Related papers: Order Statistics and Probabilistic Robust Control
``Behind every limit theorem, there is an inequality'' said Kolmogorov. We say ``for every inequality, there is an approximate inequality under approximate regularity conditions.'' Suppose $X, X'$ are independent and identically distributed…
This work proposes a notion of robust reachability of one set from another set under constant control. This notion is used to construct a control strategy, involving sequential set-to-set reachability, which guarantees robust global…
A random set is a generalisation of a random variable, i.e. a set-valued random variable. The random set theory allows a unification of other uncertainty descriptions such as interval variable, mass belief function in Dempster-Shafer theory…
In this paper we wish to tackle stochastic programs affected by ambiguity about the probability law that governs their uncertain parameters. Using optimal transport theory, we construct an ambiguity set that exploits the knowledge about the…
Distributionally balanced sampling designs are low-discrepancy probability designs obtained by minimizing the expected discrepancy between the auxiliary-variable distribution of a random sample and the target population distribution.…
In the past couple of years, various approaches to representing and quantifying different types of predictive uncertainty in machine learning, notably in the setting of classification, have been proposed on the basis of second-order…
Uncertainties influencing the dynamical systems pose a significant challenge in estimating the achievable performance of a controller aiming to control such uncertain systems. When the uncertainties are of stochastic nature, obtaining hard…
We observe a $n$-sample, the distribution of which is assumed to belong, or at least to be close enough, to a given mixture model. We propose an estimator of this distribution that belongs to our model and possesses some robustness…
Split conformal prediction has recently sparked great interest due to its ability to provide formally guaranteed uncertainty sets or intervals for predictions made by black-box neural models, ensuring a predefined probability of containing…
In this paper we are interested in the joint distribution of two order statistics from overlapping samples. We give an explicit formula for the distribution of such a pair of random variables under the assumption that the parent…
The problem of quickest detection of a change in the distribution of a sequence of random variables is studied. The objective is to detect the change with the minimum possible delay, subject to constraints on the rate of false alarms and…
In applied probability, the normal approximation is often used for the distribution of data with assumed additive structure. This tradition is based on the central limit theorem for sums of (independent) random variables. However, it is…
The principle of maximum entropy is a broadly applicable technique for computing a distribution with the least amount of information possible constrained to match empirical data, for instance, feature expectations. We seek to generalize…
Stochastic programs where the uncertainty distribution must be inferred from noisy data samples are considered. The stochastic programs are approximated with distributionally-robust optimizations that minimize the worst-case expected cost…
Algorithmic stability is a central concept in statistics and learning theory that measures how sensitive an algorithm's output is to small changes in the training data. Stability plays a crucial role in understanding generalization,…
We study control of constrained linear systems with only partial statistical information about the uncertainty affecting the system dynamics and the sensor measurements. Specifically, given a finite collection of disturbance realizations…
Robust control theory studies the effect of noise, disturbances, and other uncertainty on system performance. Despite growing recognition across science and engineering that robustness and efficiency tradeoffs dominate the evolution and…
This paper studies optimal control problems of unknown linear systems subject to stochastic disturbances of uncertain distribution. Uncertainty about the stochastic disturbances is usually described via ambiguity sets of probability…
The measurement of dispersion is one of the most fundamental and ubiquitous statistical concepts, in both applied and theoretical contexts. For dispersion measures, such as the standard deviation, to effectively capture the variability of a…
Distribution testing is a fundamental statistical task with many applications, but we are interested in a variety of problems where systematic mislabelings of the sample prevent us from applying the existing theory. To apply distribution…