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Meta-learning methods have shown an impressive ability to train models that rapidly learn new tasks. However, these methods only aim to perform well in expectation over tasks coming from some particular distribution that is typically…

For many machine learning algorithms such as $k$-Nearest Neighbor ($k$-NN) classifiers and $ k $-means clustering, often their success heavily depends on the metric used to calculate distances between different data points. An effective…

Nowadays, low-rank approximations of matrices are an important component of many methods in science and engineering. Traditionally, low-rank approximations are considered in unitary invariant norms, however, recently element-wise…

We study the approximate nearest neighbour method for cost-sensitive classification on low-dimensional manifolds embedded within a high-dimensional feature space. We determine the minimax learning rates for distributions on a smooth…

In this paper, we introduce a novel methodology for characterising the performance of deep learning networks (ResNets and DenseNet) with respect to training convergence and generalisation as a function of mini-batch size and learning rate…

A rich line of recent work has studied distributionally robust learning approaches that seek to learn a hypothesis that performs well, in the worst-case, on many different distributions over a population. We argue that although the most…

Learning of the cell-load in radio access networks (RANs) has to be performed within a short time period. Therefore, we propose a learning framework that is robust against uncertainties resulting from the need for learning based on a…

This paper shows a Min-Max property existing in the connection weights of the convolutional layers in a neural network structure, i.e., the LeNet. Specifically, the Min-Max property means that, during the back propagation-based training for…

We consider the problem of finite-time identification of linear dynamical systems from $T$ samples of a single trajectory. Recent results have predominantly focused on the setup where either no structural assumption is made on the system…

This paper uses techniques from Random Matrix Theory to find the ideal training-testing data split for a simple linear regression with m data points, each an independent n-dimensional multivariate Gaussian. It defines "ideal" as satisfying…

An inexact Newton type method for numerical minimization of convex piecewise quadratic functions is considered and its convergence is analyzed. Earlier, a similar method was successfully applied to optimizaton problems arising in numerical…

The first part of this paper is devoted to introducing an approach to compute the approximate minimum time function of control problems which is based on reachable set approximation and uses arithmetic operations for convex compact sets. In…

This paper considers an optimization problem for a dynamical system whose evolution depends on a collection of binary decision variables. We develop scalable approximation algorithms with provable suboptimality bounds to provide…

Motivated by establishing theoretical foundations for various manifold learning algorithms, we study the problem of Mahalanobis distance (MD), and the associated precision matrix, estimation from high-dimensional noisy data. By relying on…

The $\chi^2$-principle generalizes the Morozov discrepancy principle (MDP) to the augmented residual of the Tikhonov regularized least squares problem. Weighting of the data fidelity by a known Gaussian noise distribution on the measured…

Recent focus on robustness to adversarial attacks for deep neural networks produced a large variety of algorithms for training robust models. Most of the effective algorithms involve solving the min-max optimization problem for training…

Matrix rank minimization problems are gaining a plenty of recent attention in both mathematical and engineering fields. This class of problems, arising in various and across-discipline applications, is known to be NP-hard in general. In…

Finite difference schemes are here solved by means of a linear matrix equation. The theoretical study of the related algebraic system is exposed, and enables us to minimize the error due to a finite difference approximation, while building…

We study the problem of supervised learning a metric space under discriminative constraints. Given a universe $X$ and sets ${\cal S}, {\cal D}\subset {X \choose 2}$ of similar and dissimilar pairs, we seek to find a mapping $f:X\to Y$, into…

High-dimensional models often have a large memory footprint and must be quantized after training before being deployed on resource-constrained edge devices for inference tasks. In this work, we develop an information-theoretic framework for…