arXiv research

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…

Three privacy-preserving methods for median regression are proposed.

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…

A new method for fast and robust sparsity learning over networks.

DiPriMe forests use private medians to create balanced tree splits for privacy-protected data.

A regularized risk minimization procedure for regression function estimation is introduced that achieves near optimal accuracy and confidence under general conditions, including heavy-tailed predictor and response variables. The procedure is based on median-of-means tournaments, introduced by the authors in [8]. It is …

A main goal of regression is to derive statistical conclusions on the conditional distribution of the output variable Y given the input values x. Two of the most important characteristics of a single distribution are location and scale. Support vector machines (SVMs) are well established to estimate location functions …

New method improves mean estimation for heavy-tailed data.

Study robust linear regression without distributional assumptions for heavy-tailed responses.

Optimal multitask learning method for sparse heterogeneous datasets.

New method certifies regression robustness without data distribution assumptions.

Quantile regression improves urban water demand forecasting.

We show how to reduce the process of predicting general order statistics (and the median in particular) to solving classification. The accompanying theoretical statement shows that the regret of the classifier bounds the regret of the quantile regression under a quantile loss. We also test this reduction empirically ag…

This paper extends Median-of-Means to new learning problems involving pairwise comparisons.

We survey some of the recent advances in mean estimation and regression function estimation. In particular, we describe sub-Gaussian mean estimators for possibly heavy-tailed data both in the univariate and multivariate settings. We focus on estimators based on median-of-means techniques but other methods such as the t…

We develop a unified approach for classification and regression support vector machines for data subject to right censoring. We provide finite sample bounds on the generalization error of the algorithm, prove risk consistency for a wide class of probability measures, and study the associated learning rates. We apply th…

For massive data sets, efficient computation commonly relies on distributed algorithms that store and process subsets of the data on different machines, minimizing communication costs. Our focus is on regression and classification problems involving many features. A variety of distributed algorithms have been proposed …

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…

New method speeds up NIR spectroscopy calibration by 400x.

New method for neural networks to predict histogram data.

New concept of coarse medians for higher rank symmetric spaces.

Unique median structures found in hyperbolic spaces.

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

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 …

R2T hybrid model improves robust regression for asymmetric noise.

Convex cores found for group actions on median spaces.

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…

Private statistical inference methods improve confidence interval lengths.

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.

Tukey median performance analyzed under TV corruptions.

Consider a regression problem where there is no labeled data and the only observations are the predictions $f_i(x_j)$ of $m$ experts $f_{i}$ over many samples $x_j$. With no knowledge on the accuracy of the experts, is it still possible to accurately estimate the unknown responses $y_{j}$? Can one still detect the leas…

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…

New robust regression method works with fewer data points than previous methods.

New subspace prototype flag median improves clustering on noisy data.

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

Improved median of means estimator with tighter bounds.

In this paper, we consider the problem of linear regression with heavy-tailed distributions. Different from previous studies that use the squared loss to measure the performance, we choose the absolute loss, which is capable of estimating the conditional median. To address the challenge that both the input and output c…

Empirical median performs well in estimating location with varying scales.

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

Paper develops a new algorithm for sparse signal recovery.

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.