Related papers: Likelihood Ratio Exponential Families
In this paper we propose a new lifetime model, called the odd generalized exponential linear failure rate distribution. Some statistical properties of the proposed distribution such as the moments, the quantiles, the median, and the mode…
On a compact group the Haar probability measure plays the role of uniform distribution. The entropy and rate distortion theory for this uniform distribution is studied. New results and simplified proofs on convergence of convolutions on…
Unifying the generalized Marshall-Olkin (GMO) and Poisson-G (P-G) a new family of distribution is proposed. Density and the survival function are expressed as infinite mixtures of P-G family. The quantile function, asymptotes, shapes,…
The advent of data science has spurred interest in estimating properties of distributions over large alphabets. Fundamental symmetric properties such as support size, support coverage, entropy, and proximity to uniformity, received most…
Recent work in unsupervised representation learning has focused on learning deep directed latent-variable models. Fitting these models by maximizing the marginal likelihood or evidence is typically intractable, thus a common approximation…
Exponential random graphs are used extensively in the sociology literature. This model seeks to incorporate in random graphs the notion of reciprocity, that is, the larger than expected number of triangles and other small subgraphs.…
Sequential likelihood ratio testing is found to be most powerful in sequential studies with early stopping rules when grouped data come from the one-parameter exponential family. First, to obtain this elusive result, the probability measure…
This study considers multi-objective Bayesian optimization (MOBO) through the information gain of the Pareto-frontier. To calculate the information gain, a predictive distribution conditioned on the Pareto-frontier plays a key role, which…
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 {\mu}…
The Principle of Maximum Entropy, a powerful and general method for inferring the distribution function given a set of constraints, is applied to deduce the overall distribution of 3D plasmoids (flux ropes/tubes) for systems where resistive…
The Generalized Mallows Model (GMM) is a well known family of models for ranking data. A GMM is a distribution over $\mathbb{S}_n$, the set of permutations of n objects, characterized by a location parameter $\sigma \in \mathbb{S}_n$, known…
Traditional likelihood based methods for parameter estimation get highly affected when the given data is contaminated by outliers even in a small proportion. In this paper, we consider a robust parameter estimation method, namely the…
A well-known result across information theory, machine learning, and statistical physics shows that the maximum entropy distribution under a mean constraint has an exponential form called the Gibbs-Boltzmann distribution. This is used for…
The EM (Expectation-Maximization) algorithm is regarded as an MM (Majorization-Minimization) algorithm for maximum likelihood estimation of statistical models. Expanding this view, this paper demonstrates that by choosing an appropriate…
We study the problem of maximum likelihood (ML) estimation for statistical models defined by reflexive polytopes. Our focus is on the maximum likelihood degree of these models as an algebraic measure of complexity of the corresponding…
The Mixture Transition Distribution (MTD) model was introduced by Raftery to face the need for parsimony in the modeling of high-order Markov chains in discrete time. The particularity of this model comes from the fact that the effect of…
This article gives a formal definition of a lognormal family of probability distributions on the set of symmetric positive definite (PD) matrices, seen as a matrix-variate extension of the univariate lognormal family of distributions. Two…
We develop the laws of thermodynamics in terms of general exponential families. By casting learning (log-loss minimization) problems in max-entropy and statistical mechanics terms, we translate thermodynamics results to learning scenarios.…
Lately, a New Transmuted Logistic-exponential (NTLE) distribution was introduced and studied as an extension of the Logistic-Exponential Distribution (LED) with wider applicability in lifetime modelling. However, the maximum likelihood…
Hierarchical structures, which include multiple levels, are prevalent in statistical and machine-learning models as well as physical systems. Extending the foundational result that the maximum entropy distribution under mean constraints is…