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Probabilistic graphical models are a key tool in machine learning applications. Computing the partition function, i.e., normalizing constant, is a fundamental task of statistical inference but it is generally computationally intractable,…
We further develop the \emph{Multivariate Decomposition Method} (MDM) for the Lebesgue integration of functions of infinitely many variables $x_1,x_2,x_3,\ldots$ with respect to a corresponding product of a one dimensional probability…
We construct a class of real-valued nonnegative binary functions on a set of jointly distributed random variables, which satisfy the triangle inequality and vanish at identical arguments (pseudo-quasi-metrics). These functions are useful in…
This article introduces probabilistic disjunctive normal forms (PDNFs) as a framework for representing and reasoning about uncertainty in logical systems. Unlike classical DNFs, PDNFs assign real-valued weights to variables, encoding…
We consider a type of nonnormal approximation of infinitely divisible distributions that incorporates compound Poisson, Gamma, and normal distributions. The approximation relies on achieving higher orders of cumulant matching, to obtain…
We consider structured optimisation problems defined in terms of the sum of a smooth and convex function, and a proper, l.s.c., convex (typically non-smooth) one in reflexive variable exponent Lebesgue spaces $L_{p(\cdot)}(\Omega)$. Due to…
Composite likelihood provides approximate inference when the full likelihood is intractable and sub-likelihood functions of marginal events can be evaluated relatively easily. It has been successfully applied for many complex models.…
The No Unmeasured Confounding Assumption is widely used to identify causal effects in observational studies. Recent work on proximal inference has provided alternative identification results that succeed even in the presence of unobserved…
The likelihood function is a fundamental component in Bayesian statistics. However, evaluating the likelihood of an observation is computationally intractable in many applications. In this paper, we propose a non-parametric approximation of…
We describe a technique that can be used for the fusion of multiple sources of information as well as for the evaluation and selection of alternatives under multi-criteria. Three important properties contribute to the uniqueness of the…
This paper concerns the universal approximation property with neural networks in variable Lebesgue spaces. We show that, whenever the exponent function of the space is bounded, every function can be approximated with shallow neural networks…
Bayesian reasoning is a powerful mechanism for probabilistic inference in smart edge-devices. During such inferences, a low-precision arithmetic representation can enable improved energy efficiency. However, its impact on inference accuracy…
To better understand complexity in neural networks, we theoretically investigate the idealised phenomenon of lossless network compressibility, whereby an identical function can be implemented with fewer hidden units. In the setting of…
Despite widespread success in language understanding and generation, large language models (LLMs) exhibit unclear and often inconsistent behavior when faced with tasks that require probabilistic reasoning. In this work, we present the first…
We propose a novel use of a recent new computational tool for Bayesian inference, namely the Approximate Bayesian Computation (ABC) methodology. ABC is a way to handle models for which the likelihood function may be intractable or even…
Two semimetrics on probability distributions are proposed, given as the sum of differences of expectations of analytic functions evaluated at spatial or frequency locations (i.e, features). The features are chosen so as to maximize the…
This paper presents a probabilistic perspective on iterative methods for approximating the solution $\mathbf{x}_* \in \mathbb{R}^d$ of a nonsingular linear system $\mathbf{A} \mathbf{x}_* = \mathbf{b}$. In the approach a standard iterative…
A multiplicative stochastic process with the lower bound lognormally distributed is investigated. For the process, the model is constructed, and its distribution function (involving four parameters) and the related statistical properties…
The declining response rates in probability surveys along with the widespread availability of unstructured data has led to growing research into non-probability samples. Existing robust approaches are not well-developed for non-Gaussian…
Due to their flexibility, Gaussian processes (GPs) have been widely used in nonparametric function estimation. A prior information about the underlying function is often available. For instance, the physical system (computer model output)…