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马蹄先验下的预测推断AI 解读

Predictive inference in the sparse Gaussian sequence model has received considerably less attention than its non-sparse, finite-sample counterpart. Existing work has largely been confined to discrete mixture priors. In this paper, we study predictive inference under a widely used continuous mixture prior, the Horseshoe. We provide new theoretical results establishing exact asymptotic minimax optimality of the predictive Bayes estimator when the sparsity level is known.…

使用 IQ-BART 的生成式回归AI 解读

Implicit Quantile BART (IQ-BART) posits a non-parametric Bayesian model on the conditional quantile function, acting as a model over a conditional model for $Y$ given $X$. One of the key ingredients is augmenting the observed data $\{(Y_i,X_i)\}_{i=1}^n$ with uniformly sampled values $τ_i$ for $1\leq i\leq n$ which serve as training data for quantile function estimation. Using the fact that the location parameter $μ$ in a $τ$-tilted asymmetric Laplace distribution…

通过分类实现近似贝叶斯计算AI 解读

Approximate Bayesian Computation (ABC) enables statistical inference in simulator-based models whose likelihoods are difficult to calculate but easy to simulate from. ABC constructs a kernel-type approximation to the posterior distribution through an accept/reject mechanism which compares summary statistics of real and simulated data. To obviate the need for summary statistics, we directly compare empirical distributions with a Kullback-Leibler (KL) divergence estimator…