Related papers: A Model for Understanding Numerical Stability
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…
Reliability analysis is a sub-field of uncertainty quantification that assesses the probability of a system performing as intended under various uncertainties. Traditionally, this analysis relies on deterministic models, where experiments…
This paper considers a probabilistic model for floating-point computation in which the roundoff errors are represented by bounded random variables with mean zero. Using this model, a probabilistic bound is derived for the forward error of…
We compare the divergence of orbits and the reversibility error for discrete time dynamical systems. These two quantities are used to explore the behavior of the global error induced by round off in the computation of orbits. The similarity…
Understanding the stability and long-time behavior of generative models is a fundamental problem in modern machine learning. This paper provides quantitative bounds on the sampling error of score-based generative models by leveraging…
Finite-precision floating point arithmetic unavoidably introduces rounding errors which are traditionally bounded using a worst-case analysis. However, worst-case analysis might be overly conservative because worst-case errors can be…
We discuss recent work for causal inference and predictive robustness in a unifying way. The key idea relies on a notion of probabilistic invariance or stability: it opens up new insights for formulating causality as a certain risk…
Optimization under uncertainty and risk is indispensable in many practical situations. Our paper addresses stability of optimization problems using composite risk functionals which are subjected to measure perturbations. Our main focus is…
Stability is a central property in learning and statistics promising the output of an algorithm $A$ does not change substantially when applied to similar datasets $S$ and $S'$. It is an elementary fact that any sufficiently stable algorithm…
Robustness of linear systems with constant coefficients is considered. There exist methods and tools for analyzing the stability of systems with random or deterministic uncertainties. At the same time, there are no approaches for the…
Stability selection is a widely adopted resampling-based framework for high-dimensional variable selection. This paper seeks to broaden the use of an established stability estimator to evaluate the overall stability of the stability…
Missing data is pervasive in econometric applications, and rarely is it plausible that the data are missing (completely) at random. This paper proposes a methodology for studying the robustness of results drawn from incomplete datasets.…
This work represents a natural coalescence of two important lines of work: learning mixtures of Gaussians and algorithmic robust statistics. In particular we give the first provably robust algorithm for learning mixtures of any constant…
Can we conclude the stability of an unknown dynamical system from the knowledge of a finite number of snapshots of trajectories? We tackle this black-box problem for switched linear systems. We show that, for any given random set of…
The conventional rounding error analysis provides worst-case bounds with an associated failure probability and ignores the statistical property of the rounding errors. In this paper, we develop a new statistical rounding error analysis for…
In this note we study the numerical stability problem that may take place when calculating the cumulative distribution function of the {\it Hypoexponential} random variable. This computation is extensively used during the execution of Monte…
While stability analysis is a mainstay for control science, especially computing regions of attraction of equilibrium points, until recently most stability analysis tools always required explicit knowledge of the model or a high-fidelity…
Round-off errors arising from the difference between real numbers and their floating-point representation cause the control flow of conditional floating-point statements to deviate from the ideal flow of the real-number computation. This…
Nested error regression models are useful tools for analysis of grouped data, especially in the case of small area estimation. This paper suggests a nested error regression model using uncertain random effects in which the random effect in…
Enhancing the stability of machine learning algorithms under distributional shifts is at the heart of the Out-of-Distribution (OOD) Generalization problem. Derived from causal learning, recent works of invariant learning pursue strict…