The TAP free energy for high-dimensional linear regression

03/14/2022
by   Jiaze Qiu, et al.
0

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.

READ FULL TEXT

Please sign up or login with your details

Forgot password? Click here to reset