Ery Arias-Castro

About

Ery Arias-Castro received his Ph.D. in Statistics from Stanford University in 2004. Following his doctoral studies, he held postdoctoral positions at the Institute for Pure and Applied Mathematics (IPAM), where he participated in the program on Multiscale Geometry and Analysis in High Dimensions, and at the Mathematical Sciences Research Institute (MSRI), where he engaged in the program on Mathematical, Computational and Statistical Aspects of Image Analysis. He joined the faculty of the Department of Mathematics at UCSD in 2005. His research interests encompass high-dimensional statistics, machine learning, spatial statistics, image processing, and applied probability.

Research topics

• Computer Science
• Mathematics
• Artificial Intelligence
• Statistics
• Mathematical analysis
• Combinatorics
• Data science
• Discrete mathematics
• Algorithm
• Theoretical computer science

Selected publications

• On the estimation of latent distances using graph distances

  Electronic Journal of Statistics · 2021 · 9 citations

  1st authorCorresponding

  We are given the adjacency matrix of a geometric graph and the task of recovering the latent positions. We study one of the most popular approaches which consists in using the graph distances and derive error bounds under various assumptions on the link function. In the simplest case where the link function is proportional to an indicator function, the bound matches an information lower bound that we derive.

  DOI

• Principles of Statistical Analysis

  2022 · 5 citations

  1st authorCorresponding

  This compact course is written for the mathematically literate reader who wants to learn to analyze data in a principled fashion. The language of mathematics enables clear exposition that can go quite deep, quite quickly, and naturally supports an axiomatic and inductive approach to data analysis. Starting with a good grounding in probability, the reader moves to statistical inference via topics of great practical importance – simulation and sampling, as well as experimental design and data coll…

  PublisherOA PDFDOI

• A unifying view of modal clustering

  Information and Inference A Journal of the IMA · 2022-12-01 · 4 citations

  article1st author

  Abstract Two important non-parametric approaches to clustering emerged in the 1970s: clustering by level sets or cluster tree as proposed by Hartigan, and clustering by gradient lines or gradient flow as proposed by Fukunaga and Hostetler. In a recent paper, we draw a connection between these two approaches, in particular, by showing that the gradient flow provides a way to move along the cluster tree. Here, we argue the case that these two approaches are fundamentally the same. We do so by prop…

  PublisherDOI

• Minimax estimation of distances on a surface and minimax manifold learning in the isometric-to-convex setting

  Information and Inference A Journal of the IMA · 2023-09-18 · 3 citations

  article1st authorCorresponding

  Abstract We start by considering the problem of estimating intrinsic distances on a smooth submanifold. We show that minimax optimality can be obtained via a reconstruction of the surface, and discuss the use of a particular mesh construction—the tangential Delaunay complex—for that purpose. We then turn to manifold learning and argue that a variant of Isomap where the distances are instead computed on a reconstructed surface is minimax optimal for the isometric variant of the problem.

  PublisherDOI

• Anomaly Detection for a Large Number of Streams: A Permutation-Based Higher Criticism Approach

  Journal of the American Statistical Association · 2022-09-22 · 3 citations

  articleOpen access

  Anomaly detection when observing a large number of data streams is essential in a variety of applications, ranging from epidemiological studies to monitoring of complex systems. High-dimensional scenarios are usually tackled with scan-statistics and related methods, requiring stringent modeling assumptions for proper calibration. In this work we take a nonparametric stance, and propose a permutation-based variant of the higher criticism statistic not requiring knowledge of the null distribution.…

  PublisherOA PDFDOI

Recent grants

• Stable and Robust Graph Embedding, and Related Problems

  NSF · $140k · 2019–2022

• Theory and practice of nonparametric detection

  NSF · $120k · 2006–2011

• ATD: Detection of Clusters in Spatial Data and Images

  NSF · $885k · 2012–2017

Frequent coauthors

• Emmanuel J. Candès

  37 shared

• Bruno Pelletier

  Institut de recherche mathématique de Rennes

  23 shared

• David L. Donoho

  Stanford University

  20 shared

• Nicolas Verzélen

  Mathématiques, Informatique et Statistique pour l'Environnement et l'Agronomie

  19 shared

• Gábor Lugosi

  17 shared

• Arnaud Durand

  Institut de Mathématiques de Jussieu-Paris Rive Gauche

  16 shared

• Xiaoming Huo

  15 shared

• Clément Berenfeld

  14 shared

Awards & honors

• Hellman Fellowship

Similar researchers at University of California, San Diego

• Natalia Komarovah-62
• David Meyerh-45
• Dimitris Politish-45