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用于改进估计与推断的贝叶斯迁移学习AI 解读

Transfer learning enhances model performance in a target population with limited samples by leveraging knowledge from related studies. While many works focus on improving predictive performance, challenges persist in statistical inference. Bayesian approaches naturally provide uncertainty quantification for parameter estimates; however, existing Bayesian transfer learning methods are typically limited to single-source scenarios or require individual-level data. We introduce…

多层随机点积图：估计与在线变点检测AI 解读

Abstract We study the multilayer random dot product graph (MRDPG) model, a generalization of the random dot product graph model to multilayer networks. To estimate the edge probabilities, we deploy a tensor-based methodology and demonstrate its superiority over existing approaches. Moving to dynamic MRDPGs, we formulate and analyse an online change point detection framework, where, at each time point, we observe a realization from an MRDPG. Across layers, we assume fixed…

高维潜在面板分位数回归及其资产定价应用AI 解读

We propose a generalization of the linear panel quantile regression model to accommodate both sparse and dense parts: sparse means that while the number of covariates available is large, potentially only a much smaller number of them have a nonzero impact on each conditional quantile of the response variable; while the dense part is represent by a low-rank matrix that can be approximated by latent factors and their loadings. Such a structure poses problems for traditional…

分位数趋势滤波的风险界AI 解读

Summary We study quantile trend filtering, a recently proposed method for nonparametric quantile regression, with the goal of generalizing existing risk bounds for the usual trend-filtering estimators that perform mean regression. We study both the penalized and the constrained versions, of order $r \geqslant 1$, of univariate quantile trend filtering. Our results show that both the constrained and the penalized versions of order $r \geqslant 1$ attain the minimax rate up to…

利用 K 近邻融合套索的自适应非参数回归AI 解读

Summary The fused lasso, also known as total-variation denoising, is a locally adaptive function estimator over a regular grid of design points. In this article, we extend the fused lasso to settings in which the points do not occur on a regular grid, leading to a method for nonparametric regression. This approach, which we call the $K$-nearest-neighbours fused lasso, involves computing the $K$-nearest-neighbours graph of the design points and then performing the fused lasso…

分布变化的序贯非参数检验：放射性异常检测应用AI 解读

We propose a sequential nonparametric test for detecting a change in distribution, based on windowed Kolmogorov–Smirnov statistics. The approach is simple, robust, highly computationally efficient, easy to calibrate, and requires no parametric assumptions about the underlying null and alternative distributions. We show that both the false-alarm rate and the power of our procedure are amenable to rigorous analysis, and that the method outperforms existing sequential testing…

由负二项过程族构造的随机计数矩阵先验AI 解读

We define a family of probability distributions for random count matrices with a potentially unbounded number of rows and columns. The three distributions we consider are derived from the gamma-Poisson, gamma-negative binomial, and beta-negative binomial processes, which we refer to generically as a family of negative-binomial processes. Because the models lead to closed-form update equations within the context of a Gibbs sampler, they are natural candidates for…