2.5k citations · 10k across the 171 of their papers we have counts for
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Optimization of the Sherrington-Kirkpatrick Hamiltonian
Andrea Montanari
Let be a symmetric random matrix with independent and identically distributed Gaussian entries above the diagonal. We consider the probl…
Adapting to Unknown Noise Distribution in Matrix Denoising
Andrea Montanari, Feng Ruan, Jun Yan
We consider the problem of estimating an unknown matrix , from observations where $\bold…
The distribution of the Lasso: Uniform control over sparse balls and adaptive parameter tuning
Léo Miolane, Andrea Montanari
The Lasso is a popular regression method for high-dimensional problems in which the number of parameters , is larger than the number of samples: . A useful…
TAP free energy, spin glasses, and variational inference
Zhou Fan, Song Mei, Andrea Montanari
We consider the Sherrington-Kirkpatrick model of spin glasses with ferromagnetically biased couplings. For a specific choice of the couplings mean, the resulting Gibbs measure is e…
Contextual Stochastic Block Models
Yash Deshpande, Andrea Montanari, Elchanan Mossel +1
We provide the first information theoretic tight analysis for inference of latent community structure given a sparse graph along with high dimensional node covariates, correlated w…
The threshold for SDP-refutation of random regular NAE-3SAT
Yash Deshpande, Andrea Montanari, Ryan O'Donnell +2
Unlike its cousin 3SAT, the NAE-3SAT (not-all-equal-3SAT) problem has the property that spectral/SDP algorithms can efficiently refute random instances when the constraint density…
A Mean Field View of the Landscape of Two-Layers Neural Networks
Song Mei, Andrea Montanari, Phan-Minh Nguyen
Multi-layer neural networks are among the most powerful models in machine learning, yet the fundamental reasons for this success defy mathematical understanding. Learning a neural…
An Instability in Variational Inference for Topic Models
Behrooz Ghorbani, Hamid Javadi, Andrea Montanari
Topic models are Bayesian models that are frequently used to capture the latent structure of certain corpora of documents or images. Each data element in such a corpus (for instanc…
On the Connection Between Learning Two-Layers Neural Networks and Tensor Decomposition
Marco Mondelli, Andrea Montanari
We establish connections between the problem of learning a two-layer neural network and tensor decomposition. We consider a model with feature vectors $\boldsymbol x \in \mathbb R^…