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通过测度分解实现稀疏线性回归的高效后验采样AI 解读

We consider the problem of sampling from the posterior distribution of a d-dimensional coefficient vector θ, given linear observations y=Xθ+ε. For sparse Bayesian models, such posteriors are in general multimodal, and therefore challenging to sample from. This observation has prompted the exploration of various heuristics that aim at approximating the posterior distribution. In this article, we study a different approach based on decomposing the posterior distribution into a…

长宽比发散时低秩矩阵估计的基本极限AI 解读

We consider the problem of estimating the factors of a low-rank n×d matrix, when this is corrupted by additive Gaussian noise. A special example of our setting corresponds to clustering mixtures of Gaussians with equal (known) covariances. Simple spectral methods do not take into account the distribution of the entries of these factors and are therefore often suboptimal. Here, we characterize the asymptotics of the minimum estimation error under the assumption that the…