Related papers: Fully bilinear generic and lifted random processes…

Since its introduction, the partial information decomposition (PID) has emerged as a powerful, information-theoretic technique useful for studying the structure of (potentially higher-order) interactions in complex systems. Despite its…

We prove (adjoint) bilinear restriction estimates for general phases at different scales in the full non-endpoint mixed norm range, and give bounds with a sharp and explicit dependence on the phases. These estimates have applications to…

First-order probabilistic models combine representational power of first-order logic with graphical models. There is an ongoing effort to design lifted inference algorithms for first-order probabilistic models. We analyze lifted inference…

Loss-based updating, including generalized Bayes, Gibbs, and quasi-posteriors, replaces likelihoods by a user-chosen loss and produces a posterior-like distribution via exponential tilt. We give a decision-theoretic characterization that…

Mixup is a highly successful technique to improve generalization of neural networks by augmenting the training data with combinations of random pairs. Selective mixup is a family of methods that apply mixup to specific pairs, e.g. only…

We extend the branching process based numerical algorithm of Bouchard et al. [3], that is dedicated to semilinear PDEs (or BSDEs) with Lipschitz nonlinearity, to the case where the nonlinearity involves the gradient of the solution. As in…

We shall discuss a higher-rank Khovanskii-Teissier inequality, generalizing a theorem of Li. In the course of the proof, we develop new Hodge-Riemann bilinear relations in certain mixed settings, which in themselves slightly extend the…

A class of nonparametric two-sample tests has been proposed in this article. As a generalization of the original \v{S}id\'aks' test, the proposed test statistic is developed as the sum of the maximal precedence and maximal exceedance…

Bayesian Filtering for plan and activity recognition is challenging for scenarios that contain many observation equivalent entities (i.e. entities that produce the same observations). This is due to the combinatorial explosion in the number…

Many behavioural equivalences or preorders for probabilistic processes involve a lifting operation that turns a relation on states into a relation on distributions of states. We show that several existing proposals for lifting relations can…

We consider all 16 unary operations that, given a homogeneous binary relation R, define a new one by a boolean combination of xRy and yRx. Operations can be composed, and connected by pointwise-defined logical junctors. We consider the…

We present pairwise fairness metrics for ranking models and regression models that form analogues of statistical fairness notions such as equal opportunity, equal accuracy, and statistical parity. Our pairwise formulation supports both…

The recently developed semi-parametric generalized linear model (SPGLM) offers more flexibility as compared to the classical GLM by including the baseline or reference distribution of the response as an additional parameter in the model.…

This paper proposes the asymmetric linear double autoregression, which jointly models the conditional mean and conditional heteroscedasticity characterized by asymmetric effects. A sufficient condition is established for the existence of a…

Given an observation of the uniform empirical process $\alp_n$, its functional increments $\alp_n(u+a_n\cdot)-\alp_n(u)$ can be viewed as a single random process, when $u$ is distributed under the Lebesgue measure. We investigate the almost…

In this paper we develop a new approach for studying overlapping iterated function systems. This approach is inspired by a famous result due to Khintchine from Diophantine approximation. This result shows that for a family of limsup sets,…

Many representation schemes combining first-order logic and probability have been proposed in recent years. Progress in unifying logical and probabilistic inference has been slower. Existing methods are mainly variants of lifted variable…

We show that an arbitrary nilprogression can be approximated by a proper coset nilprogression in upper-triangular form. This can be thought of as a nilpotent version of the Freiman-Bilu result that a generalised arithmetic progression can…

In this work, we propose a novel framework for large-scale Gaussian process (GP) modeling. Contrary to the global, and local approximations proposed in the literature to address the computational bottleneck with exact GP modeling, we employ…

The multiresolution Gaussian process (GP) has gained increasing attention as a viable approach towards improving the quality of approximations in GPs that scale well to large-scale data. Most of the current constructions assume full…