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The Large Deviation Principle (LDP) and the Central Limit Theorem (CLT) are central pillars of probability theory. While their formulations are established under the i.i.d. assumption, the probabilistic foundation for power-law…
The article is devoted to the study of exponential statistical structures of type B, which constitute a subclass of exponential families of probability distributions. This class is characterized by a number of analytical and probabilistic…
This study introduces the Exponentiated-Exponential-Pareto-Half Normal Mixture Distribution (EEPHND), a novel hybrid model developed to overcome the limitations of classical distributions in modeling complex real-world data. By compounding…
Several populational networks present complex topologies when implemented in evolutionary algorithms. A common feature of these topologies is the emergence of a power law. Power law behavior with different scaling factors can also be…
Recent advancements in graph representation learning have shifted attention towards dynamic graphs, which exhibit evolving topologies and features over time. The increased use of such graphs creates a paramount need for generative models…
Generative modeling can be formulated as learning a mapping f such that its pushforward distribution matches the data distribution. The pushforward behavior can be carried out iteratively at inference time, for example in diffusion and…
The evolution of the pion distribution amplitude in next-to-leading order is studied for a fixed and a running coupling constant. In both cases, the evolution provides a logarithmic modification in the endpoint region. Assuming a simple…
The main object of this article is to present an extension of the zero-inflated Poisson-Lindley distribution, called of zero-modified Poisson-Lindley. The additional parameter $\pi$ of the zero-modified Poisson-Lindley has a natural…
Selective inference methods are developed for group lasso estimators for use with a wide class of distributions and loss functions. The method includes the use of exponential family distributions, as well as quasi-likelihood modeling for…
Probabilistic regression models the entire predictive distribution of a response variable, offering richer insights than classical point estimates and directly allowing for uncertainty quantification. While diffusion-based generative models…
We define a four-parameter extended Rayleigh distribution, and obtain several mathematical properties including a stochastic representation. We construct a regression from the new distribution. The estimation is done by maximum likelihood.…
A common statistical situation concerns inferring an unknown distribution Q(x) from a known distribution P(y), where X (dimension n), and Y (dimension m) have a known functional relationship. Most commonly, n<m, and the task is relatively…
In this paper, we present a general method that can improve the sample quality of pre-trained likelihood based generative models. Our method constructs an energy function on the latent variable space that yields an energy function on…
The exponential family is well known in machine learning and statistical physics as the maximum entropy distribution subject to a set of observed constraints, while the geometric mixture path is common in MCMC methods such as annealed…
We investigate statistical properties of a likelihood approach to nonparametric estimation of a singular distribution using deep generative models. More specifically, a deep generative model is used to model high-dimensional data that are…
For domains that involve numerical simulation, it can be computationally expensive to run an ensemble of simulations spanning a parameter space of interest to a user. To this end, an attractive surrogate for simulation is the generative…
Recent advances in generative modeling, namely Diffusion models, have revolutionized generative modeling, enabling high-quality image generation tailored to user needs. This paper proposes a framework for the generative design of structural…
In this paper we define the class of matrix Mittag-Leffler distributions and study some of its properties. We show that it can be interpreted as a particular case of an inhomogeneous phase-type distribution with random scaling factor, and…
Generative AI (GenAI) has revolutionized data-driven modeling by enabling the synthesis of high-dimensional data across various applications, including image generation, language modeling, biomedical signal processing, and anomaly…
Products between phase-type distributed random variables and any independent, positive and continuous random variable are studied. Their asymptotic properties are established, and an expectation-maximization algorithm for their effective…