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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.
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[author] Barbier, JeanJ. and Macris, NicolasN. (2019). The adaptive interpolation method: a simple scheme to prove replica formulas in Bayesian inference. Probability theory and related fields 174 1133–1185
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[author] Chen, Wei-KuoW.-K. and Panchenko, DmitryD. (2018). On the TAP free energy in the mixed p-spin models. Communications in Mathematical Physics 362 219–252
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[author] Barbier, JeanJ., Krzakala, FlorentF., Macris, NicolasN., Miolane, LéoL. and Zdeborová, LenkaL. (2019). Optimal errors and phase transitions in high-dimensional generalized linear models. Proceedings of the National Academy of Sciences 116 5451–5460
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2021
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[author] Chen, Wei-KuoW.-K., Panchenko, DmitryD. and Subag, EliranE. (2021). The generalized TAP free energy II. Communications in Mathematical Physics 381 257–291
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