论文标题
部分可观测时空混沌系统的无模型预测
The TAP free energy for high-dimensional linear regression
论文作者
论文摘要
我们得出了贝叶斯线性回归中后验分布的对数正差常数的变异表示，并具有均匀的球形先验和i.i.d.高斯设计。我们以“比例”的渐近状态工作，观测值和特征数量以成比例的速度增长。严格地建立了由旋转玻璃理论引起的无thou-anderson-palmer（TAP）近似，并证明了Krzakala等人的猜想。 al。 （2014）在球形先验的特殊情况下。
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.
