Related papers: Generalized Score Distribution
In this article, a generalized version of Negative binomial-beta exponential distribution with five parameters have been introduced. Some interesting submodels have been derived from it. A comprehensive mathematical treatment of proposed…
In this paper, some new results on the distribution of the generalized singular value decomposition (GSVD) are presented.
In this work, the probability of an event under some joint distribution is bounded by measuring it with the product of the marginals instead (which is typically easier to analyze) together with a measure of the dependence between the two…
This paper presents Probabilistic Video Contrastive Learning, a self-supervised representation learning method that bridges contrastive learning with probabilistic representation. We hypothesize that the clips composing the video have…
Certain extremum estimators have asymptotic distributions that are non-Gaussian, yet characterizable as the distribution of the $\argmax$ of a Gaussian process. This paper presents high-level sufficient conditions under which such…
Standard Bayesian analyses can be difficult to perform when the full likelihood, and consequently the full posterior distribution, is too complex and difficult to specify or if robustness with respect to data or to model misspecifications…
\cite{tsagris2025a} proposed the generalized circular projected Cauchy (GCPC) distribution, whose special case is the wrapped Cauchy distribution. In this paper we first derive the relationship with the wrapped Cauchy distribution, and then…
The classical paradigm of scoring rules is to discriminate between two different forecasts by comparing them with observations. The probability distribution of the observed record is assumed to be perfect as a verification benchmark. In…
We introduce Generalized Discrete Diffusion from Snapshots (GDDS), a unified framework for discrete diffusion modeling that supports arbitrary noising processes over large discrete state spaces. Our formulation encompasses all existing…
Despite its empirical success, deep learning still lacks a comprehensive theoretical understanding of model fitting and generalization. This paper proposes the probability distribution (PD) learning framework to analyze the optimization and…
Analyzing neural network dynamics via stochastic gradient descent (SGD) is crucial to building theoretical foundations for deep learning. Previous work has analyzed structured inputs within the \textit{hidden manifold model}, often under…
In this paper, a distributed stochastic gradient (SG) algorithm is proposed where the estimators are aimed to collectively estimate an unknown time-invariant parameter from a set of noisy measurements obtained by distributed sensors. The…
We consider parameter estimation in distributed networks, where each sensor in the network observes an independent sample from an underlying distribution and has $k$ bits to communicate its sample to a centralized processor which computes…
Failure of machine learning models to generalize to new data is a core problem limiting the reliability of AI systems, partly due to the lack of simple and robust methods for comparing new data to the original training dataset. We propose a…
This paper considers distributed average consensus using finite-bit bounded quantizer with possibly unbounded data. Under the framework of the alternating direction method of multipliers (ADMM), we develop distributed averaging algorithms…
Fisheries scientists use regression models to estimate population quantities, such as biomass or abundance, for use in climate, habitat, stock, and ecosystem assessments. However, these models are sensitive to the chosen probability…
Score diffusion methods can learn probability densities from samples. The score of the noise-corrupted density is estimated using a deep neural network, which is then used to iteratively transport a Gaussian white noise density to a target…
The Gumbel trick is a method to sample from a discrete probability distribution, or to estimate its normalizing partition function. The method relies on repeatedly applying a random perturbation to the distribution in a particular way, each…
As datasets grow larger, they are often distributed across multiple machines that compute in parallel and communicate with a central machine through short messages. In this paper, we focus on sparse regression and propose a new procedure…
G-computation has become a widely used robust method for estimating unconditional (marginal) treatment effects with covariate adjustment in the analysis of randomized clinical trials. Statistical inference in this context typically relies…