Strong replica symmetry in high-dimensional optimal Bayesian inference
From MaRDI portal
Publication:2159230
DOI10.1007/s00220-022-04387-wzbMath1494.82020arXiv2005.03115OpenAlexW3021187121MaRDI QIDQ2159230
Jean Barbier, Dmitriy Panchenko
Publication date: 28 July 2022
Published in: Communications in Mathematical Physics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2005.03115
Bayesian inference (62F15) Signal theory (characterization, reconstruction, filtering, etc.) (94A12) Disordered systems (random Ising models, random Schrödinger operators, etc.) in equilibrium statistical mechanics (82B44)
Related Items
The TAP free energy for high-dimensional linear regression, Mutual information for the sparse stochastic block model
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Structure of finite-RSB asymptotic Gibbs measures in the diluted spin glass models
- Spin glass models from the point of view of spin distributions
- On the replica symmetric solution of the \(K\)-sat model
- Representations for partially exchangeable arrays of random variables
- The Sherrington-Kirkpatrick model: A challenge for mathematicians
- Information-theoretic thresholds from the cavity method
- Fundamental limits of symmetric low-rank matrix estimation
- Free energy in the Potts spin Glass
- Free energy in the mixed \(p\)-spin models with vector spins
- Charting the replica symmetric phase
- Bounds for diluted mean-fields spin glass models
- Optimality and sub-optimality of PCA. I: Spiked random matrix models
- On the stability of the quenched state in mean-field spin-glass models
- On the distribution of the largest eigenvalue in principal components analysis
- The thermodynamic limit in mean field spin glass models
- Replica bounds for optimization problems and diluted spin systems
- Broken replica symmetry bounds in the mean field spin glass model
- The replica-symmetric solution without replica trick for the Hopfield model
- The Parisi ultrametricity conjecture
- Absence of replica symmetry breaking in the random field Ising model
- Statistical limits of spiked tensor models
- Concentration of multi-overlaps for random dilute ferromagnetic spin models
- Phase transition in random tensors with multiple independent spikes
- Structure of 1-RSB asymptotic Gibbs measures in the diluted \(p\)-spin models
- A connection between the Ghirlanda-Guerra identities and ultrametricity
- The Ghirlanda-Guerra identities for mixed \(p\)-spin model
- On the structure of quasi-stationary competing particle systems
- The adaptive interpolation method: a simple scheme to prove replica formulas in Bayesian inference
- Phase transition in the spiked random tensor with Rademacher prior
- The Parisi formula for mixed \(p\)-spin models
- The Parisi formula
- Phase transition of the largest eigenvalue for nonnull complex sample covariance matrices
- Harnessing the Bethe free energy
- Modern Coding Theory
- Mutual Information and Minimum Mean-Square Error in Gaussian Channels
- Griffith–Kelly–Sherman Correlation Inequalities: A Useful Tool in the Theory of Error Correcting Codes
- Self-Averaging Identities for Random Spin Systems
- Information, Physics, and Computation
- General properties of overlap probability distributions in disordered spin systems. Towards Parisi ultrametricity
- Community Detection and Stochastic Block Models
- Statistical Physics of Spin Glasses and Information Processing
- The Sherrington-Kirkpatrick Model
- Spin glass polynomial identities from entropic constraints
- The Spiked Matrix Model With Generative Priors
- Sharp Bounds for Optimal Decoding of Low-Density Parity-Check Codes
- The replica symmetric phase of random constraint satisfaction problems
- The adaptive interpolation method for proving replica formulas. Applications to the Curie–Weiss and Wigner spike models
- Mutual Information and Optimality of Approximate Message-Passing in Random Linear Estimation
- Overlap matrix concentration in optimal Bayesian inference
- Optimal errors and phase transitions in high-dimensional generalized linear models
- Capacity-Achieving Sparse Superposition Codes via Approximate Message Passing Decoding
- Tight Bounds on the Capacity of Binary Input Random CDMA Systems
- Approximate Message-Passing Decoder and Capacity Achieving Sparse Superposition Codes
- Gibbs states and the set of solutions of random constraint satisfaction problems
- Replica bounds for diluted non-Poissonian spin systems
- Entropy and mutual information in models of deep neural networks*
- The committee machine: computational to statistical gaps in learning a two-layers neural network
- Mean Field Models for Spin Glasses
- The high temperature case for the random \(K\)-sat problem