Asymptotics of Bayesian Uncertainty Estimation in Random Features Regression.

ABSTRACT: In this paper, we compare and contrast the behavior of the posterior predictive distribution to the risk of the maximum a posteriori (MAP) estimator for the random features regression model in the overparameterized regime. We will focus on the variance of the posterior predictive distribution (Bayesian model average) and compare its asymptotics to that of the risk of the MAP estimator. In the regime where the model dimensions grow faster than any constant multiple of the number of samples, asymptotic agreement between these two quantities is governed by the phase transition in the signal-to-noise ratio. They also asymptotically agree with each other when the number of samples grows faster than any constant multiple of model dimensions. Numerical simulations illustrate finer distributional

SUBMITTER: Baek Y 

PROVIDER: S-EPMC12700357 | biostudies-literature | 2023 Dec

REPOSITORIES: biostudies-literature