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This work examines the Conditional Approval Framework for elections involving multiple interdependent issues, specifically focusing on the Conditional Minisum Approval Voting Rule. We first conduct a detailed analysis of the computational…

This paper studies the problem of control strategy synthesis for dynamical systems with differential constraints to fulfill a given reachability goal while satisfying a set of safety rules. Particular attention is devoted to goals that…

Statistical inference, a central tool of science, revolves around the study and the usage of statistical estimators: functions that map finite samples to predictions about unknown distribution parameters. In the frequentist framework,…

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…

The classical representation of random variables as the Ito integral of nonanticipative integrands is extended to include Banach space valued random variables on an abstract Wiener space equipped with a filtration induced by a resolution of…

Regularization is often used in high-dimensional regression settings to generate a sparse model, which can save tremendous computing resources and identify predictors that are most strongly associated with the response. When the predictors…

We consider a class of statistical inverse problems involving the estimation of a regression operator from a Polish space to a separable Hilbert space, where the target lies in a vector-valued reproducing kernel Hilbert space induced by an…

We consider a framework for the construction of iterative schemes for operator equations that combine low-rank approximation in tensor formats and adaptive approximation in a basis. Under fairly general assumptions, we obtain a rigorous…

Data-driven neural Koopman operator theory has emerged as a powerful tool for linearizing and controlling nonlinear robotic systems. However, the performance of these data-driven models fundamentally depends on the trade-off between sample…

Recent progress in deep latent variable models has largely been driven by the development of flexible and scalable variational inference methods. Variational training of this type involves maximizing a lower bound on the log-likelihood,…

Operator learning offers a powerful paradigm for solving parametric partial differential equations (PDEs), but scaling probabilistic neural operators such as the recently proposed Gaussian Processes Operators (GPOs) to high-dimensional,…

We study the foundations of variational inference, which frames posterior inference as an optimisation problem, for probabilistic programming. The dominant approach for optimisation in practice is stochastic gradient descent. In particular,…

Regularized estimators in the context of group variables have been applied successfully in model and feature selection in order to preserve interpretability. We formulate a Distributionally Robust Optimization (DRO) problem which recovers…

We study a class of dynamical systems modelled as Markov chains that admit an invariant distribution via the corresponding transfer, or Koopman, operator. While data-driven algorithms to reconstruct such operators are well known, their…

The authors study the spectral theory of self-adjoint operators that are subject to certain types of perturbations. An iterative introduction of infinitely many randomly coupled rank-one perturbations is one of our settings. Spectral…

In this paper, we focus on subspace-based learning problems, where data elements are linear subspaces instead of vectors. To handle this kind of data, Grassmann kernels were proposed to measure the space structure and used with classifiers,…

Modeling and inference with multivariate sequences is central in a number of signal processing applications such as acoustics, social network analysis, biomedical, and finance, to name a few. The linear-Gaussian state-space model is a…

Graph Neural Networks (GNNs) have established themselves as the leading models for learning on graph-structured data, generally categorized into spatial and spectral approaches. Central to these architectures is the Graph Shift Operator…

Neural operators (NOs) employ deep neural networks to learn mappings between infinite-dimensional function spaces. Deep operator network (DeepONet), a popular NO architecture, has demonstrated success in the real-time prediction of complex…

Many machine learning problems encode their data as a matrix with a possibly very large number of rows and columns. In several applications like neuroscience, image compression or deep reinforcement learning, the principal subspace of such…