The adaptive interpolation method: a simple scheme to prove replica formulas in Bayesian inference
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Publication:2312689
DOI10.1007/s00440-018-0879-0zbMath1478.60253arXiv1705.02780OpenAlexW2963765569WikidataQ129035488 ScholiaQ129035488MaRDI QIDQ2312689
Publication date: 17 July 2019
Published in: Probability Theory and Related Fields (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1705.02780
Estimation in multivariate analysis (62H12) Bayesian inference (62F15) Interacting random processes; statistical mechanics type models; percolation theory (60K35) Statistical mechanics of random media, disordered materials (including liquid crystals and spin glasses) (82D30)
Related Items (31)
The adaptive interpolation method for proving replica formulas. Applications to the Curie–Weiss and Wigner spike models ⋮ Hamilton-Jacobi equations for inference of matrix tensor products ⋮ Strong replica symmetry in high-dimensional optimal Bayesian inference ⋮ Information theoretic limits of learning a sparse rule ⋮ Statistical thresholds for tensor PCA ⋮ Hamilton-Jacobi equations for finite-rank matrix inference ⋮ Remarks on the interpolation method ⋮ Replica symmetry breaking in dense Hebbian neural networks ⋮ Thermodynamics of bidirectional associative memories ⋮ Hopfield model with planted patterns: a teacher-student self-supervised learning model ⋮ Minimax formula for the replica symmetric free energy of deep restricted Boltzmann machines ⋮ The TAP free energy for high-dimensional linear regression ⋮ Concentration of multi-overlaps for random dilute ferromagnetic spin models ⋮ A Friendly Tutorial on Mean-Field Spin Glass Techniques for Non-Physicists ⋮ Mutual information for the sparse stochastic block model ⋮ Free energy of multi-layer generalized linear models ⋮ Statistical inference of finite-rank tensors ⋮ The decimation scheme for symmetric matrix factorization ⋮ TAP free energy, spin glasses and variational inference ⋮ The solution of the deep Boltzmann machine on the Nishimori line ⋮ Phase transition in random tensors with multiple independent spikes ⋮ Spin systems on Bethe lattices ⋮ Hamilton-Jacobi equations for mean-field disordered systems ⋮ Phase transition in the spiked random tensor with Rademacher prior ⋮ Hamilton-Jacobi equations for nonsymmetric matrix inference ⋮ Marginals of a spherical spin Glass model with correlated disorder ⋮ Entropy and mutual information in models of deep neural networks* ⋮ The committee machine: computational to statistical gaps in learning a two-layers neural network ⋮ LASSO risk and phase transition under dependence ⋮ Replica analysis of overfitting in generalized linear regression models ⋮ Replica symmetry breaking in neural networks: a few steps toward rigorous results
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