Related papers: Small Errors Imply Large Instabilities
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…
The parametric instability arising when ordinary differential equations (ODEs) are numerically integrated with Runge-Kutta-Nystr\"om (RKN) methods with varying step sizes is investigated. It is shown that when linear constant coefficient…
This paper proposes a novel method for determining the number of factors in linear factor models under stability considerations. An instability measure is proposed based on the principal angle between the estimated loading spaces obtained…
The choice of a point set, to be used in numerical integration, determines, to a large extent, the error estimate of the integral. Point sets can be characterized by their discrepancy, which is a measure of its non-uniformity. Point sets…
In this paper we propose a method to define the range of stability of fixed points for a variety of discrete fractional systems of the order $0 < \alpha <2$. The method is tested on various forms of fractional generalizations of the…
Improving algorithms via predictions is a very active research topic in recent years. This paper initiates the systematic study of mechanism design in this model. In a number of well-studied mechanism design settings, we make use of…
Trade-offs between accuracy and efficiency pervade law, public health, and other non-computing domains, which have developed policies to guide how to balance the two in conditions of uncertainty. While computer science also commonly studies…
Discrete numerical methods with finite time-steps represent a practical technique to solve initial-value problems involving nonlinear differential equations. These methods seem particularly useful to the study of chaos since no analytical…
We precisely quantify the impact of statistical error in the quality of a numerical approximation to a random matrix eigendecomposition, and under mild conditions, we use this to introduce an optimal numerical tolerance for residual error…
Output uncertainty indicates whether the probabilistic properties reflect objective characteristics of the model output. Unlike most loss functions and metrics in machine learning, uncertainty pertains to individual samples, but validating…
In data-based control, dissipativity can be a powerful tool for attaining stability guarantees for nonlinear systems if that dissipativity can be inferred from data. This work provides a tutorial on several existing methods for data-based…
It is well known that, when defining Householder transformations, the correct choice of sign in the standard formula is important to avoid cancellation and hence numerical instability. In this note we point out that when the "wrong" choice…
Probabilistic solvers for ordinary differential equations assign a posterior measure to the solution of an initial value problem. The joint covariance of this distribution provides an estimate of the (global) approximation error. The…
This paper presents a theoretical analysis of sample selection bias correction. The sample bias correction technique commonly used in machine learning consists of reweighting the cost of an error on each training point of a biased sample to…
Two-sided matching markets, environments in which two disjoint groups of agents seek to partner with one another, arise in several contexts. In static, centralized markets where agents know their preferences, standard algorithms can yield a…
This paper presents a novel method for transient stability analysis (TSA) that circumvents the limitations of sequential numerical integration and energy functions. The proposed method begins by constructing a trajectory-dependent stability…
With the growing adoption of machine learning (ML) systems in areas like law enforcement, criminal justice, finance, hiring, and admissions, it is increasingly critical to guarantee the fairness of decisions assisted by ML. In this paper,…
In multi-agent environments in which coordination is desirable, the history of play often causes lock-in at sub-optimal outcomes. Notoriously, technologies with a significant environmental footprint or high social cost persist despite the…
Recently, many regularized procedures have been proposed for variable selection in linear regression, but their performance depends on the tuning parameter selection. Here a criterion for the tuning parameter selection is proposed, which…
In this work, we systematically investigate linear multi-step methods for differential equations with memory. In particular, we focus on the numerical stability for multi-step methods. According to this investigation, we give some…