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自适应变分贝叶斯：最优性、计算与应用AI 解读

In this paper, we explore adaptive inference based on variational Bayes. Although several studies have been conducted to analyze the contraction properties of variational posteriors, there is still a lack of a general and computationally tractable variational Bayes method that performs adaptive inference. To fill this gap, we propose a novel adaptive variational Bayes framework, which can operate on a collection of models. The proposed framework first computes a variational…

无标签网络的平均：几何刻画与渐近行为AI 解读

It is becoming increasingly common to see large collections of network data objects, that is, data sets in which a network is viewed as a fundamental unit of observation. As a result, there is a pressing need to develop network-based analogues of even many of the most basic tools already standard for scalar and vector data. In this paper, our focus is on averages of unlabeled, undirected networks with edge weights. Specifically, we (i) characterize a certain notion of the…

稀疏 Cholesky 因子高维 DAG 模型的极小极大后验收敛率与选择一致性AI 解读

In this paper we study the high-dimensional sparse directed acyclic graph (DAG) models under the empirical sparse Cholesky prior. Among our results, strong model selection consistency or graph selection consistency is obtained under more general conditions than those in the existing literature. Compared to Cao, Khare and Ghosh [Ann. Statist. (2019) 47 319–348], the required conditions are weakened in terms of the dimensionality, sparsity and lower bound of the nonzero…

复杂约束域上的内蕴高斯过程AI 解读

Summary We propose a class of intrinsic Gaussian processes (GPs) for interpolation, regression and classification on manifolds with a primary focus on complex constrained domains or irregularly shaped spaces arising as subsets or submanifolds of R, R2, R3 and beyond. For example, intrinsic GPs can accommodate spatial domains arising as complex subsets of Euclidean space. Intrinsic GPs respect the potentially complex boundary or interior conditions as well as the intrinsic…

流形值数据的外在局部回归AI 解读

We propose an extrinsic regression framework for modeling data with manifold valued responses and Euclidean predictors. Regression with manifold responses has wide applications in shape analysis, neuroscience, medical imaging and many other areas. Our approach embeds the manifold where the responses lie onto a higher dimensional Euclidean space, obtains a local regression estimate in that space, and then projects this estimate back onto the image of the manifold. Outside the…

基于拒绝采样的模型的数据增广AI 解读

We present a data augmentation scheme to perform Markov chain Monte Carlo inference for models where data generation involves a rejection sampling algorithm. Our idea is a simple scheme to instantiate the rejected proposals preceding each data point. The resulting joint probability over observed and rejected variables can be much simpler than the marginal distribution over the observed variables, which often involves intractable integrals. We consider three problems:…