260 , 2007 Maximum Entropy Density Estimation with Incomplete Presence-Only Data In practice, data often exhibit Gaussian-like proper-ties, so this method is rather e?ective. Another e?ec-tive method stemming from classical statistical anal-ysis is multiple imputation (Little & Rubin, 1986), in which data is imputed multiple times to create multi- We consider the problem of estimating an unknown probability distribution from samples using the principle of maximum entropy (maxent). To alleviate overfitting with a very large number of features, we propose applying the maxent principle with relaxed constraints on the expectations of the features. These additional measures require knowing a probability density function, which we estimate by using a nonparametric maximum entropy method that quantifies rare events well. A new maximum-entropy density estimation method is developed for multivariate data. Four examples demonstrated the accuracy and efficiency of the proposed method. The method is compared with the conventional kernel density-based importance sampling. The maximum entropy (maxent) approach to probability density estimation was ?rst proposed by Jaynes [9] in 1957, and has since been used in many areas of computer science and statistical learning, especially natural language processing [1,6]. In max-ent, one is given a set of samples from a target distribution over some space, and a set Browse other questions tagged pdf entropy order-statistics density-estimation maximum-entropy or ask your own question. Featured on Meta Feedback post: Moderator review and reinstatement processes. Post for clarifications on the updated pronouns FAQ MEDDE: MAXIMUM ENTROPY DEREGULARIZED DENSITY ESTIMATION 3 view of prior likelihood experience that our dual formulation involves maximizing Shan-non entropy, since we are already well aware of the close connection to Kullback-Leibler divergence. One potentially disturbing aspect of foregoing formulation is the nding that assuming. The probability density function with maximum entropy, satisfying whatever constraints we impose, is the one that should be least surprising in terms of the predictions it makes. It is important to clear up an easy misconception: the principle of maximum entropy does not give us something for nothing. assuming. The probability density f