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The effectiveness of supervised learning techniques has made them ubiquitous in research and practice. In high-dimensional settings, supervised learning commonly relies on dimensionality reduction to improve performance and identify the…

The worst-case robust adaptive beamforming problem for general-rank signal model is considered. This is a nonconvex problem, and an approximate version of it (obtained by introducing a matrix decomposition on the presumed covariance matrix…

The effectiveness of dimensionality reduction with quadratic manifolds hinges on the choice of a reduced basis and the associated quadratic correction terms. Existing approaches typically rely on subspaces spanned by the leading principal…

The problem of high-dimensional and large-scale representation of visual data is addressed from an unsupervised learning perspective. The emphasis is put on discrete representations, where the description length can be measured in bits and…

Subspace preserving quantum circuits are a class of quantum algorithms that, relying on some symmetries in the computation, can offer theoretical guarantees for their training. Those algorithms have gained extensive interest as they can…

We address the problem of learning the parameters of a mean square stable switched linear systems (SLS) with unknown latent space dimension, or \textit{order}, from its noisy input--output data. In particular, we focus on learning a good…

This work presents a fast and non-convex algorithm for robust subspace recovery. The data sets considered include inliers drawn around a low-dimensional subspace of a higher dimensional ambient space, and a possibly large portion of…

We consider a distributionally robust formulation of stochastic optimization problems arising in statistical learning, where robustness is with respect to uncertainty in the underlying data distribution. Our formulation builds on…

Nonnegative Matrix Factorization (NMF) is a widely applied technique in the fields of machine learning and data mining. Graph Regularized Non-negative Matrix Factorization (GNMF) is an extension of NMF that incorporates graph regularization…

Many learning tasks, such as cross-validation, parameter search, or leave-one-out analysis, involve multiple instances of similar problems, each instance sharing a large part of learning data with the others. We introduce a robust framework…

Compressed Sensing refers to extracting a low-dimensional structured signal of interest from its incomplete random linear observations. A line of recent work has studied that, with the extra prior information about the signal, one can…

We consider the challenging problem of learning Signed Distance Functions (SDF) from sparse and noisy 3D point clouds. In contrast to recent methods that depend on smoothness priors, our method, rooted in a distributionally robust…

If learning methods are to scale to the massive sizes of modern datasets, it is essential for the field of machine learning to embrace parallel and distributed computing. Inspired by the recent development of matrix factorization methods…

We study the problem of estimating an unknown deterministic signal that is observed through an unknown deterministic data matrix under additive noise. In particular, we present a minimax optimization framework to the least squares problems,…

Locating a target is key in many applications, namely in high-stakes real-world scenarios, like detecting humans or obstacles in vehicular networks. In scenarios where precise statistics of the measurement noise are unavailable,…

Classical multidimensional scaling only works well when the noisy distances observed in a high dimensional space can be faithfully represented by Euclidean distances in a low dimensional space. Advanced models such as Maximum Variance…

We investigate the minimization of a quadratic function over Stiefel manifolds (the set of all orthogonal $r$- frames in $\mathbf{R}^n$), which has applications in high-dimensional semi-supervised classification tasks. To reduce the…

Supervised learning is all about the ability to generalize knowledge. Specifically, the goal of the learning is to train a classifier using training data, in such a way that it will be capable of classifying new unseen data correctly. In…

In structured output learning, obtaining labelled data for real-world applications is usually costly, while unlabelled examples are available in abundance. Semi-supervised structured classification has been developed to handle large amounts…

Certified robustness is a critical property for deploying neural networks (NN) in safety-critical applications. A principle approach to achieving such guarantees is to constrain the global Lipschitz constant of the network. However,…