Related papers: Generating and solving the mean field and pair app…
Higher-order interactions play an important role in complex contagion processes. Mean-field approximations have been used to characterize the onset of spreading in the presence of group interactions. However, individual-based mean-field…
This article presents some aspects and experience in the use of algebraic manipulation software applied to general relativity. Some years ago certain results were reported using computer algebra platforms, but the growing popularity of…
In infectious disease modelling, the expected time from endemicity to extinction (of infection) may be analysed via WKB approximation, a method with origins in mathematical physics. The method is very general, but its uptake to date may…
Given that hierarchical count data in many fields are not Normally-distributed and include random effects, this paper extends the Generalized Linear Mixed Models (GLMMs) into Poisson Mixed-Effect Linear Model (PMELM) and do numerical…
Ordinary Differential Equations are generally too complex to be solved analytically. Approximations thereof can be obtained by general purpose numerical methods. However, even though accurate schemes have been developed, they remain…
One plus two-body embedded Gaussian orthogonal ensemble of random matrices with parity [EGOE(1+2)-$\pi$] generated by a random two-body interaction (modeled by GOE in two particle spaces) in the presence of a mean-field, for spinless…
In this article we review a theoretical framework for pair production from strong external electromagnetic fields. We propose a numerical method to solve the resulting equations of motion and present results for both cases of spatially…
Most modern supervised statistical/machine learning (ML) methods are explicitly designed to solve prediction problems very well. Achieving this goal does not imply that these methods automatically deliver good estimators of causal…
Despite empirical risk minimization (ERM) is widely applied in the machine learning community, its performance is limited on data with spurious correlation or subpopulation that is introduced by hidden attributes. Existing literature…
We introduce polynomial couplings, a generalization of probabilistic couplings, to develop an algorithm for the computation of equivalence relations which can be interpreted as a lifting of probabilistic bisimulation to polynomial…
Spatial regression models are central to the field of spatial statistics. Nevertheless, their estimation in case of large and irregular gridded spatial datasets presents considerable computational challenges. To tackle these computational…
Originally introduced in cooperative game theory, Shapley values have become a very popular tool to explain machine learning predictions. Based on Shapley's fairness axioms, every input (feature component) gets a credit how it contributes…
In this work we consider the problem of fitting Random Utility Models (RUMs) to user choices. Given the winner distributions of the subsets of size $k$ of a universe, we obtain a polynomial-time algorithm that finds the RUM that best…
An epidemiological model for COVID-19 was developed and implemented in MATLAB/GNU Octave for use by public health practitioners, policy makers and the general public. The model distinguishes four stages in the disease: infected, sick,…
We explore ways in which the covariance ellipsoid ${\cal B}=\{v \in \mathbb{R}^d : \mathbb{E} <X,v>^2 \leq 1\}$ of a centred random vector $X$ in $\mathbb{R}^d$ can be approximated by a simple set. The data one is given for constructing the…
Complex models used to describe biological processes in epidemiology and ecology often have computationally intractable or expensive likelihoods. This poses significant challenges in terms of Bayesian inference but more significantly in the…
Traditionally, spline or kernel approaches in combination with parametric estimation are used to infer the linear coefficient (fixed effects) in a partially linear mixed-effects model for repeated measurements. Using machine learning…
We present a fast algorithm that constructs a data-sparse approximation of matrices arising in the context of integral equation methods for elliptic partial differential equations. The new algorithm uses Green's representation formula in…
Since the introduction of Stein's method in the early 1970s, much research has been done in extending and strengthening it; however, there does not exist a version of Stein's original method of exchangeable pairs for multivariate normal…
Approximate Bayesian Computation (ABC) methods have become essential tools for performing inference when likelihood functions are intractable or computationally prohibitive. However, their scalability remains a major challenge in…