Related papers: Lower Error Bounds for Randomized Multilevel and C…

Many application areas rely on models that can be readily simulated but lack a closed-form likelihood, or an accurate approximation under arbitrary parameter values. Existing parameter estimation approaches in this setting are generally…

This paper focuses on regularisation methods using models up to the third order to search for up to second-order critical points of a finite-sum minimisation problem. The variant presented belongs to the framework of [3]: it employs random…

There is a growing body of work on sorting and selection in models other than the unit-cost comparison model. This work is the first treatment of a natural stochastic variant of the problem where the cost of comparing two elements is a…

This paper proposes hybrid high-order eigensolvers for the computation of guaranteed lower eigenvalue bounds. These bounds display higher order convergence rates and are accessible to adaptive mesh-refining algorithms. The involved…

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…

We provide tools to help automate the error analysis of algorithms that evaluate simple functions over the floating-point numbers. The aim is to obtain tight relative error bounds for these algorithms, expressed as a function of the unit…

In applications with significant class imbalance or asymmetric costs, metrics such as the $F_\beta$-measure, AM measure, Jaccard similarity coefficient, and weighted accuracy offer more suitable evaluation criteria than standard binary…

Infinite-dimensional, holomorphic functions have been studied in detail over the last several decades, due to their relevance to parametric differential equations and computational uncertainty quantification. The approximation of such…

We develop a new theoretical framework to analyze the generalization error of deep learning, and derive a new fast learning rate for two representative algorithms: empirical risk minimization and Bayesian deep learning. The series of…

This paper considers the problem of matrix-variate logistic regression. It derives the fundamental error threshold on estimating low-rank coefficient matrices in the logistic regression problem by obtaining a lower bound on the minimax…

We present and analyze an algorithm designed for addressing vector-valued regression problems involving possibly infinite-dimensional input and output spaces. The algorithm is a randomized adaptation of reduced rank regression, a technique…

This paper extends algorithms that remove the fixed point bias of decentralized gradient descent to solve the more general problem of distributed optimization over subspace constraints. Leveraging the integral quadratic constraint…

This paper studies regret minimization with randomized value functions in reinforcement learning. In tabular finite-horizon Markov Decision Processes, we introduce a clipping variant of one classical Thompson Sampling (TS)-like algorithm,…

We consider derivative-free algorithms for stochastic and non-stochastic convex optimization problems that use only function values rather than gradients. Focusing on non-asymptotic bounds on convergence rates, we show that if pairs of…

Robust estimation is much more challenging in high dimensions than it is in one dimension: Most techniques either lead to intractable optimization problems or estimators that can tolerate only a tiny fraction of errors. Recent work in…

We contribute the first randomized algorithm that is an integration of arbitrarily many deterministic algorithms for the fully online multiprocessor scheduling with testing problem. When there are two machines, we show that with two…

We present a novel kernel-based machine learning algorithm for identifying the low-dimensional geometry of the effective dynamics of high-dimensional multiscale stochastic systems. Recently, the authors developed a mathematical framework…

In this article we present and analyse new multilevel adaptations of stochastic approximation algorithms for the computation of a zero of a function $f\colon D \to \mathbb R^d$ defined on a convex domain $D\subset \mathbb R^d$, which is…

We analyze an adaptive boundary element method for the weakly-singular and hypersingular integral equations for the 2D and 3D Helmholtz problem. The proposed adaptive algorithm is steered by a residual error estimator and does not rely on…

We consider derivatives written on multiple underlyings in a one-period financial market, and we are interested in the computation of model-free upper and lower bounds for their arbitrage-free prices. We work in a completely realistic…