Andrea Montanari

About

Andrea Montanari is the John D. and Sigrid Banks Professor of Statistics and Mathematics at Stanford University. He holds a joint appointment in the Department of Statistics and the Wu Tsai Neurosciences Institute. Montanari has been recognized with the appointment as the Robert and Barbara Kleist Professor in the School of Engineering, an honor endowed in 1997 to honor faculty members in information systems technology. His research interests include high-dimensional statistics, machine learning, and probability theory. Montanari's contributions are acknowledged through his appointment and recognition within the academic community, reflecting his significant role in advancing research in these areas.

Research topics

• Machine Learning
• Artificial Intelligence
• Computer Science
• Business
• Risk analysis (engineering)
• Engineering
• Physics
• Geometry
• Quantum mechanics
• Software engineering

Selected publications

• Surprises in high-dimensional ridgeless least squares interpolation

  The Annals of Statistics · 2022-04-01 · 493 citations

  articleOpen access

  Interpolators—estimators that achieve zero training error—have attracted growing attention in machine learning, mainly because state-of-the art neural networks appear to be models of this type. In this paper, we study minimum ℓ2 norm (“ridgeless”) interpolation least squares regression, focusing on the high-dimensional regime in which the number of unknown parameters p is of the same order as the number of samples n. We consider two different models for the feature distribution: a linear model,…

  PublisherOA PDFDOI

• Underspecification Presents Challenges for Credibility in Modern Machine Learning

  arXiv (Cornell University) · 2020 · 431 citations

  ML models often exhibit unexpectedly poor behavior when they are deployed in real-world domains. We identify underspecification as a key reason for these failures. An ML pipeline is underspecified when it can return many predictors with equivalently strong held-out performance in the training domain. Underspecification is common in modern ML pipelines, such as those based on deep learning. Predictors returned by underspecified pipelines are often treated as equivalent based on their training dom…

  DOI

• Optimization of mean-field spin glasses

  arXiv (Cornell University) · 2021 · 27 citations

  Mean-field spin glasses are families of random energy functions (Hamiltonians) on high-dimensional product spaces. In this paper, we consider the case of Ising mixed p-spin models,; namely, Hamiltonians HN:ΣN→R on the Hamming hypercube ΣN={±1}N, which are defined by the property that {HN(σ)}σ∈ΣN is a centered Gaussian process with covariance E{HN(σ1)HN(σ2)} depending only on the scalar product ⟨σ1,σ2⟩. The asymptotic value of the optimum maxσ∈ΣNHN(σ) was characterized in terms of a variational p…

• Equivalence of approximate message passing and low-degree polynomials in rank-one matrix estimation

  Probability Theory and Related Fields · 2024-10-14 · 10 citations

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• The generalization error of max-margin linear classifiers: Benign overfitting and high dimensional asymptotics in the overparametrized regime

  The Annals of Statistics · 2025-04-01 · 7 citations

  article1st authorCorresponding
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Recent grants

• CIF: Small: Learning and estimation with rough non-convex objectives: Fundamental limits and efficient algorithms

  NSF · $330k · 2020–2023

• The game dynamics of social interaction: Algorithms and applications

  NSF · $500k · 2009–2013

• CIF:Small:Information-theoretic and Computational Thresholds in Statistical Learning

  NSF · $450k · 2017–2021

Frequent coauthors

• Rüdiger Urbanke

  78 shared

• Adel Javanmard

  58 shared

• Sergio Caracciolo

  University of Milan

  48 shared

• Cyril Méasson

  Nokia (France)

  47 shared

• Andrea Pelissetto

  Istituto Nazionale di Fisica Nucleare, Roma Tor Vergata

  41 shared

• Marc Mézard

  Bocconi University

  37 shared

• Federico Ricci‐Tersenghi

  Istituto Nanoscienze

  35 shared

• Mei Song

  Beijing University of Posts and Telecommunications

  31 shared

Awards & honors

• John D. and Sigrid Banks Professor
• Robert and Barbara Kleist Professor in the School of Enginee…
• 2021 IMS Medallion Lecture

Similar researchers at Stanford University

• David Donohoh-119
• Emmanuel J. Candèsh-114
• Bradley Efronh-106