Topic
Natural exponential family
About: Natural exponential family is a research topic. Over the lifetime, 1973 publications have been published within this topic receiving 60189 citations. The topic is also known as: NEF.
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TL;DR: In this article, the authors considered a problem of selecting a best k one parameter exponential families with quadratic variance functions which is associated with the largest mean and showed that the minimax value under the "0-1" loss function is 1 − 1/k.
9 citations
TL;DR: A new class of conjugate priors which is invariant with respect to smooth reparameterization is proposed which contains the Je reys prior as a special case, according to the value of the hyperparameters.
Abstract: There are several ways to parameterize a distribution belonging to an exponential family, each one leading to a different Bayesian analysis of the data under standard conjugate priors. To overcome this problem, we propose a new class of conjugate priors which is invariant with respect to smooth reparameterization. This class of priors contains the Jeffreys prior as a special case, according to the value of the hyperparameters. Moreover, these conjugate distributions coincide with the posterior distributions resulting from a Jeffreys prior. Then these priors appear naturally when several datasets are analyzed sequentially and when the Jeffreys prior is chosen for the first dataset. We apply our approach to inverse Gaussian models and propose full invariant analyses of three datasets.
9 citations
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TL;DR: This work characterizes a certain strong convexity property of general exponential families, which allow their generalization ability to be quantified, and shows how this property can be used to analyze generic exponential families under L_1 regularization.
Abstract: The versatility of exponential families, along with their attendant convexity properties, make them a popular and effective statistical model. A central issue is learning these models in high-dimensions, such as when there is some sparsity pattern of the optimal parameter. This work characterizes a certain strong convexity property of general exponential families, which allow their generalization ability to be quantified. In particular, we show how this property can be used to analyze generic exponential families under L_1 regularization.
9 citations
TL;DR: Results based on the minimized log-likelihood, Akaike information criterion, Bayesian information criterion and the generalized Cramér–von Mises W⋆ statistics shows that the EETE distribution provides a more reasonable fit than the one based upon the other competing distributions.
9 citations
9 citations