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生成式贝叶斯推断中的树型多臂老虎机方法AI 解读

In generative models with intractable likelihood, Approximate Bayesian Computation (ABC) is often the tool of last resort for inference. However, ABC demands many prior parameter proposals to keep only the small fraction of them that meet the acceptance criterion. To accelerate ABC rejection sampling, this paper develops a self-aware framework that learns from past proposals: both acceptances and rejections. We apply recursive partitioning classifiers on the ABC lookup table…

稀疏贝叶斯多维项目反应理论AI 解读

Multivariate Item Response Theory (MIRT) is sought-after widely by applied researchers looking for interpretable (sparse) explanations underlying response patterns in questionnaire data. There is, however, an unmet demand for such sparsity discovery tools in practice. Our article develops a Bayesian platform for binary and ordinal item MIRT which requires minimal tuning and scales well on large datasets due to its parallelizable features. Bayesian methodology for MIRT models…

理想的贝叶斯局部自适应AI 解读

Many real-life applications involve estimation of curves that exhibit complicated shapes including jumps or varying-frequency oscillations. Practical methods have been devised that can adapt to a locally varying complexity of an unknown function (e.g. variable-knot splines, sparse wavelet reconstructions, kernel methods or trees/forests). However, the overwhelming majority of existing asymptotic minimaxity theory is predicated on homogeneous smoothness assumptions. Focusing…

通过分类实现 Metropolis–Hastings 后验采样AI 解读

This article develops a Bayesian computational platform at the interface between posterior sampling and optimization in models whose marginal likelihoods are difficult to evaluate. Inspired by contrastive learning and Generative Adversarial Networks (GAN), we reframe the likelihood function estimation problem as a classification problem. Pitting a Generator, who simulates fake data, against a Classifier, who tries to distinguish them from the real data, one obtains…

贝叶斯 Bootstrap 尖峰厚尾 LASSOAI 解读

The impracticality of posterior sampling has prevented the widespread adoption of spike-and-slab priors in high-dimensional applications. To alleviate the computational burden, optimization strategies have been proposed that quickly find local posterior modes. Trading off uncertainty quantification for computational speed, these strategies have enabled spike-and-slab deployments at scales that would be previously unfeasible. We build on one recent development in this strand…

通过 Thompson 抽样进行变量选择AI 解读

–Thompson sampling is a heuristic algorithm for the multi-armed bandit problem which has a long tradition in machine learning. The algorithm has a Bayesian spirit in the sense that it selects arms based on posterior samples of reward probabilities of each arm. By forging a connection between combinatorial binary bandits and spike-and-slab variable selection, we propose a stochastic optimization approach to subset selection called Thompson variable selection (TVS). TVS is a…

贝叶斯 CART 的不确定性量化AI 解读

This work affords new insights into Bayesian CART in the context of structured wavelet shrinkage. The main thrust is to develop a formal inferential framework for Bayesian tree-based regression. We reframe Bayesian CART as a g-type prior which departs from the typical wavelet product priors by harnessing correlation induced by the tree topology. The practically used Bayesian CART priors are shown to attain adaptive near rate-minimax posterior concentration in the supremum…

利用 ABC 贝叶斯森林进行变量选择AI 解读

Abstract Few problems in statistics are as perplexing as variable selection in the presence of very many redundant covariates. The variable selection problem is most familiar in parametric environments such as the linear model or additive variants thereof. In this work, we abandon the linear model framework, which can be quite detrimental when the covariates impact the outcome in a non-linear way, and turn to tree-based methods for variable selection. Such variable screening…

贝叶斯回归树与森林的后验集中AI 解读

Since their inception in the 1980s, regression trees have been one of the more widely used nonparametric prediction methods. Tree-structured methods yield a histogram reconstruction of the regression surface, where the bins correspond to terminal nodes of recursive partitioning. Trees are powerful, yet susceptible to overfitting. Strategies against overfitting have traditionally relied on pruning greedily grown trees. The Bayesian framework offers an alternative remedy…

用于变量选择的粒子 EM 算法AI 解读

Despite its long history of success, the EM algorithm has been vulnerable to local entrapment when the posterior/likelihood is multi-modal. This is particularly pronounced in spike-and-slab posterior distributions for Bayesian variable selection. The main thrust of this article is to introduce the particle EM algorithm, a new population-based optimization strategy that harvests multiple modes in search spaces that present many local maxima. Motivated by nonparametric…

采用连续尖峰与厚尾混合先验的稀疏信号贝叶斯估计AI 解读

We introduce a new framework for estimation of sparse normal means, bridging the gap between popular frequentist strategies (LASSO) and popular Bayesian strategies (spike-and-slab). The main thrust of this paper is to introduce the family of Spike-and-Slab LASSO (SS-LASSO) priors, which form a continuum between the Laplace prior and the point-mass spike-and-slab prior. We establish several appealing frequentist properties of SS-LASSO priors, contrasting them with these two…

尖峰与厚尾LASSOAI 解读

Despite the wide adoption of spike-and-slab methodology for Bayesian variable selection, its potential for penalized likelihood estimation has largely been overlooked. In this article, we bridge this gap by cross-fertilizing these two paradigms with the Spike-and-Slab LASSO procedure for variable selection and parameter estimation in linear regression. We introduce a new class of self-adaptive penalty functions that arise from a fully Bayes spike-and-slab formulation,…

通过自动稀疏旋转实现快速贝叶斯因子分析AI 解读

Rotational post hoc transformations have traditionally played a key role in enhancing the interpretability of factor analysis. Regularization methods also serve to achieve this goal by prioritizing sparse loading matrices. In this work, we bridge these two paradigms with a unifying Bayesian framework. Our approach deploys intermediate factor rotations throughout the learning process, greatly enhancing the effectiveness of sparsity inducing priors. These automatic rotations…

EMVS：基于 EM 算法的贝叶斯变量选择AI 解读

Despite rapid developments in stochastic search algorithms, the practicality of Bayesian variable selection methods has continued to pose challenges. High-dimensional data are now routinely analyzed, typically with many more covariates than observations. To broaden the applicability of Bayesian variable selection for such high-dimensional linear regression contexts, we propose EMVS, a deterministic alternative to stochastic search based on an EM algorithm which exploits a…