Related papers: A Framework for Algorithm Stability
Solutions of bilevel optimization problems tend to suffer from instability under changes to problem data. In the optimistic setting, we construct a lifted formulation that exhibits desirable stability properties under mild assumptions that…
Many problems in systems and control theory can be formulated in terms of robust D-stability analysis, which aims at verifying if all the eigenvalues of an uncertain matrix lie in a given region D of the complex plane. Robust D-stability…
This paper is about the surprising interaction of a foundational result from model theory, about stability of theories, with algorithmic stability in learning. First, in response to gaps in existing learning models, we introduce a new…
The solution of linear inverse problems arising, for example, in signal and image processing is a challenging problem since the ill-conditioning amplifies, in the solution, the noise present in the data. Recently introduced algorithms based…
This paper deals with stability of discrete-time switched linear systems whose all subsystems are unstable. We present sufficient conditions on the subsystems matrices such that a switched system is globally exponentially stable under a set…
Model averaging techniques based on resampling methods (such as bootstrapping or subsampling) have been utilized across many areas of statistics, often with the explicit goal of promoting stability in the resulting output. We provide a…
We consider the problem of designing uniformly stable first-order optimization algorithms for empirical risk minimization. Uniform stability is often used to obtain generalization error bounds for optimization algorithms, and we are…
In this paper we consider stable matchings subject to assignment constraints. These are matchings that require certain assigned pairs to be included, insist that some other assigned pairs are not, and, importantly, are stable. Our main…
Standard stochastic optimization methods are brittle, sensitive to stepsize choices and other algorithmic parameters, and they exhibit instability outside of well-behaved families of objectives. To address these challenges, we investigate…
Fourier matrices naturally appear in many applications and their stability is closely tied to performance guarantees of algorithms. The starting point of this article is a result that characterizes properties of an exponential system on a…
High-dimensional datasets present substantial challenges in statistical modeling across various disciplines, necessitating effective dimensionality reduction methods. Deep learning approaches, notable for their capacity to distill essential…
Extensively evaluating the capabilities of (large) language models is difficult. Rapid development of state-of-the-art models induce benchmark saturation, while creating more challenging datasets is labor-intensive. Inspired by the recent…
While unbiased machine learning models are essential for many applications, bias is a human-defined concept that can vary across tasks. Given only input-label pairs, algorithms may lack sufficient information to distinguish stable (causal)…
In this paper, we consider robust stability analysis of large-scale sparsely interconnected uncertain systems. By modeling the interconnections among the subsystems with integral quadratic constraints, we show that robust stability analysis…
The persistence barcode is a topological descriptor of data that plays a fundamental role in topological data analysis. Given a filtration of data, the persistence barcode tracks the evolution of its homology groups. In this paper, we…
We study stable matchings that are robust to preference changes in the two-sided stable matching setting of Gale and Shapley [GS62]. Given two instances $A$ and $B$ on the same set of agents, a matching is said to be robust if it is stable…
The stability of solutions to evolution equations with respect to small stochastic perturbations is considered. The stability of a stochastic dynamical system is characterized by the local stability index. The limit of this index with…
This paper studies robustness of MIMO control systems with parametric uncertainties, and establishes a lower dimensional robust stability criterion. For control systems with interval transfer matrices, we identify the minimal testing set…
A key property for systems subject to uncertainty in their operating environment is robustness, ensuring that unmodelled, but bounded, disturbances have only a proportionally bounded effect upon the behaviours of the system. Inspired by…
Dynamic response of loads has a significant effect on system stability and directly determines the stability margin of the operating point. Inherent uncertainty and natural variability of load models make the stability assessment especially…