The TAP free energy for high-dimensional linear regression
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Abstract (arXiv)
We derive a variational representation for the log-normalizing constant of the posterior distribution in Bayesian linear regression with a uniform spherical prior and an i.i.d. Gaussian design. We work under the "proportional" asymptotic regime, where the number of observations and the number of features grow at a proportional rate. This rigorously establishes the Thouless-Anderson-Palmer (TAP) approximation arising from spin glass theory, and proves a conjecture of Krzakala et. al. (2014) in the special case of the spherical prior.
Key facts. Cited by 3 papers in the map (data through 7 Oct 2026). Builds on 5 of its 34 references that are in the map. First posted on arXiv 14 Mar 2022.
Builds on
5 of 34 references.
References · 5
- 2016Variational Inference: A Review for Statisticianscited by 1,466
- 2017Optimal Errors and Phase Transitions in High-Dimensional Generalized Linear Modelscited by 115
- 2021Local convexity of the TAP free energy and AMP convergence for Z2-synchronizationcited by 15
- 2018An Instability in Variational Inference for Topic Modelscited by 11
- 2021Variational Inference in high-dimensional linear regressioncited by 10
Built on by
Citing papers per year: 2023: 2; 2024: 0; 2025: 0; 2026: 1.
3 papers.
- 2023High-dimensional scaling limits and fluctuations of online least-squares SGD with smooth covariancecited by 5
- 2023A Mean Field Approach to Empirical Bayes Estimation in High-dimensional Linear Regressioncited by 4
- 2026TAP Accuracy Below the Fluctuation Scale and Universal Posterior Geometry in Spherical Linear Modelscited by 0
- 2026TAP Accuracy Below the Fluctuation Scale and Universal Posterior Geometry in Spherical Linear Models17 Sep 2026
- 2023A Mean Field Approach to Empirical Bayes Estimation in High-dimensional Linear Regression28 Sep 2023
- 2023High-dimensional scaling limits and fluctuations of online least-squares SGD with smooth covariance3 Apr 2023