Related papers: Mean absolute deviations about the mean, the cut n…
A distance mean function measures the average distance of points from the elements of a given set of points (focal set) in the space. The level sets of a distance mean function are called generalized conics. In case of infinite focal points…
Mean absolute deviation function is used to explore the pattern and the distribution of the data graphically to enable analysts gaining greater understanding of raw data and to foster quick and a deep understanding of the data as an…
The positive discrepancy of a graph $G$ of edge density $p=e(G)/\binom{v(G)}{2}$ is defined as $$\mbox{disc}^{+}(G)=\max_{U\subset V(G)}e(G[U])-p\binom{|U|}{2}.$$ In 1993, Alon proved (using the equivalent terminology of minimum bisections)…
We show that the maximum expected inner product between a random vector and the standard normal vector over all couplings subject to a mutual information constraint or regularization is equivalent to a truncated integral involving the…
Consider a population of $N$ individuals, each having $d\geq 1$ different traits, and an additive measure, called dispersion, which rewards large pairwise separations between traits. The goal is to select $M\leq N$ individuals such that…
Motivated by the need for distributed learning and optimization algorithms with low communication cost, we study communication efficient algorithms for distributed mean estimation. Unlike previous works, we make no probabilistic assumptions…
This paper presents a class of new algorithms for distributed statistical estimation that exploit divide-and-conquer approach. We show that one of the key benefits of the divide-and-conquer strategy is robustness, an important…
It is well-known that trimmed sample means are robust against heavy tails and data contamination. This paper analyzes the performance of trimmed means and related methods in two novel contexts. The first one consists of estimating…
We consider the problem of estimating the mean of a random vector based on i.i.d. observations and adversarial contamination. We introduce a multivariate extension of the trimmed-mean estimator and show its optimal performance under minimal…
Robust estimation of location is a fundamental problem in statistics, particularly in scenarios where data contamination by outliers or model misspecification is a concern. In univariate settings, methods such as the sample median and…
Contrastive representation learning has been outstandingly successful in practice. In this work, we identify two key properties related to the contrastive loss: (1) alignment (closeness) of features from positive pairs, and (2) uniformity…
We propose a divide-and-conquer (DAC) algorithm for constrained convex optimization over networks, where the global objective is the sum of local objectives attached to individual agents. The algorithm is fully distributed: each iteration…
The median absolute deviation (MAD) is a popular robust measure of statistical dispersion. However, when it is applied to non-parametric distributions (especially multimodal, discrete, or heavy-tailed), lots of statistical inference issues…
The maximum mean discrepancy (MMD) is a kernel-based nonparametric statistic for two-sample testing, whose inferential accuracy depends critically on variance characterization. Existing work provides various finite-sample estimators of the…
We consider the problem of distributed mean estimation (DME), in which $n$ machines are each given a local $d$-dimensional vector $x_v \in \mathbb{R}^d$, and must cooperate to estimate the mean of their inputs $\mu = \frac 1n\sum_{v = 1}^n…
We study a counterfactual mean-variance optimization, where the mean and variance are defined as functionals of counterfactual distributions. The optimization problem defines the optimal resource allocation under various constraints in a…
Part I of this work [2] developed the exact diffusion algorithm to remove the bias that is characteristic of distributed solutions for deterministic optimization problems. The algorithm was shown to be applicable to a larger set of…
Consider a set of agents collaboratively solving a distributed convex optimization problem, asynchronously, under stringent communication constraints. In such situations, when an agent is activated and is allowed to communicate with only…
In this paper, we establish the convergence properties for a majorized alternating direction method of multipliers (ADMM) for linearly constrained convex optimization problems whose objectives contain coupled functions. Our convergence…
The main theme of this paper is error analysis for approximations derived from two variants of dimensional decomposition of a multivariate function: the referential dimensional decomposition (RDD) and analysis-of-variance dimensional…