Related papers: The Unifed Distribution
A new class of probability distributions closely connected to generalized hyperbolic distributions is introduced. It is more adapted to study the distributions of sums of random number of random variables. The properties of these…
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…
This paper investigates the large sample properties of local regression distribution estimators, which include a class of boundary adaptive density estimators as a prime example. First, we establish a pointwise Gaussian large sample…
Generative modeling is typically framed as learning mapping rules, but from an observer's perspective without access to these rules, the task becomes disentangling the geometric support from the probability distribution. We propose that…
The polygonal distributions are a class of distributions that can be defined via the mixture of triangular distributions over the unit interval. The class includes the uniform and trapezoidal distributions, and is an alternative to the beta…
Bayesian Federated Learning (BFL) enables uncertainty quantification and robust adaptation in distributed learning. In contrast to the frequentist approach, it estimates the posterior distribution of a global model, offering insights into…
This paper presents a new Unified pre-trained Language Model (UniLM) that can be fine-tuned for both natural language understanding and generation tasks. The model is pre-trained using three types of language modeling tasks: unidirectional,…
The inverse Gaussian (IG) is one of the most famous and considered distributions with positive support. We propose a convenient mode-based parameterization yielding the reparametrized IG (rIG) distribution; it allows/simplifies the use of…
In this paper we propose an objective Bayesian estimation approach for the parameters of the generalized gamma distribution. Various reference priors are obtained, but showing that they lead to improper posterior distributions. We overcome…
Semisupervised learning has emerged as a popular framework for improving modeling accuracy while controlling labeling cost. Based on an extension of stochastic composite likelihood we quantify the asymptotic accuracy of generative…
Graph-based Retrieval-Augmented Generation (RAG) has proven effective in integrating external knowledge into large language models (LLMs), improving their factual accuracy, adaptability, interpretability, and trustworthiness. A number of…
Generalized linear models (GLM) are link function based statistical models. Many supervised learning algorithms are extensions of GLMs and have link functions built into the algorithm to model different outcome distributions. There are two…
We consider a family of problems that are concerned about making predictions for the majority of unlabeled, graph-structured data samples based on a small proportion of labeled samples. Relational information among the data samples, often…
The distribution of unicyclic components in a random graph is obtained analytically. The number of unicyclic components of a given size approaches a self-similar form in the vicinity of the gelation transition. At the gelation point, this…
In this paper we consider a variety of procedures for numerical statistical inference in the family of univariate and multivariate stable distributions. In connection with univariate distributions (i) we provide approximations by finite…
A functional composition of the cumulative distribution function of one probability distribution with the inverse cumulative distribution function of another is called the transmutation map. In this article, we will use the quadratic rank…
In this paper, some new results on the distribution of the generalized singular value decomposition (GSVD) are presented.
In this paper we introduce a new class of multivariate unimodal distributions, motivated by Khintchine's representation. We start by proposing a univariate model, whose support covers all the unimodal distributions on the real line. The…
In this paper we propose a new family of distribution considering Generalized Marshal-Olkin distribution as the base line distribution in the Beta-G family of Construction. The new family includes Beta-G (Eugene et al. 2002 and Jones, 2004)…
Decentralized stochastic optimization methods have gained a lot of attention recently, mainly because of their cheap per iteration cost, data locality, and their communication-efficiency. In this paper we introduce a unified convergence…