Andrea Montanari

research

∙ 08/25/2023

Six Lectures on Linearized Neural Networks

In these six lectures, we examine what can be learnt about the behavior ...

0 Theodor Misiakiewicz, et al. ∙

research

∙ 05/18/2023

Sampling, Diffusions, and Stochastic Localization

Diffusions are a successful technique to sample from high-dimensional di...

0 Andrea Montanari, et al. ∙

research

∙ 04/22/2023

Posterior Sampling from the Spiked Models via Diffusion Processes

Sampling from the posterior is a key technical problem in Bayesian stati...

0 Andrea Montanari, et al. ∙

research

∙ 02/28/2023

Learning time-scales in two-layers neural networks

Gradient-based learning in multi-layer neural networks displays a number...

0 Raphaël Berthier, et al. ∙

research

∙ 02/20/2023

Compressing Tabular Data via Latent Variable Estimation

Data used for analytics and machine learning often take the form of tabl...

0 Andrea Montanari, et al. ∙

research

∙ 12/14/2022

Equivalence of Approximate Message Passing and Low-Degree Polynomials in Rank-One Matrix Estimation

We consider the problem of estimating an unknown parameter vector θ∈ℝ^n,...

0 Andrea Montanari, et al. ∙

research

∙ 11/01/2022

Fundamental Limits of Low-Rank Matrix Estimation with Diverging Aspect Ratios

We consider the problem of estimating the factors of a low-rank n × d ma...

0 Andrea Montanari, et al. ∙

research

∙ 10/16/2022

Dimension free ridge regression

Random matrix theory has become a widely useful tool in high-dimensional...

0 Chen Cheng, et al. ∙

research

∙ 06/14/2022

Overparametrized linear dimensionality reductions: From projection pursuit to two-layer neural networks

Given a cloud of n data points in ℝ^d, consider all projections onto m-d...

0 Andrea Montanari, et al. ∙

research

∙ 04/06/2022

A Short Tutorial on Mean-Field Spin Glass Techniques for Non-Physicists

This tutorial is based on lecture notes written for a class taught in th...

0 Andrea Montanari, et al. ∙

research

∙ 03/31/2022

Adversarial Examples in Random Neural Networks with General Activations

A substantial body of empirical work documents the lack of robustness in...

0 Andrea Montanari, et al. ∙

research

∙ 03/10/2022

Sampling from the Sherrington-Kirkpatrick Gibbs measure via algorithmic stochastic localization

We consider the Sherrington-Kirkpatrick model of spin glasses at high-te...

0 Ahmed El Alaoui, et al. ∙

research

∙ 02/17/2022

Universality of empirical risk minimization

Consider supervised learning from i.i.d. samples { x_i,y_i}_i≤ n where x...

0 Andrea Montanari, et al. ∙

research

∙ 01/13/2022

Statistically Optimal First Order Algorithms: A Proof via Orthogonalization

We consider a class of statistical estimation problems in which we are g...

0 Andrea Montanari, et al. ∙

research

∙ 12/14/2021

The high-dimensional asymptotics of first order methods with random data

We study a class of deterministic flows in ℝ^d× k, parametrized by a ran...

0 Michael Celentano, et al. ∙

research

∙ 11/12/2021

Local algorithms for Maximum Cut and Minimum Bisection on locally treelike regular graphs of large degree

Given a graph G of degree k over n vertices, we consider the problem of ...

0 Ahmed El Alaoui, et al. ∙

research

∙ 10/28/2021

Tractability from overparametrization: The example of the negative perceptron

In the negative perceptron problem we are given n data points ( x_i,y_i)...

0 Andrea Montanari, et al. ∙

research

∙ 09/02/2021

An Information-Theoretic View of Stochastic Localization

Given a probability measure μ over ℝ^n, it is often useful to approximat...

0 Ahmed El Alaoui, et al. ∙

research

∙ 07/29/2021

CAD: Debiasing the Lasso with inaccurate covariate model

We consider the problem of estimating a low-dimensional parameter in hig...

0 Michael Celentano, et al. ∙

research

∙ 06/09/2021

Streaming Belief Propagation for Community Detection

The community detection problem requires to cluster the nodes of a netwo...

0 Yuchen Wu, et al. ∙

research

∙ 03/30/2021

Minimum complexity interpolation in random features models

Despite their many appealing properties, kernel methods are heavily affe...

0 Michael Celentano, et al. ∙

research

∙ 03/16/2021

Deep learning: a statistical viewpoint

The remarkable practical success of deep learning has revealed some majo...

13 Peter L. Bartlett, et al. ∙

research

∙ 02/25/2021

Learning with invariances in random features and kernel models

A number of machine learning tasks entail a high degree of invariance: t...

0 Song Mei, et al. ∙

research

∙ 01/26/2021

Generalization error of random features and kernel methods: hypercontractivity and kernel matrix concentration

Consider the classical supervised learning problem: we are given data (y...

0 Song Mei, et al. ∙

research

∙ 11/06/2020

Underspecification Presents Challenges for Credibility in Modern Machine Learning

ML models often exhibit unexpectedly poor behavior when they are deploye...

30 Alexander D'Amour, et al. ∙

research

∙ 07/27/2020

The Lasso with general Gaussian designs with applications to hypothesis testing

The Lasso is a method for high-dimensional regression, which is now comm...

15 Michael Celentano, et al. ∙

research

∙ 07/25/2020

The Interpolation Phase Transition in Neural Networks: Memorization and Generalization under Lazy Training

Modern neural networks are often operated in a strongly overparametrized...

0 Andrea Montanari, et al. ∙

research

∙ 06/24/2020

When Do Neural Networks Outperform Kernel Methods?

For a certain scaling of the initialization of stochastic gradient desce...

93 Behrooz Ghorbani, et al. ∙

research

∙ 02/28/2020

The estimation error of general first order methods

Modern large-scale statistical models require to estimate thousands to m...

11 Michael Celentano, et al. ∙

research

∙ 01/24/2020

Imputation for High-Dimensional Linear Regression

We study high-dimensional regression with missing entries in the covaria...

0 Kabir Aladin Chandrasekher, et al. ∙

research

∙ 11/05/2019

The generalization error of max-margin linear classifiers: High-dimensional asymptotics in the overparametrized regime

Modern machine learning models are often so complex that they achieve va...

34 Andrea Montanari, et al. ∙

research

∙ 08/14/2019

The generalization error of random features regression: Precise asymptotics and double descent curve

Deep learning methods operate in regimes that defy the traditional stati...

1 Song Mei, et al. ∙

research

∙ 06/21/2019

Limitations of Lazy Training of Two-layers Neural Networks

We study the supervised learning problem under either of the following t...

0 Behrooz Ghorbani, et al. ∙

research

∙ 04/27/2019

Linearized two-layers neural networks in high dimension

We consider the problem of learning an unknown function f_ on the d-dime...

0 Behrooz Ghorbani, et al. ∙

research

∙ 04/05/2019

On the computational tractability of statistical estimation on amenable graphs

We consider the problem of estimating a vector of discrete variables (θ_...

0 Ahmed El Alaoui, et al. ∙

research

∙ 03/25/2019

Fundamental Barriers to High-Dimensional Regression with Convex Penalties

In high-dimensional regression, we attempt to estimate a parameter vecto...

0 Michael Celentano, et al. ∙

research

∙ 03/19/2019

Surprises in High-Dimensional Ridgeless Least Squares Interpolation

Interpolators -- estimators that achieve zero training error -- have att...

0 Trevor Hastie, et al. ∙

research

∙ 02/16/2019

Mean-field theory of two-layers neural networks: dimension-free bounds and kernel limit

We consider learning two layer neural networks using stochastic gradient...

0 Song Mei, et al. ∙

research

∙ 01/05/2019

Analysis of a Two-Layer Neural Network via Displacement Convexity

Fitting a function by using linear combinations of a large number N of `...

0 Adel Javanmard, et al. ∙

research

∙ 11/03/2018

The distribution of the Lasso: Uniform control over sparse balls and adaptive parameter tuning

The Lasso is a popular regression method for high-dimensional problems i...

0 Léo Miolane, et al. ∙

research

∙ 10/06/2018

Adapting to Unknown Noise Distribution in Matrix Denoising

We consider the problem of estimating an unknown matrix ∈^m× n, from obs...

0 Andrea Montanari, et al. ∙

research

∙ 08/23/2018

TAP free energy, spin glasses, and variational inference

We consider the Sherrington-Kirkpatrick model of spin glasses with ferro...

0 Zhou Fan, et al. ∙

research

∙ 07/23/2018

Contextual Stochastic Block Models

We provide the first information theoretic tight analysis for inference ...

0 Yash Deshpande, et al. ∙

research

∙ 04/18/2018

A Mean Field View of the Landscape of Two-Layers Neural Networks

Multi-layer neural networks are among the most powerful models in machin...

0 Song Mei, et al. ∙

research

∙ 04/14/2018

The threshold for SDP-refutation of random regular NAE-3SAT

Unlike its cousin 3SAT, the NAE-3SAT (not-all-equal-3SAT) problem has th...

0 Yash Deshpande, et al. ∙

research

∙ 02/20/2018

On the Connection Between Learning Two-Layers Neural Networks and Tensor Decomposition

We establish connections between the problem of learning a two-layers ne...

0 Marco Mondelli, et al. ∙

research

∙ 02/02/2018

An Instability in Variational Inference for Topic Models

Topic models are Bayesian models that are frequently used to capture the...

0 Behrooz Ghorbani, et al. ∙

research

∙ 11/15/2017

The landscape of the spiked tensor model

We consider the problem of estimating a large rank-one tensor u^⊗ k∈( R...

0 Gérard Ben Arous, et al. ∙

research

∙ 11/06/2017

Estimation of Low-Rank Matrices via Approximate Message Passing

Consider the problem of estimating a low-rank symmetric matrix when its ...

0 Andrea Montanari, et al. ∙

research

∙ 09/19/2017

Inference in Graphical Models via Semidefinite Programming Hierarchies

Maximum A posteriori Probability (MAP) inference in graphical models amo...

0 Murat A. Erdogdu, et al. ∙

Andrea Montanari

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