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Fully computable a posteriori error estimates in the energy norm are given for singularly perturbed semilinear reaction-diffusion equations posed in polygonal domains. Linear finite elements are considered on anisotropic triangulations. To…

Compositional data, representing proportions constrained to the simplex, arise in diverse fields such as geosciences, ecology, genomics, and microbiome research. Existing nonparametric density estimation methods often rely on…

Semi-supervised segmentation tackles the scarcity of annotations by leveraging unlabeled data with a small amount of labeled data. A prominent way to utilize the unlabeled data is by consistency training which commonly uses a…

Active learning (AL) has found wide applications in medical image segmentation, aiming to alleviate the annotation workload and enhance performance. Conventional uncertainty-based AL methods, such as entropy and Bayesian, often rely on an…

Lack of enough labeled data is a major problem in building machine learning based models when the manual annotation (labeling) is error-prone, expensive, tedious, and time-consuming. In this paper, we introduce an iterative deep learning…

We give the following characterization of rectifiable metric spaces. A metric space with positive lower Hausdorff density is rectifiable if and only if, for any subset $F$ and $f:F\to Y$, a Lipschitz map into a metric space with positive…

This work deals with the ill-posed inverse problem of reconstructing a function $f$ given implicitly as the solution of $g = Af$, where $A$ is a compact linear operator with unknown singular values and known eigenfunctions. We observe the…

Markov chain Monte Carlo samplers produce dependent streams of variates drawn from the limiting distribution of the Markov chain. With this as motivation, we introduce novel univariate kernel density estimators which are appropriate for the…

In microscopy image cell segmentation, it is common to train a deep neural network on source data, containing different types of microscopy images, and then fine-tune it using a support set comprising a few randomly selected and annotated…

This paper addresses the problem of data-driven model discrimination for unknown switched systems with unknown linear temporal logic (LTL) specifications, representing tasks, that govern their mode sequences, where only sampled data of the…

We present a new Bayesian methodology to learn the unknown material density of a given sample by inverting its two-dimensional images that are taken with a Scanning Electron Microscope. An image results from a sequence of projections of the…

A large portion of volumetric medical data, especially magnetic resonance imaging (MRI) data, is anisotropic, as the through-plane resolution is typically much lower than the in-plane resolution. Both 3D and purely 2D deep learning-based…

We consider the problem of deriving from experimental data an approximation of an unknown function, whose derivatives also approximate the unknown function derivatives. Solving this problem is useful, for instance, in the context of…

We propose a new approach to non-parametric density estimation that is based on regularizing a Sobolev norm of the density. This method is statistically consistent, and makes the inductive bias of the model clear and interpretable. While…

Combining information both within and between sample realizations, we propose a simple estimator for the local regularity of surfaces in the functional data framework. The independently generated surfaces are measured with errors at…

We show that DBSCAN can estimate the connected components of the $\lambda$-density level set $\{ x : f(x) \ge \lambda\}$ given $n$ i.i.d. samples from an unknown density $f$. We characterize the regularity of the level set boundaries using…

Spatial variables can be observed in many different forms, such as regularly sampled random fields (lattice data), point processes, and randomly sampled spatial processes. Joint analysis of such collections of observations is clearly…

We present a new approach to automate the spectroscopic redshift reliability assessment based on machine learning (ML) and characteristics of the redshift probability density function (PDF). We propose to rephrase the spectroscopic redshift…

We consider the problem of uncertainty estimation in the context of (non-Bayesian) deep neural classification. In this context, all known methods are based on extracting uncertainty signals from a trained network optimized to solve the…

Given an i.i.d. sample $X_1,...,X_n$ with common bounded density $f_0$ belonging to a Sobolev space of order $\alpha$ over the real line, estimation of the quadratic functional $\int_{\mathbb{R}}f_0^2(x) \mathrm{d}x$ is considered. It is…