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We present a stochastic constrained output-feedback data-driven predictive control scheme for linear time-invariant systems subject to bounded additive disturbances. The approach uses data-driven predictors based on an extension of Willems'…

Systems and Control · Electrical Eng. & Systems 2025-10-07 Johannes Teutsch , Sebastian Kerz , Dirk Wollherr , Marion Leibold

In many real-world scenarios, interested variables are often represented as discretized values due to measurement limitations. Applying Conditional Independence (CI) tests directly to such discretized data, however, can lead to incorrect…

Artificial Intelligence · Computer Science 2025-06-11 Boyang Sun , Yu Yao , Xinshuai Dong , Zongfang Liu , Tongliang Liu , Yumou Qiu , Kun Zhang

We consider noisy non-synchronous discrete observations of a continuous semimartingale with random volatility. Functional stable central limit theorems are established under high-frequency asymptotics in three setups: one-dimensional for…

Statistics Theory · Mathematics 2015-07-28 Randolf Altmeyer , Markus Bibinger

In this paper we extend the notion of a continuous bundle random dynamical system to the setting where the action of $\R$ or $\N$ is replaced by the action of an infinite countable discrete amenable group. Given such a system, and a…

Dynamical Systems · Mathematics 2013-06-21 Anthony H. Dooley , Guohua Zhang

In the standard stochastic block model for networks, the probability of a connection between two nodes, often referred to as the edge probability, depends on the unobserved communities each of these nodes belongs to. We consider a flexible…

Econometrics · Economics 2024-02-27 Yuichi Kitamura , Louise Laage

We investigate the convergence in distribution of sequential empirical processes of dependent data indexed by a class of functions F. Our technique is suitable for processes that satisfy a multiple mixing condition on a space of functions…

Probability · Mathematics 2014-09-26 Herold Dehling , Olivier Durieu , Marco Tusche

We present limit theorems for a sequence of Piecewise Deterministic Markov Processes (PDMPs) taking values in a separable Hilbert space. This class of processes provides a rigorous framework for stochastic spatial models in which discrete…

Probability · Mathematics 2012-04-13 Martin G. Riedler , Michèle Thieullen , Gilles Wainrib

The algorithmic Markov condition states that the most likely causal direction between two random variables X and Y can be identified as that direction with the lowest Kolmogorov complexity. Due to the halting problem, however, this notion…

Machine Learning · Computer Science 2017-02-23 Kailash Budhathoki , Jilles Vreeken

This paper develops limit theorems for random variables with network dependence, without requiring the individuals in the network to be located in a Euclidean or metric space. This distinguishes our approach from most existing limit…

Econometrics · Economics 2026-03-20 Wen Jiang , Yachen Wang , Zeqi Wu , Xingbai Xu

We establish a multivariate empirical process central limit theorem for stationary $\R^d$-valued stochastic processes $(X_i)_{i\geq 1}$ under very weak conditions concerning the dependence structure of the process. As an application we can…

Probability · Mathematics 2011-01-28 Herold Dehling , Olivier Durieu

The martingale method is used to establish concentration inequalities for a class of dependent random sequences on a countable state space, with the constants in the inequalities expressed in terms of certain mixing coefficients. Along the…

Probability · Mathematics 2009-01-22 Leonid , Kontorovich , Kavita Ramanan

We consider the problem of bounding large deviations for non-i.i.d. random variables that are allowed to have arbitrary dependencies. Previous works typically assumed a specific dependence structure, namely the existence of independent…

Probability · Mathematics 2018-11-06 Christoph H. Lampert , Liva Ralaivola , Alexander Zimin

Motivation: Algorithms that discover variables which are causally related to a target may inform the design of experiments. With observational gene expression data, many methods discover causal variables by measuring each variable's degree…

Quantitative Methods · Quantitative Biology 2014-07-30 Eric V. Strobl , Shyam Visweswaran

A dynamical model consists of a continuous self-map $T: \mathcal{X} \to \mathcal{X}$ of a compact state space $\mathcal{X}$ and a continuous observation function $f: \mathcal{X} \to \mathbb{R}$. This paper considers the fitting of a…

Statistics Theory · Mathematics 2018-01-24 Kevin McGoff , Andrew B. Nobel

A particular type of random dynamical processes is considered, in which the stochasticity is introduced through randomly fluctuating parameters. A method of local multipliers is developed for treating the local stability of such dynamical…

Disordered Systems and Neural Networks · Physics 2015-06-25 V. I. Yukalov

This paper introduces new efficient algorithms for two problems: sampling conditional on vertex degrees in unweighted graphs, and sampling conditional on vertex strengths in weighted graphs. The algorithms can sample conditional on the…

Methodology · Statistics 2018-09-19 James Scott , Axel Gandy

We introduce a statistical mechanics formalism for the study of constrained graph evolution as a Markovian stochastic process, in analogy with that available for spin systems, deriving its basic properties and highlighting the role of the…

Disordered Systems and Neural Networks · Physics 2015-05-13 A. C. C. Coolen , A. De Martino , A. Annibale

This paper investigates the behavior of statistical ensembles under iteration map induced by discrete integrable Hamiltonian systems in deterministic case and stochastic case, addressing the problem from two perspectives: the Law of Large…

Probability · Mathematics 2025-09-26 Xinyu Liu , Xinze Zhang , Yong Li

Let (X_n) be a sequence of random variables (with values in a separable metric space) and (N_n) a sequence of random indices. Conditions for X_{N_n} to converge stably (in particular, in distribution) are provided. Some examples, where such…

Probability · Mathematics 2012-10-01 Patrizia Berti , Irene Crimaldi , Luca Pratelli , Pietro Rigo

Conditional independence (CI) testing is a fundamental task in modern statistics and machine learning. The conditional randomization test (CRT) was recently introduced to test whether two random variables, $X$ and $Y$, are conditionally…

Machine Learning · Statistics 2024-12-19 Yanfeng Yang , Shuai Li , Yingjie Zhang , Zhuoran Sun , Hai Shu , Ziqi Chen , Renming Zhang