Related papers: Distributional Robustness and Uncertainty Quantifi…
In natural phenomena, data distributions often deviate from normality. One can think of cataclysms as a self-explanatory example: events that occur almost never, and at the same time are many standard deviations away from the common…
Risk measures such as Conditional Value-at-Risk (CVaR) focus on extreme losses, where scarce tail data makes model error unavoidable. To hedge misspecification, one evaluates worst-case tail risk over an ambiguity set. Using Extreme Value…
In a number of applications, particularly in financial and actuarial mathematics, it is of interest to characterize the tail distribution of a random variable $V$ satisfying the distributional equation $V\stackrel{\mathcal{D}}{=}f(V)$,…
We study distributional robustness in the context of Extreme Value Theory (EVT). We provide a data-driven method for estimating extreme quantiles in a manner that is robust against incorrect model assumptions underlying the application of…
Conventional methods for extreme event estimation rely on well-chosen parametric models asymptotically justified from extreme value theory (EVT). These methods, while powerful and theoretically grounded, could however encounter a difficult…
Estimation of tail quantities, such as expected shortfall or Value at Risk, is a difficult problem. We show how the theory of nonlinear expectations, in particular the Data-robust expectation introduced in [5], can assist in the…
Chebyshev's inequality provides an upper bound on the tail probability of a random variable based on its mean and variance. While tight, the inequality has been criticized for only being attained by pathological distributions that abuse the…
Expected risk minimization (ERM) is at the core of many machine learning systems. This means that the risk inherent in a loss distribution is summarized using a single number - its average. In this paper, we propose a general approach to…
We consider settings in which the distribution of a multivariate random variable is partly ambiguous. We assume the ambiguity lies on the level of the dependence structure, and that the marginal distributions are known. Furthermore, a…
Distributionally robust control is a well-studied framework for optimal decision making under uncertainty, with the objective of minimizing an expected cost function over control actions, assuming the most adverse probability distribution…
Neural networks (NNs) are now routinely implemented on systems that must operate in uncertain environments, but the tools for formally analyzing how this uncertainty propagates to NN outputs are not yet commonplace. Computing tight bounds…
We consider the problem of probabilistic quantification of dynamical systems that have heavy-tailed characteristics. These heavy-tailed features are associated with rare transient responses due to the occurrence of internal instabilities.…
A new paradigm is proposed for the robustification of the LQG controller against distributional uncertainties on the noise process. Our controller optimizes the closed-loop performances in the worst possible scenario under the constraint…
In the Bayesian literature, a line of research called resolution of conflict is about the characterization of robustness against outliers of statistical models. The robustness characterization of a model is achieved by establishing the…
In this work, we study how to ensure probabilistic safety for nonlinear systems under distributional ambiguity. Our approach builds on a backup-based safety filtering framework that switches between a high-performance nominal policy and a…
For nonlinear supervised learning models, assessing the importance of predictor variables or their interactions is not straightforward because it can vary in the domain of the variables. Importance can be assessed locally with sensitivity…
We use a decision-theoretic framework to study the problem of forecasting discrete outcomes when the forecaster is unable to discriminate among a set of plausible forecast distributions because of partial identification or concerns about…
In this paper, by proposing two new kinds of distributional uncertainty sets, we explore robustness of distortion risk measures against distributional uncertainty. To be precise, we first consider a distributional uncertainty set which is…
We introduce a framework for quantifying propagation of uncertainty arising in a dynamic setting. Specifically, we define dynamic uncertainty sets designed explicitly for discrete stochastic processes over a finite time horizon. These…
This paper provides tight bounds on the R\'enyi entropy of a function of a discrete random variable with a finite number of possible values, where the considered function is not one-to-one. To that end, a tight lower bound on the R\'enyi…