Related papers: Robustness and Conditional Independence Ideals
We study the concept of financial bubble in a market model endowed with a set of probability measures, typically mutually singular to each other. In this setting we introduce the notions of robust bubble and robust fundamental value in a…
This paper deals with the stochastic control of nonlinear systems in the presence of state and control constraints, for uncertain discrete-time dynamics in finite dimensional spaces. In the deterministic case, the viability kernel is known…
This article aims to introduce the paradigm of distributional robustness from the field of convex optimization to tackle optimal design problems under uncertainty. We consider realistic situations where the physical model, and thereby the…
We consider regression in which one predicts a response $Y$ with a set of predictors $X$ across different experiments or environments. This is a common setup in many data-driven scientific fields and we argue that statistical inference can…
We study the connection between probability distributions satisfying certain conditional independence (CI) constraints, and point and line arrangements in incidence geometry. To a family of CI statements, we associate a polynomial ideal…
We utilize quantum superposition principle to establish the improvable upper and lower bounds on the stronger uncertainty relation, i.e., the "weighted-like" sum of the variances of observables. Our bounds include some free parameters which…
Although regular conditional distributions (r.c.d.) are well-defined and widely used measure-theoretic objects, they can violate our intuition from the classical definition of a conditional probability given an event. For that purpose, the…
We examine the relationship between learnability and robust (or agnostic) learnability for the problem of distribution learning. We show that, contrary to other learning settings (e.g., PAC learning of function classes), realizable…
This paper proposes a model predictive controller for discrete-time linear systems with additive, possibly unbounded, stochastic disturbances and subject to chance constraints. By computing a polytopic probabilistic positively invariant set…
We consider the problem of conditional independence testing of $X$ and $Y$ given $Z$ where $X,Y$ and $Z$ are three real random variables and $Z$ is continuous. We focus on two main cases - when $X$ and $Y$ are both discrete, and when $X$…
In this paper we study a rational inattention model in environments where the decision maker faces uncertainty about the true prior distribution over states. The decision maker seeks to select a stochastic choice rule over a finite set of…
We define generalized innovations associated with generalized error models having arbitrary distributions, that is, distributions that can be mixtures of continuous and discrete distributions. These models include stochastic volatility…
In this paper, we investigate the robust models for $\Lambda$-quantiles with partial information regarding the loss distribution, where $\Lambda$-quantiles extend the classical quantiles by replacing the fixed probability level with a…
A set of independence statements may define the independence structure of interest in a family of joint probability distributions. This structure is often captured by a graph that consists of nodes representing the random variables and of…
Uncertain information on input parameters of reliability models is usually modeled by considering these parameters as random, and described by marginal distributions and a dependence structure of these variables. In numerous real-world…
This paper studies the robustness of large-scale interconnected systems with respect to external disturbances, focussing on their scalability properties. Specifically, a notion of scalability is introduced that asks for these robustness…
We provide a unified framework for independence and mean independence tests based on the Hilbert-Schmidt independence criterion, extending some previous results in the literature to hold in general topological spaces. We also present a…
Independence testing plays a central role in statistical and causal inference from observational data. Standard independence tests assume that the data samples are independent and identically distributed (i.i.d.) but that assumption is…
Probabilistic separation logic offers an approach to reasoning about imperative probabilistic programs in which a separating conjunction is used as a mechanism for expressing independence properties. Crucial to the effectiveness of the…
We obtain the posterior distribution of a random process conditioned on observing the empirical frequencies of a finite sample path. We find under a rather broad assumption on the "dependence structure" of the process, {\em c.f.}…