Related papers: Local mixture models of exponential families
We show that if an exponential sum with multiplicative coefficients is large then the associated multiplicative function is "pretentious". This leads to applications in the circle method, and a natural interpretation of the local-global…
Log-concave distributions are an attractive choice for modeling and inference, for several reasons: The class of log-concave distributions contains most of the commonly used parametric distributions and thus is a rich and flexible…
The likelihood function is central to both frequentist and Bayesian formulations of parametric statistical inference, and large-sample approximations to the sampling distributions of estimators and test statistics, and to posterior…
This article studies exponential families $\mathcal{E}$ on finite sets such that the information divergence $D(P\|\mathcal{E})$ of an arbitrary probability distribution from $\mathcal{E}$ is bounded by some constant $D>0$. A particular…
Nowadays, exponential random graphs (ERGs) are among the most widely-studied network models. Different analytical and numerical techniques for ERG have been developed that resulted in the well-established theory with true predictive power.…
When training automated systems, it has been shown to be beneficial to adapt the representation of data by learning a problem-specific metric. This metric is global. We extend this idea and, for the widely used family of k nearest neighbors…
Selective inference aims at providing valid inference after a data-driven selection of models or hypotheses. It is essential to avoid overconfident results and replicability issues. While significant advances have been made in this area for…
We present an efficient algorithm for maximum likelihood estimation (MLE) of exponential family models, with a general parametrization of the energy function that includes neural networks. We exploit the primal-dual view of the MLE with a…
Probabilistic models often have parameters that can be translated, scaled, permuted, or otherwise transformed without changing the model. These symmetries can lead to strong correlation and multimodality in the posterior distribution over…
We introduce generalized notions of a divergence function and a Fisher information matrix. We propose to generalize the notion of an exponential family of models by reformulating it in terms of the Fisher information matrix. Our methods are…
Many of the conjectures of current interest in the representation theory of finite groups in characteristic $p$ are local-to-global statements, in that they predict consequences for the representations of a finite group $G$ given data about…
A sequence of random variables is exchangeable if its joint distribution is invariant under variable permutations. We introduce exchangeable variable models (EVMs) as a novel class of probabilistic models whose basic building blocks are…
Families of mixtures of multivariate power exponential (MPE) distributions have been previously introduced and shown to be competitive for cluster analysis in comparison to other elliptical mixtures including mixtures of Gaussian…
Finite mixture models are useful in applied econometrics. They can be used to model unobserved heterogeneity, which plays major roles in labor economics, industrial organization and other fields. Mixtures are also convenient in dealing with…
The problem of selecting a small, yet high quality subset of patterns from a larger collection of itemsets has recently attracted lot of research. Here we discuss an approach to this problem using the notion of decomposable families of…
Limits of densities belonging to an exponential family appear in many applications, {e.g.} Gibbs models in Statistical Physics, relaxed combinatorial optimization, coding theory, critical likelihood computations, Bayes priors with singular…
We describe convolutional deep exponential families (CDEFs) in this paper. CDEFs are built based on deep exponential families, deep probabilistic models that capture the hierarchical dependence between latent variables. CDEFs greatly reduce…
Exponential family distributions are highly useful in machine learning since their calculation can be performed efficiently through natural parameters. The exponential family has recently been extended to the t-exponential family, which…
Exponential-family Random Graph Models (ERGMs) constitute a large statistical framework for modeling sparse and dense random graphs, short- and long-tailed degree distributions, covariates, and a wide range of complex dependencies. Special…
Congruence families, i.e., $\ell$-adic convergence for well-defined arithmetic subsequences, is a commonplace phenomenon for the coefficients of modular forms. Such families superficially resemble one another, but they often vary…