Related papers: Robustness and Conditional Independence Ideals

A Markov tree is a random vector indexed by the nodes of a tree whose distribution is determined by the distributions of pairs of neighbouring variables and a list of conditional independence relations. Upon an assumption on the tails of…

Mining frequent patterns is plagued by the problem of pattern explosion making pattern reduction techniques a key challenge in pattern mining. In this paper we propose a novel theoretical framework for pattern reduction. We do this by…

This paper studies convergence of empirical risks in reproducing kernel Hilbert spaces (RKHS). A conventional assumption in the existing research is that empirical training data do not contain any noise but this may not be satisfied in some…

This work studies the distributionally robust evaluation of expected values over temporal data. A set of alternative measures is characterized by the causal optimal transport. We prove the strong duality and recast the causality constraint…

Linear systems with many degrees of freedom containing multiplicative and additive noise are considered. The steady state probability distribution for equations of this kind is examined. With multiplicative white noise it is shown that…

We study the robustness of system estimation to parametric perturbations in system dynamics and initial conditions. We define the problem of sensitivity-based parametric uncertainty quantification in dynamical system estimation. The main…

To every toric ideal one can associate an oriented matroid structure, consisting of a graph and another toric ideal, called bouquet ideal. The connected components of this graph are called bouquets. Bouquets are of three types; free, mixed…

In this paper, we develop efficient randomized algorithms for estimating probabilistic robustness margin and constructing robustness degradation curve for uncertain dynamic systems. One remarkable feature of these algorithms is their…

Let $E$ be a space of observables in a sequence of trials $\xi_n$ and define $m_n$ to be the empirical distributions of the outcomes. We discuss the almost sure convergence of the sequence $m_n$ in terms of the $\psi$-weak topology of…

A collection of $n$ random events is said to be $(n - 1)$-wise independent if any $n - 1$ events among them are mutually independent. We characterise all probability measures with respect to which $n$ random events are $(n - 1)$-wise…

It is becoming increasingly apparent that probabilistic approaches can overcome conservatism and computational complexity of the classical worst-case deterministic framework and may lead to designs that are actually safer. In this paper we…

Economists often estimate economic models on data and use the point estimates as a stand-in for the truth when studying the model's implications for optimal decision-making. This practice ignores model ambiguity, exposes the decision…

Robust control theory has been successfully applied to numerous real-world problems using a small set of devices called {\it controllers}. However, the real systems represented by networks contain unreliable components and modern robust…

Stochastic and soft optimal policies resulting from entropy-regularized Markov decision processes (ER-MDP) are desirable for exploration and imitation learning applications. Motivated by the fact that such policies are sensitive with…

This work reports the most relevant technical aspects in the problem of learning the \emph{Markov network structure} from data. Such problem has become increasingly important in machine learning, and many other application fields of machine…

In recent years probabilistic model checking has become an important area of research because of the diffusion of computational systems of stochastic nature. Despite its great success, standard probabilistic model checking suffers the…

An ordinal view of independence is studied in the framework of possibility theory. We investigate three possible definitions of dependence, of increasing strength. One of them is the counterpart to the multiplication law in probability…

Starting with Gilmer et al. (2018), several works have demonstrated the inevitability of adversarial examples based on different assumptions about the underlying input probability space. It remains unclear, however, whether these results…

We study the problem of testing \emph{conditional independence} for discrete distributions. Specifically, given samples from a discrete random variable $(X, Y, Z)$ on domain $[\ell_1]\times[\ell_2] \times [n]$, we want to distinguish, with…

We study the design of information acquisition games-environments where a designer contracts their action on Sender's choice of experiment and the realized signals about some state-and identify which predictions can be made absent knowledge…