Related papers: Developing multivariate distributions using Dirich…
We introduce the beta generalized exponential distribution that includes the beta exponential and generalized exponential distributions as special cases. We provide a comprehensive mathematical treatment of this distribution. We derive the…
The Poisson distribution has been widely studied and used for modeling univariate count-valued data. Multivariate generalizations of the Poisson distribution that permit dependencies, however, have been far less popular. Yet, real-world…
Learning the multivariate distribution of data is a core challenge in statistics and machine learning. Traditional methods aim for the probability density function (PDF) and are limited by the curse of dimensionality. Modern neural methods…
Multitudinous probabilistic and combinatorial objects are associated with generating functions satisfying a composition scheme $F(z)=G(H(z))$. The analysis becomes challenging when this scheme is critical (i.e., $G$ and $H$ are…
Generative modeling of physical systems, such as molecules, requires learning distributions that are invariant under global symmetries, such as rotations in three-dimensional space. Equivariant diffusion and flow matching models can…
Standard regression approaches assume that some finite number of the response distribution characteristics, such as location and scale, change as a (parametric or nonparametric) function of predictors. However, it is not always appropriate…
Dirichlet-multinomial (DMN) distribution is commonly used to model over-dispersion in count data. Precise and fast numerical computation of the DMN log-likelihood function is important for performing statistical inference using this…
In general, while obtaining the probability density function of sums and products of shifted random variables, ordinary analytical methods such as Fourier and Mellin transforms tend to provide integrals which cannot be expressed in terms of…
We develop deep Poisson-gamma dynamical systems (DPGDS) to model sequentially observed multivariate count data, improving previously proposed models by not only mining deep hierarchical latent structure from the data, but also capturing…
Bayesian paradigm takes advantage of well fitting complicated survival models and feasible computing in survival analysis owing to the superiority in tackling the complex censoring scheme, compared with the frequentist paradigm. In this…
Many real-world networks are characterized by directionality; however, the absence of an appropriate Fourier basis hinders the effective implementation of graph signal processing techniques. Inspired by discrete signal processing, where…
Generating visual layouts is an essential ingredient of graphic design. The ability to condition layout generation on a partial subset of component attributes is critical to real-world applications that involve user interaction. Recently,…
Background: The analysis of DNA methylation is a key component in the development of personalized treatment approaches. A common way to measure DNA methylation is the calculation of beta values, which are bounded variables of the form M =…
Distributions are fundamental statistical elements that play essential theoretical and practical roles. The article discusses experiences of training neural networks to classify univariate empirical distributions and to represent them on…
Motivated by applications in Bayesian analysis we introduce a multidimensional beta distribution in an ordered simplex. We study properties of this distribution and connect them with the generalized incomplete beta function. This function…
Probability distribution theory helps in studying the impact of various dimensions in life while the Mittag-Leffler function and bicomplex are used in electromagnetism, quantum mechanics, and signal theory. Considering the importance of…
Diffusion models, a powerful and universal generative AI technology, have achieved tremendous success in computer vision, audio, reinforcement learning, and computational biology. In these applications, diffusion models provide flexible…
A new method for multinomial inference is proposed by representing the cell probabilities as unordered segments on the unit interval and following Dempster-Shafer (DS) theory. The resulting DS posterior is then strengthened to improve…
This paper proposes DiffPF, a differentiable particle filter that leverages diffusion models for state estimation in dynamic systems. Unlike conventional differentiable particle filters, which require importance weighting and typically rely…
A new family of matrix variate distributions indexed by elliptical models are proposed in this work. The so called \emph{multimatricvariate distributions} emerge as a generalization of the bimatrix variate distributions based on matrix…