Related papers: Regularized Loss Minimizers with Local Data Pertur…

Inverse problems are inherently ill-posed and therefore require regularization techniques to achieve a stable solution. While traditional variational methods have well-established theoretical foundations, recent advances in machine learning…

The ability to learn different tasks sequentially is essential to the development of artificial intelligence. In general, neural networks lack this capability, the major obstacle being catastrophic forgetting. It occurs when the…

Phase retrieval (PR) is a popular research topic in signal processing and machine learning. However, its performance degrades significantly when the measurements are corrupted by noise or outliers. To address this limitation, we propose a…

Machine unlearning offers a practical alternative to avoid full model re-training by approximately removing the influence of specific user data. While existing methods certify unlearning via statistical indistinguishability from re-trained…

Inverse problems arise in a variety of imaging applications including computed tomography, non-destructive testing, and remote sensing. The characteristic features of inverse problems are the non-uniqueness and instability of their…

From a numerical analysis perspective, assessing the robustness of l1-minimization is a fundamental issue in compressed sensing and sparse regularization. Yet, the recovery guarantees available in the literature usually depend on a priori…

We present a unified information-theoretic framework elucidating the interplay between stability, privacy, and the generalization performance of quantum learning algorithms. We establish a bound on the expected generalization error in terms…

We consider a general statistical learning problem where an unknown fraction of the training data is corrupted. We develop a robust learning method that only requires specifying an upper bound on the corrupted data fraction. The method…

The notion of replicable algorithms was introduced in Impagliazzo et al. [STOC '22] to describe randomized algorithms that are stable under the resampling of their inputs. More precisely, a replicable algorithm gives the same output with…

Neural networks have achieved remarkable success in many cognitive tasks. However, when they are trained sequentially on multiple tasks without access to old data, their performance on early tasks tend to drop significantly. This problem is…

Machine learning models have recently enjoyed a significant increase in size and popularity. However, this growth has created concerns about dataset privacy. To counteract data leakage, various privacy frameworks guarantee that the output…

Methods for the reduction of the complexity of computational problems are presented, as well as their connections to renormalization, scaling, and irreversible statistical mechanics. Several statistically stationary cases are analyzed; for…

We deal with the shape reconstruction of inclusions in elastic bodies. For solving this inverse problem in practice, data fitting functionals are used. Those work better than the rigorous monotonicity methods from [5], but have no…

The problem of sparse linear regression is relevant in the context of linear system identification from large datasets. When data are collected from real-world experiments, measurements are always affected by perturbations or low-precision…

Distribution shifts are problems where the distribution of data changes between training and testing, which can significantly degrade the performance of a model deployed in the real world. Recent studies suggest that one reason for the…

Algorithms increasingly operate within complex physical, social, and engineering systems where they are exposed to disturbances, noise, and interconnections with other dynamical systems. This article extends known convergence guarantees of…

Private machine learning involves addition of noise while training, resulting in lower accuracy. Intuitively, greater stability can imply greater privacy and improve this privacy-utility tradeoff. We study this role of stability in private…

We focus on the robustness of neural networks for classification. To permit a fair comparison between methods to achieve robustness, we first introduce a standard based on the mensuration of a classifier's degradation. Then, we propose…

We design and mathematically analyze sampling-based algorithms for regularized loss minimization problems that are implementable in popular computational models for large data, in which the access to the data is restricted in some way. Our…

Updating machine learning models with new information usually improves their predictive performance, yet, in many applications, it is also desirable to avoid changing the model predictions too much. This property is called stability. In…