Related papers: Likelihood Ratio Exponential Families
Competing and Complementary risk (CCR) problems are often modelled using a class of distributions of the maximum, or minimum, of a random number of i.i.d. random variables; we call this class the CCR class of distributions. While the CCR…
Recent advancements have established Reinforcement Learning (RL) as a pivotal paradigm for aligning generative models with human intent. However, group-based optimization frameworks (e.g., GRPO) face a critical limitation: the rapid decay…
The problem of assigning probability distributions which objectively reflect the prior information available about experiments is one of the major stumbling blocks in the use of Bayesian methods of data analysis. In this paper the method of…
We study three fundamental statistical-learning problems: distribution estimation, property estimation, and property testing. We establish the profile maximum likelihood (PML) estimator as the first unified sample-optimal approach to a wide…
In algebraic statistics, the maximum likelihood degree of a statistical model refers to the number of solutions (counted with multiplicity) of the score equations over the complex field. In this paper, the maximum likelihood degree of the…
The principle of maximum entropy is a broadly applicable technique for computing a distribution with the least amount of information possible constrained to match empirical data, for instance, feature expectations. We seek to generalize…
The generalized Laplace (GL) distribution, which falls in the larger family of generalized hyperbolic distributions, provides a versatile model to deal with a variety of applications thanks to its shape parameters. The elliptically…
Diffusion models have emerged as powerful tools for solving inverse problems, yet prior work has primarily focused on observations with Gaussian measurement noise, restricting their use in real-world scenarios. This limitation persists due…
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…
Bayes' rule describes how to infer posterior beliefs about latent variables given observations, and inference is a critical step in learning algorithms for latent variable models (LVMs). Although there are exact algorithms for inference and…
We propose an analytical solution for approximating the gradient of the Evidence Lower Bound (ELBO) in variational inference problems where the statistical model is a Bayesian network consisting of observations drawn from a mixture of a…
Many Imitation and Reinforcement Learning approaches rely on the availability of expert-generated demonstrations for learning policies or value functions from data. Obtaining a reliable distribution of trajectories from motion planners is…
The growing availability of network data and of scientific interest in distributed systems has led to the rapid development of statistical models of network structure. Typically, however, these are models for the entire network, while the…
Through viewing out the literature, many generated distributions took a new special form of probability density function (PDF) in which it is written as a linear combination of n other distributions. Therefore, we define in this paper a new…
Minimization problems with respect to a one-parameter family of generalized relative entropies are studied. These relative entropies, which we term relative $\alpha$-entropies (denoted $\mathscr{I}_{\alpha}$), arise as redundancies under…
Since its introduction, the skew-$t$ distribution has received much attention in the literature both for the study of theoretical properties and as a model for data fitting in empirical work. A major motivation for this interest is the high…
This paper studies a basic notion of distributional shape known as orthounimodality (OU) and its use in shape-constrained distributionally robust optimization (DRO). As a key motivation, we argue how such type of DRO is well-suited to…
We introduce a new generalization of the Pseudo-Lindley distribution by applying alpha power transformation. The obtained distribution is referred as the Pseudo-Lindley alpha power transformed distribution (\textit{PL-APT}). Some tractable…
The two-parameter distribution known as exponential-Poisson (EP) distribution, which has decreasing failure rate, was introduced by Kus (2007). In this paper we generalize the EP distribution and show that the failure rate of the new…
We introduce and motivate generative modeling as a central task for machine learning and provide a critical view of the algorithms which have been proposed for solving this task. We overview how generative modeling can be defined…