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pro vyhledávání: '"Montanari, Andrea"'
High-dimensional logistic regression with missing data: Imputation, regularization, and universality
We study high-dimensional, ridge-regularized logistic regression in a setting in which the covariates may be missing or corrupted by additive noise. When both the covariates and the additive corruptions are independent and normally distributed, we pr
Externí odkaz:
http://arxiv.org/abs/2410.01093
Empirically-determined scaling laws have been broadly successful in predicting the evolution of large machine learning models with training data and number of parameters. As a consequence, they have been useful for optimizing the allocation of limite
Externí odkaz:
http://arxiv.org/abs/2407.17954
Autor:
Montanari, Andrea, Wu, Yuchen
We consider the problem of sampling from the posterior distribution of a $d$-dimensional coefficient vector $\boldsymbol{\theta}$, given linear observations $\boldsymbol{y} = \boldsymbol{X}\boldsymbol{\theta}+\boldsymbol{\varepsilon}$. In general, su
Externí odkaz:
http://arxiv.org/abs/2406.19550
Autor:
Montanari, Andrea, Zhou, Kangjie
Given $d$-dimensional standard Gaussian vectors $\boldsymbol{x}_1,\dots, \boldsymbol{x}_n$, we consider the set of all empirical distributions of its $m$-dimensional projections, for $m$ a fixed constant. Diaconis and Freedman (1984) proved that, if
Externí odkaz:
http://arxiv.org/abs/2406.02970
Autor:
Montanari, Andrea, Subag, Eliran
We consider the problem of efficiently solving a system of $n$ non-linear equations in ${\mathbb R}^d$. Addressing Smale's 17th problem stated in 1998, we consider a setting whereby the $n$ equations are random homogeneous polynomials of arbitrary de
Externí odkaz:
http://arxiv.org/abs/2405.01735
We consider the problem of algorithmically sampling from the Gibbs measure of a mixed $p$-spin spherical spin glass. We give a polynomial-time algorithm that samples from the Gibbs measure up to vanishing total variation error, for any model whose mi
Externí odkaz:
http://arxiv.org/abs/2404.15651
Collecting large quantities of high-quality data can be prohibitively expensive or impractical, and a bottleneck in machine learning. One may instead augment a small set of $n$ data points from the target distribution with data from more accessible s
Externí odkaz:
http://arxiv.org/abs/2402.04376
Autor:
Montanari, Andrea
This is the text of my report presented at the 29th Solvay Conference on Physics on `The Structure and Dynamics of Disordered Systems' held in Bruxelles from October 19 to 21, 2023. I consider the problem of minimizing a random energy function $H(\si
Externí odkaz:
http://arxiv.org/abs/2401.11348
We consider Ising mixed $p$-spin glasses at high-temperature and without external field, and study the problem of sampling from the Gibbs distribution $\mu$ in polynomial time. We develop a new sampling algorithm with complexity of the same order as
Externí odkaz:
http://arxiv.org/abs/2310.08912