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Unsupervised registration strategies bypass requirements in ground truth transforms or segmentations by optimising similarity metrics between fixed and moved volumes. Among these methods, a recent subclass of approaches based on…

We start presenting an $L^{\infty}$-gradient bound for solutions to non-homogeneous $p$-Laplacean type systems and equations, via suitable non-linear potentials of the right hand side. Such a bound implies a Lorentz space characterization…

Lossy compression algorithms take advantage of the inherent limitations of the human eye and discard information that cannot be seen. In the present paper, a technique termed as Lossy Data Compression using Logarithm (LDCL) is proposed to…

Statistical inference based on lossy or incomplete samples is often needed in research areas such as signal/image processing, medical image storage, remote sensing, signal transmission. In this paper, we propose a nonparametric testing…

We present a general variational framework for the training of freeform nonlinearities in layered computational architectures subject to some slope constraints. The regularization that we add to the traditional training loss penalizes the…

This paper focuses on investigating an inexact stochastic model-based optimization algorithm that integrates preconditioning techniques for solving stochastic composite optimization problems. The proposed framework unifies and extends the…

Loss functions drive the optimization of machine learning algorithms. The choice of a loss function can have a significant impact on the training of a model, and how the model learns the data. Binary classification is one of the major…

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…

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…

We consider the problem of optimising the expected value of a loss functional over a nonlinear model class of functions, assuming that we have only access to realisations of the gradient of the loss. This is a classical task in statistics,…

We obtain Lipschitz estimates for bounded minimizers of functionals with nonstandard $(p,q)$-growth satisfying the dimension-independent restriction $q<p+2$ with $p \geq 2$. This relation improves existing restrictions when $p \leq N-1$,…

A nonparametric regression setting is considered with a real-valued covariate and responses from a metric space. One may approach this setting via Fr\'echet regression, where the value of the regression function at each point is estimated…

Binary embedding is a nonlinear dimension reduction methodology where high dimensional data are embedded into the Hamming cube while preserving the structure of the original space. Specifically, for an arbitrary $N$ distinct points in…

Regularization methods have been recently developed to construct stable approximate solutions to classical partial differential equations considered as final value problems. In this paper, we investigate the backward parabolic problem with…

Deep reinforcement learning excels in numerous large-scale practical applications. However, existing performance analyses ignores the unique characteristics of continuous-time control problems, is unable to directly estimate the…

This paper proposes a new algorithm based on multi-scale stochastic local search with binary representation for training neural networks. In particular, we study the effects of neighborhood evaluation strategies, the effect of the number of…

In this paper we prove global bounds on the spatial gradient of viscosity solutions to second order linear and nonlinear parabolic equations in $(0,T) \times \R^N$. Our assumptions include the case that the coefficients be both unbounded…

We introduce Lipschitz-Killing curvature (LKC) regression, a new method to produce $(1-\alpha)$ thresholds for signal detection in random fields that does not require knowledge of the spatial correlation structure. The idea is to fit…

We study adversarial online nonparametric regression with general convex losses and propose a parameter-free learning algorithm that achieves minimax optimal rates. Our approach leverages chaining trees to compete against H{\"o}lder…

We develop a minimax theory for operator learning, where the goal is to estimate an unknown operator between separable Hilbert spaces from finitely many noisy input-output samples. For uniformly bounded Lipschitz operators, we prove…