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This work deals with the stability analysis of nonlinear sampled-data systems under nonuniform sampling. It establishes novel relationships between the stability property of the exact discrete-time model for a given sequence of (aperiodic)…
There is an emerging interest in generating robust counterfactual explanations that would remain valid if the model is updated or changed even slightly. Towards finding robust counterfactuals, existing literature often assumes that the…
Conditional stability estimates allow us to characterize the degree of ill-posedness of many inverse problems, but without further assumptions they are not sufficient for the stable solution in the presence of data perturbations. We here…
Estimation of the degree of stability and the bounds of solutions to non-autonomous nonlinear systems present major concerns in numerous applied problems. Yet, current techniques are frequently yield overconservative conditions which are…
We introduce \emph{Information Topology}: a framework that unifies information theory and algebraic topology by treating \emph{cycle closure} as the primitive operation of inference. The starting point is the \emph{dot-cycle dichotomy},…
We establish generalization error bounds for stochastic gradient Langevin dynamics (SGLD) with constant learning rate under the assumptions of dissipativity and smoothness, a setting that has received increased attention in the…
Common information (CI) is ubiquitous in information theory and related areas such as theoretical computer science and discrete probability. However, because there are multiple notions of CI, a unified understanding of the deep…
Symmetries are known to improve the empirical performance of machine learning models, yet theoretical guarantees explaining these gains remain limited. Prior work has focused mainly on compact group symmetries and often assumes that the…
We establish stability inequalities for the problem of determining the potential, appearing in a Sch\"odinger equation, from partial boundary data in the high frequency limit. These stability inequalities hold under the assumption that the…
Estimation of solution norms and stability for time-dependent nonlinear systems is ubiquitous in numerous engineering, natural science and control problems. Yet, practically valuable results are rare in this area. This paper develops a…
Algorithmic stability is a classical approach to understanding and analysis of the generalization error of learning algorithms. A notable weakness of most stability-based generalization bounds is that they hold only in expectation.…
We introduce a new low-noise condition for classification, the Model Margin Noise (MM noise) assumption, and derive enhanced $\mathcal{H}$-consistency bounds under this condition. MM noise is weaker than Tsybakov noise condition: it is…
We study distribution-free predictive inference for data with group symmetries, aiming to establish near-conditional coverage guarantees beyond exchangeability for structured data. While many predictive inference methods achieve a target…
The standard quadratic optimization problem (StQP) consists of minimizing a quadratic form over the standard simplex. Without convexity or concavity of the quadratic form, the StQP is NP-hard. This problem has many relevant real-life…
Recently, generalization bounds of the non-convex empirical risk minimization paradigm using Stochastic Gradient Langevin Dynamics (SGLD) have been extensively studied. Several theoretical frameworks have been presented to study this…
Push-Sum-based decentralized learning enables optimization over directed communication networks, where information exchange may be asymmetric. While convergence properties of such methods are well understood, their finite-iteration…
In context-specific applications such as robotics, telecommunications, and healthcare, artificial intelligence systems often face the challenge of limited training data. This scarcity introduces epistemic uncertainty, i.e., reducible…
In the presence of sample selection, Lee's (2009) nonparametric bounds are a popular tool for estimating a treatment effect. However, the Lee bounds rely on the monotonicity assumption, whose empirical validity is sometimes unclear.…
In this paper, we provide new theoretical results on the generalization properties of learning algorithms for multiclass classification problems. The originality of our work is that we propose to use the confusion matrix of a classifier as…
We introduce a new notion of the stability of computations, which holds under post-processing and adaptive composition. We show that the notion is both necessary and sufficient to ensure generalization in the face of adaptivity, for any…