Related papers: Geometric median and robust estimation in Banach s…

In this paper, two generalized algorithms for solving the variational inequality problem in Banach spaces are proposed. Then the strong convergence of the sequences generated by these algorithms will be proved under the suitable conditions.…

This paper will focus on three different aspects in improving the current practice of stable random projections. Firstly, we propose {\em very sparse stable random projections} to significantly reduce the processing and storage cost, by…

Creating geometric abstracted models from image-based scene reconstructions is difficult due to noise and irregularities in the reconstructed model. In this paper, we present a geometric modeling method for noisy reconstructions dominated…

Wasserstein distributionally robust optimization estimators are obtained as solutions of min-max problems in which the statistician selects a parameter minimizing the worst-case loss among all probability models within a certain distance…

This tutorial provides an exposition of a flexible geometric framework for high dimensional estimation problems with constraints. The tutorial develops geometric intuition about high dimensional sets, justifies it with some results of…

Robust statistics traditionally focuses on outliers, or perturbations in total variation distance. However, a dataset could be corrupted in many other ways, such as systematic measurement errors and missing covariates. We generalize the…

To accomplish correct Bayesian inference from weak lensing shear data requires a complete statistical description of the data. The natural framework to do this is a Bayesian Hierarchical Model, which divides the chain of reasoning into…

A recursive estimator of the conditional geometric median in Hilbert spaces is studied. It is based on a stochastic gradient algorithm whose aim is to minimize a weighted L1 criterion and is consequently well adapted for robust online…

We observe a $n$-sample, the distribution of which is assumed to belong, or at least to be close enough, to a given mixture model. We propose an estimator of this distribution that belongs to our model and possesses some robustness…

We address the issue of binary classification in Banach spaces in presence of uncertainty. We show that a number of results from classical support vector machines theory can be appropriately generalised to their robust counterpart in Banach…

In recent years, Generative Adversarial Networks (GANs) have shown substantial progress in modeling complex distributions of data. These networks have received tremendous attention since they can generate implicit probabilistic models that…

We propose a novel approach to Bayesian analysis that is provably robust to outliers in the data and often has computational advantages over standard methods. Our technique is based on splitting the data into non-overlapping subgroups,…

We present a Bayesian inference approach to estimating the cumulative mass profile and mean squared velocity profile of a globular cluster given the spatial and kinematic information of its stars. Mock globular clusters with a range of…

In these notes, we study nonlinear embeddings between Banach spaces which are also weakly sequentially continuous. In particular, our main result implies that if a Banach space $X$ coarsely (resp. uniformly) embeds into a Banach space $Y$…

Given a compact subset of a Banach space, the Chebyshev center problem consists of finding a minimal circumscribing ball containing the set. In this article we establish a numerically tractable algorithm for solving the Chebyshev center…

Geodesic contraction in vector-valued differential equations is readily verified by linearized operators which are uniformly negative-definite in the Riemannian metric. In the infinite-dimensional setting, however, such analysis is…

We study high-dimensional mean estimation in a collaborative setting where data is contributed by $N$ users in batches of size $n$. In this environment, a learner seeks to recover the mean $\mu$ of a true distribution $P$ from a collection…

This paper investigates the phase retrieval problem, which aims to recover a signal from the magnitudes of its linear measurements. We develop statistically and computationally efficient algorithms for the situation when the measurements…

In this paper, we study the coarse embedding into Banach space. We proved that under certain conditions, the property of embedding into Banach space can be preserved under taking the union the metric spaces. For a group $G$ strongly…

We extend and improve the work of Model Agnostic Anchors for explanations on image classification through the use of generative adversarial networks (GANs). Using GANs, we generate samples from a more realistic perturbation distribution, by…