Related papers: Tolerances, robustness and parametrization of matr…
The positive stability and D-stability of singular M-matrices, perturbed by (non-trivial) nonnegative rank one perturbations, is investigated. In special cases positive stability or D-stability can be established. In full generality this is…
Optimal solutions of combinatorial optimization problems can be sensitive to changes in the cost of one or more elements of the ground set E. Single and set tolerances measure the supremum / infimum possible change such that the current…
Algorithms for learning decision trees often include heuristic local-search operations such as (1) adjusting the threshold of a cut or (2) also exchanging the feature of that cut. We study minimizing the number of classification errors by…
Linear polarimetric transformations of light polarization states by the action of material media are fully characterized by the corresponding Mueller matrices, which contain in an implicit and intricate manner all measurable information on…
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…
Meaningful comparison between sets of observations often necessitates alignment or registration between them, and the resulting optimization problems range in complexity from those admitting simple closed-form solutions to those requiring…
Learning representations that capture the underlying data generating process is a key problem for data efficient and robust use of neural networks. One key property for robustness which the learned representation should capture and which…
A probability model exhibits instability if small changes in a data outcome result in large, and often unanticipated, changes in probability. This instability is a property of the probability model, given by a distributional form and a…
Approximations of optimization problems arise in computational procedures and sensitivity analysis. The resulting effect on solutions can be significant, with even small approximations of components of a problem translating into large…
Machine learning models are vulnerable to tiny adversarial input perturbations optimized to cause a very large output error. To measure this vulnerability, we need reliable methods that can find such adversarial perturbations. For image…
Various types of stabilizing controls lead to a deterministic difference equation with the following property: once the initial value is positive, the solution tends to the unique positive equilibrium. Introducing additive perturbations can…
While $\mathcal{H}_\infty$ methods can introduce robustness against worst-case perturbations, their nominal performance under conventional stochastic disturbances is often drastically reduced. Though this fundamental tradeoff between…
Neural networks trained on visual data are well-known to be vulnerable to often imperceptible adversarial perturbations. The reasons for this vulnerability are still being debated in the literature. Recently Ilyas et al. (2019) showed that…
This paper introduces a concept of a derivative of the optimal value function in linear programming (LP). Basically, it is the the worst case optimal value of an interval LP problem when the nominal data the data are inflated to intervals…
Density matrix perturbation theory based on recursive Fermi-operator expansions provides a computationally efficient framework for time-independent response calculations in quantum chemistry and materials science. From a perturbation in the…
We introduce highly optimized tolerance (HOT), a mechanism that connects evolving structure and power laws in interconnected systems. HOT systems arise, e.g., in biology and engineering, where design and evolution create complex systems…
Many algorithms use data structures that maintain properties of matrices undergoing some changes. The applications are wide-ranging and include for example matchings, shortest paths, linear programming, semi-definite programming, convex…
The optimal power adaptation problem is investigated for vector parameter estimation according to various Fisher information based optimality criteria. By considering an observation model that involves a linear transformation of the…
Positive definite (p.d.) matrices arise naturally in many areas within mathematics and also feature extensively in scientific applications. In modern high-dimensional applications, a common approach to finding sparse positive definite…
In this work, we propose a robust framework that employs adversarially robust training to safeguard the ML models against perturbed testing data. Our contributions can be seen from both computational and statistical perspectives. Firstly,…