Related papers: Introducing Divergence for Infinite Probabilistic …
The literature on reachability analysis methods for neural networks currently only focuses on uncertainties on the network's inputs. In this paper, we introduce two new approaches for the reachability analysis of neural networks with…
In a dynamic parametric process every subprocess may spawn arbitrarily many, identical child processes, that may communicate either over global variables, or over local variables that are shared with their parent. We show that reachability…
Estimators derived from a divergence criterion such as $\varphi-$divergences are generally more robust than the maximum likelihood ones. We are interested in particular in the so-called MD$\varphi$DE, an estimator built using a dual…
The dynamics of an agreement protocol interacting with a disagreement process over a common random network is considered. The model can represent the spreading of true and false information over a communication network, the propagation of…
There has been an increasing interest in using neural networks in closed-loop control systems to improve performance and reduce computational costs for on-line implementation. However, providing safety and stability guarantees for these…
Coherent lower previsions are general probabilistic models allowing incompletely specified probability distributions. However, for complete description of a coherent lower prevision -- even on finite underlying sample spaces -- an infinite…
Advanced inference techniques allow one to reconstruct the pattern of interaction from high dimensional data sets. We focus here on the statistical properties of inferred models and argue that inference procedures are likely to yield models…
We present an approach to approximate reachable sets for linear systems with bounded L-infinity controls in finite time. Our first approach investigates the boundaries of these sets and reveals an exact characterization for single-input,…
In decision-making problems under uncertainty, probabilistic constraints are a valuable tool to express safety of decisions. They result from taking the probability measure of a given set of random inequalities depending on the decision…
A finite dimensional abstract approximation and convergence theory is developed for estimation of the distribution of random parameters in infinite dimensional discrete time linear systems with dynamics described by regularly dissipative…
This work establishes computable bounds between f-divergences for probability measures within a generalized quasi-$\varepsilon_{(M,m)}$-neighborhood framework. We make the following key contributions. (1) a unified characterization of local…
We introduce a new information-theoretic formulation of quantum measurement uncertainty relations, based on the notion of relative entropy between measurement probabilities. In the case of a finite-dimensional system and for any approximate…
We present a data-driven framework for reachability analysis of nonlinear dynamical systems that requires no explicit model. A denoising diffusion probabilistic model learns the time-evolving state distribution of a dynamical system from…
Maximum entropy (MAXENT) method has a large number of applications in theoretical and applied machine learning, since it provides a convenient non-parametric tool for estimating unknown probabilities. The method is a major contribution of…
A general notion of bootstrapped $\phi$-divergence estimates constructed by exchangeably weighting sample is introduced. Asymptotic properties of these generalized bootstrapped $\phi$-divergence estimates are obtained, by mean of the…
This paper studies the complexity of estimating Renyi divergences of discrete distributions: $p$ observed from samples and the baseline distribution $q$ known \emph{a priori}. Extending the results of Acharya et al. (SODA'15) on estimating…
This paper tackles challenges in pricing and revenue projections due to consumer uncertainty. We propose a novel data-based approach for firms facing unknown consumer type distributions. Unlike existing methods, we assume firms only observe…
This paper proposes an algorithm to maximize reachability probabilities for rectangular automata with random clocks via a history-dependent prophetic scheduler. This model class incorporates time-induced nondeterminism on discrete behavior…
Dempster-Shafer theory is widely applied in uncertainty modelling and knowledge reasoning due to its ability of expressing uncertain information. A distance between two basic probability assignments(BPAs) presents a measure of performance…
The approximation of a discrete probability distribution $\mathbf{t}$ by an $M$-type distribution $\mathbf{p}$ is considered. The approximation error is measured by the informational divergence $\mathbb{D}(\mathbf{t}\Vert\mathbf{p})$, which…