Related papers: Risk Bounds for Learning Multiple Components with …

Dictionary learning and component analysis models are fundamental for learning compact representations that are relevant to a given task (feature extraction, dimensionality reduction, denoising, etc.). The model complexity is encoded by…

We establish risk bounds for Regularized Empirical Risk Minimizers (RERM) when the loss is Lipschitz and convex and the regularization function is a norm. In a first part, we obtain these results in the i.i.d. setup under subgaussian…

Beside the minimization of the prediction error, two of the most desirable properties of a regression scheme are stability and interpretability. Driven by these principles, we propose continuous-domain formulations for one-dimensional…

Clustering algorithms have significantly improved along with Deep Neural Networks which provide effective representation of data. Existing methods are built upon deep autoencoder and self-training process that leverages the distribution of…

We study the sample complexity of the best-case Empirical Risk Minimizer in the setting of stochastic convex optimization. We show that there exists an instance in which the sample size is linear in the dimension, learning is possible, but…

This paper examines the problem of learning with a finite and possibly large set of p base kernels. It presents a theoretical and empirical analysis of an approach addressing this problem based on ensembles of kernel predictors. This…

Machine learning techniques for the solution of inverse problems have become an attractive approach in the last decade, while their theoretical foundations are still in their infancy. In this chapter we want to pursue the study of…

Vector-valued learning, where the output space admits a vector-valued structure, is an important problem that covers a broad family of important domains, e.g. multi-task learning and transfer learning. Using local Rademacher complexity and…

For various applications, the relations between the dependent and independent variables are highly nonlinear. Consequently, for large scale complex problems, neural networks and regression trees are commonly preferred over linear models…

The dramatic increase of autonomous systems subject to variable environments has given rise to the pressing need to consider risk in both the synthesis and verification of policies for these systems. This paper aims to address a few…

During the inversion of discrete linear systems noise in data can be amplified and result in meaningless solutions. To combat this effect, characteristics of solutions that are considered desirable are mathematically implemented during…

This paper introduces an abstract framework for randomized subspace correction methods for convex optimization, which unifies and generalizes a broad class of existing algorithms, including domain decomposition, multigrid, and block…

While many approaches exist in the literature to learn low-dimensional representations for data collections in multiple modalities, the generalizability of multi-modal nonlinear embeddings to previously unseen data is a rather overlooked…

We construct data dependent bounds on the risk in function learning problems. The bounds are based on the local norms of the Rademacher process indexed by the underlying function class and they do not require prior knowledge about the…

Convex relaxations are effective for training and certifying neural networks against norm-bounded adversarial attacks, but they leave a large gap between certifiable and empirical robustness. In principle, convex relaxation can provide…

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…

Constrained coding plays a key role in optimizing performance and mitigating errors in applications such as storage and communication, where specific constraints on codewords are required. While non-parametric constraints have been…

Regularized linear regression is central to machine learning, yet its high-dimensional behavior with informative priors remains poorly understood. We provide the first exact asymptotic characterization of training and test risks for maximum…

Despite existing work on ensuring generalization of neural networks in terms of scale sensitive complexity measures, such as norms, margin and sharpness, these complexity measures do not offer an explanation of why neural networks…

Recently, contrastive learning has found impressive success in advancing the state of the art in solving various machine learning tasks. However, the existing generalization analysis is very limited or even not meaningful. In particular,…