arXiv research

Study on median algebra structures on Euclidean spaces and manifolds with local CAT(0) cubulation.

Convex cores found for group actions on median spaces.

We construct compactifications for median spaces with compact intervals, generalising Roller boundaries of ${\rm CAT}(0)$ cube complexes. Examples of median spaces with compact intervals include all finite rank median spaces and all proper median spaces of infinite rank. Our methods also work for general median algebra…

An extended Study of Dunwoody's Construction and Sageev's Theorem

New concept of coarse medians for higher rank symmetric spaces.

Unique median structures found in hyperbolic spaces.

We prove a version of the Tits alternative for groups acting on complete, finite rank median spaces. This shows that group actions on finite rank median spaces are much more restricted than actions on general median spaces. Along the way, we extend to median spaces the Caprace-Sageev machinery and part of Hagen's theor…

We show that uniform lattices of isometries of products of real hyperbolic spaces act properly discontinuously and cocompactly on a median space. For lattices in products of at least two factors, this is the strongest degree of compatibility possible with the median geometry. Our theorem is also relevant for potential …

We introduce and begin to explore the mean and median of finite sets of shapes represented as integral currents. The median can be computed efficiently in practice, and we focus most of our theoretical and computational attention on medians. We consider questions on the existence and regularity of medians. While the me…

This paper is a short summary of our recent work on the medians and means of probability measures in Riemannian manifolds. Firstly, the existence and uniqueness results of local medians are given. In order to compute medians in practical cases, we propose a subgradient algorithm and prove its convergence. After that, F…

A method for estimating the median of gradients in stochastic optimization.

This paper introduces online algorithms to estimate robust geometric median in large data streams.

The study finds that maximizing median returns is the only viable strategy in portfolio selection.

New graph properties inherited by Frechet mean and median.

The consistency of Fréchet medians is proved for probability measures in proper metric spaces. In the context of Riemannian manifolds, assuming that the probability measure has more than a half mass lying in a convex ball and verifies some concentration conditions, the positions of its Fréchet medians are estimated. It…

In high dimensions, the mean and geometric median are nearly identical.

New subspace prototype flag median improves clustering on noisy data.

Improved median of means estimator with tighter bounds.

Empirical median performs well in estimating location with varying scales.

This article is devoted to the problem of predicting the value taken by a random permutation $Σ$, describing the preferences of an individual over a set of numbered items $\{1,\; \ldots,\; n\}$ say, based on the observation of an input/explanatory r.v. $X$ e.g. characteristics of the individual), when error is measured…

New estimator for symmetric kernel expectations, robust to missing data.

Median-of-means sampling outperforms mean-of-means for large sample sizes in numerical integration.

Upper bound for Hausdorff distance between hyperbolic space and its medianization.

Paper proposes a novel method to improve matrix completion with median loss for large datasets.

Evolutionary algorithms (EAs) are a sort of nature-inspired metaheuristics, which have wide applications in various practical optimization problems. In these problems, objective evaluations are usually inaccurate, because noise is almost inevitable in real world, and it is a crucial issue to weaken the negative effect …

Marine buoys aid in the battle against Illegal, Unreported and Unregulated (IUU) fishing by detecting fishing vessels in their vicinity. Marine buoys, however, may be disrupted by natural causes and buoy vandalism. In this paper, we formulate marine buoy placement as a clustering problem, and propose dropout k-means an…

In kernel methods, the median heuristic has been widely used as a way of setting the bandwidth of RBF kernels. While its empirical performances make it a safe choice under many circumstances, there is little theoretical understanding of why this is the case. Our aim in this paper is to advance our understanding of the …

Study shows Roller compactification's median graph has limited asymptotic dimension.

Extends graph factor system to quasi-median graphs.

New method for estimating median and mean with high probability privacy.

A new depth measure and median defined on Hadamard manifolds.

Improved private geometric median estimation with nearly-linear time complexity.

Optimal benchmark design varies based on costs in financial manipulation.

New method explains survival analysis models using median-SHAP.

The paper studies automorphisms of RAAGs and RACGs, proving properties of their fixed subgroups.

We describe in this paper the theory and practice behind a new modal clustering method for binary data. Our approach (BinNNMS) is based on the nearest neighbor median shift. The median shift is an extension of the well-known mean shift, which was designed for continuous data, to handle binary data. We demonstrate that …

Study shows how certain spaces can be mapped to R^n with specific properties.

Paper proposes a robust method for federated ICA with geometric median aggregation.

Groups with specific properties have similar cubulations and coarse median structures.

We consider the non-parametric regression problem under Huber's $ε$-contamination model, in which an $ε$ fraction of observations are subject to arbitrary adversarial noise. We first show that a simple local binning median step can effectively remove the adversary noise and this median estimator is minimax optimal up t…

Characterizes ends and coends of graph pairs using quasi-median graphs.

Three privacy-preserving methods for median regression are proposed.

We prove that a hyperplane in a CAT(0) cubical complex X has no self-intersections and separates X into two convex complementary components. These facts were originally proved by Sageev. Our argument shows that his theorem is a corollary of Gromov's link condition. We also give new arguments establishing some combinato…

Sharp threshold found for Frechet mean of inhomogeneous graphs.

Paper shows how to use geometric median for robust SGD in high dimensions.

Finite rank median spaces are a simultaneous generalisation of finite dimensional ${\rm CAT}(0)$ cube complexes and real trees. If $Γ$ is an irreducible lattice in a product of rank one simple Lie groups, we show that every action of $Γ$ on a complete, finite rank median space has a global fixed point. This is in sharp…

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 are corrupted by sparse outliers that can take arbitrary values. We propose a nove…

We analyze the performance of the Tukey median estimator under total variation (TV) distance corruptions. Previous results show that under Huber's additive corruption model, the breakdown point is 1/3 for high-dimensional halfspace-symmetric distributions. We show that under TV corruptions, the breakdown point reduces …