arXiv research

Paper develops EP algorithm for t-exponential family using q-algebra.

New Thompson sampling algorithm reduces regret for exponential family bandits.

Investigates a conjugate prior for Dirichlet distribution.

Extends likelihood ratio exponential families to analyze various optimization methods.

A two-network architecture learns intractable exponential family models.

Classifies 1D exponential families with constant Hessian curvature.

We provide a classification of graphical models according to their representation as subfamilies of exponential families. Undirected graphical models with no hidden variables are linear exponential families (LEFs), directed acyclic graphical models and chain graphs with no hidden variables, including Bayesian networks …

The paper introduces a new method for graph embedding using exponential family distributions.

Thompson Sampling has been demonstrated in many complex bandit models, however the theoretical guarantees available for the parametric multi-armed bandit are still limited to the Bernoulli case. Here we extend them by proving asymptotic optimality of the algorithm using the Jeffreys prior for 1-dimensional exponential …

Kernel conditional exponential family generalizes conditional distributions.

NatPN provides fast, accurate uncertainty estimation for exponential family distributions.

Improves variational inference for sparse models using mixtures of exponential families.

New method for robust PCA with exponential family distributions.

In this paper, a Bayesian inference technique based on Taylor series approximation of the logarithm of the likelihood function is presented. The proposed approximation is devised for the case, where the prior distribution belongs to the exponential family of distributions. The logarithm of the likelihood function is li…

Estimates exponential family distributions using a novel doubly dual embedding technique.

Extends diffusion models to handle exponential family distributions for inverse problems.

We study the problem of finding the smallest $m$ such that every element of an exponential family can be written as a mixture of $m$ elements of another exponential family. We propose an approach based on coverings and packings of the face lattice of the corresponding convex support polytopes and results from coding th…

Extends Stein's lemma to exponential-family mixtures for gradient computation.

Efficiently learns exponential family distributions with i.i.d. samples.

We extend natural-gradient methods to mixtures of exponential-family distributions, improving inference speed.

New method constructs exponential families from representation theory.

A simple framework predicts unseen classes using exponential family distributions.

Inference for normal and Monte Carlo distributions using minimum relative entropy.

We study online learning under logarithmic loss with regular parametric models. Hedayati and Bartlett (2012b) showed that a Bayesian prediction strategy with Jeffreys prior and sequential normalized maximum likelihood (SNML) coincide and are optimal if and only if the latter is exchangeable, and if and only if the opti…

We consider the design of prediction market mechanisms known as automated market makers. We show that we can design these mechanisms via the mold of \emph{exponential family distributions}, a popular and well-studied probability distribution template used in statistics. We give a full development of this relationship a…

EFDA extends LDA to non-Gaussian models using exponential families.

Efficient method for learning continuous exponential families beyond Gaussian.

Undirected graphical models, or Markov networks, are a popular class of statistical models, used in a wide variety of applications. Popular instances of this class include Gaussian graphical models and Ising models. In many settings, however, it might not be clear which subclass of graphical models to use, particularly…

New method uses neural exponential families for likelihood-free inference.

We present Vector-Space Markov Random Fields (VS-MRFs), a novel class of undirected graphical models where each variable can belong to an arbitrary vector space. VS-MRFs generalize a recent line of work on scalar-valued, uni-parameter exponential family and mixed graphical models, thereby greatly broadening the class o…

New bounds for score matching in polynomial exponential families.

SMRL uses score matching for efficient RL with exponential family models.

New LVMs optimize any exponential family distribution without specific assumptions.

We propose a novel approach for density estimation with exponential families for the case when the true density may not fall within the chosen family. Our approach augments the sufficient statistics with features designed to accumulate probability mass in the neighborhood of the observed points, resulting in a non-para…

Exponential family extensions of principal component analysis (EPCA) have received a considerable amount of attention in recent years, demonstrating the growing need for basic modeling tools that do not assume the squared loss or Gaussian distribution. We extend the EPCA model toolbox by presenting the first exponentia…

MLE and CVE are equivalent under exponential families, leading to faster and more stable EM algorithms.

Chentsov's theorem proved for exponential families.

The paper classifies statistical Einstein manifolds in exponential families.

In a range of fields including the geosciences, molecular biology, robotics and computer vision, one encounters problems that involve random variables on manifolds. Currently, there is a lack of flexible probabilistic models on manifolds that are fast and easy to train. We define an extremely flexible class of exponent…

New insights into natural exponential families improve regret bounds for bandit problems.

Enhances text generation interpretability with a mixture of exponential family distributions.

Paper explores robust estimators for kernel exponential families using smoothed total variation distances.

EM algorithm converges in KL divergence for exponential families via mirror descent.

Paper defines ε-Safe Decision Regions for exponential family distributions and approximates them for unbalanced data.

A deep learning approach for fitting complex distributions.

Boosting improves data fitting while maintaining fairness guarantees.

Exponential families are a particular class of statistical manifolds which are particularly important in statistical inference, and which appear very frequently in statistics. For example, the set of normal distributions, with mean μ and deviation σ, form a 2-dimensional exponential family. In this paper, we show that …

Unified view on learning unnormalized distributions using NCE.