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坐标上升变分推断的收敛性AI 解读

As a computational alternative to Markov chain Monte Carlo approaches, variational inference (VI) is becoming more and more popular for approximating intractable posterior distributions in large-scale Bayesian models due to its comparable efficacy and superior efficiency. Several recent works provide theoretical justifications of VI by proving its statistical optimality for parameter estimation under various settings; meanwhile, formal analysis on the algorithmic convergence…

度修正及相关随机块模型的Monte Carlo拟合优度检验AI 解读

Abstract We construct Bayesian and frequentist finite-sample goodness-of-fit tests for three different variants of the stochastic blockmodel for network data. Since all of the stochastic blockmodel variants are log-linear in form when block assignments are known, the tests for the latent block model versions combine a block membership estimator with the algebraic statistics machinery for testing goodness-of-fit in log-linear models. We describe Markov bases and marginal…

截断多元正态先验的概率质量偏移现象AI 解读

We show that lower-dimensional marginal densities of dependent zero-mean normal distributions truncated to the positive orthant exhibit a mass-shifting phenomenon. Despite the truncated multivariate normal density having a mode at the origin, the marginal density assigns increasingly small mass near the origin as the dimension increases. The phenomenon accentuates with stronger correlation between the random variables. This surprising behavior has serious implications toward…

异质数据的协变量辅助贝叶斯图学习AI 解读

In a traditional Gaussian graphical model, data homogeneity is routinely assumed with no extra variables affecting the conditional independence. In modern genomic datasets, there is an abundance of auxiliary information, which often gets under-utilized in determining the joint dependency structure. In this article, we consider a Bayesian approach to model undirected graphs underlying heterogeneous multivariate observations with additional assistance from covariates. Building…

营养流行病学零膨胀数据的贝叶斯 Copula 密度反卷积AI 解读

Estimating the marginal and joint densities of the long-term average intakes of different dietary components is an important problem in nutritional epidemiology. Since these variables cannot be directly measured, data are usually collected in the form of 24-hour recalls of the intakes, which show marked patterns of conditional heteroscedasticity. Significantly compounding the challenges, the recalls for episodically consumed dietary components also include exact zeros. The…

具有统计保证的 α 变分推断AI 解读

We provide statistical guarantees for a family of variational approximations to Bayesian posterior distributions, called $\alpha $-VB, which has close connections with variational approximations of tempered posteriors in the literature. The standard variational approximation is a special case of $\alpha $-VB with $\alpha =1$. When $\alpha \in (0,1]$, a novel class of variational inequalities are developed for linking the Bayes risk under the variational approximation to the…

社区数量未知时的概率社区检测AI 解读

A fundamental problem in network analysis is clustering the nodes into groups which share a similar connectivity pattern. Existing algorithms for community detection assume the knowledge of the number of clusters or estimate it a priori using various selection criteria and subsequently estimate the community structure. Ignoring the uncertainty in the first stage may lead to erroneous clustering, particularly when the community structure is vague. We instead propose a…

贝叶斯分数后验AI 解读

We consider the fractional posterior distribution that is obtained by updating a prior distribution via Bayes theorem with a fractional likelihood function, a usual likelihood function raised to a fractional power. First, we analyze the contraction property of the fractional posterior in a general misspecified framework. Our contraction results only require a prior mass condition on certain Kullback–Leibler (KL) neighborhood of the true parameter (or the KL divergence…

贝叶斯半参数多元密度反卷积AI 解读

We consider the problem of multivariate density deconvolution when interest lies in estimating the distribution of a vector valued random variable X but precise measurements on X are not available, observations being contaminated by measurement errors U. The existing sparse literature on the problem assumes the density of the measurement errors to be completely known. We propose robust Bayesian semiparametric multivariate deconvolution approaches when the measurement error…

条件密度的自适应贝叶斯估计AI 解读

We consider a nonparametric Bayesian model for conditional densities. The model is a finite mixture of normal distributions with covariate dependent multinomial logit mixing probabilities. A prior for the number of mixture components is specified on positive integers. The marginal distribution of covariates is not modeled. We study asymptotic frequentist behavior of the posterior in this model. Specifically, we show that when the true conditional density has a certain…

用于最优收缩的 Dirichlet–Laplace 先验AI 解读

regularization, are routinely used in high-dimensional applications, and there is a rich literature on optimality properties under sparsity assumptions. In the Bayesian paradigm, sparsity is routinely induced through two-component mixture priors having a probability mass at zero, but such priors encounter daunting computational problems in high dimensions. This has motivated continuous shrinkage priors, which can be expressed as global-local scale mixtures of Gaussians,…

点云中闭合曲线的贝叶斯多尺度建模AI 解读

Modeling object boundaries based on image or point cloud data is frequently necessary in medical and scientific applications ranging from detecting tumor contours for targeted radiation therapy, to the classification of organisms based on their structural information. In low-contrast images or sparse and noisy point clouds, there is often insufficient data to recover local segments of the boundary in isolation. Thus, it becomes critical to model the entire boundary in the…

超大协方差矩阵稀疏贝叶斯因子模型的后验收缩AI 解读

Sparse Bayesian factor models are routinely implemented for parsimonious dependence modeling and dimensionality reduction in high-dimensional applications. We provide theoretical understanding of such Bayesian procedures in terms of posterior convergence rates in inferring high-dimensional covariance matrices where the dimension can be larger than the sample size. Under relevant sparsity assumptions on the true covariance matrix, we show that commonly-used point mass mixture…

利用多带宽 Gaussian 过程估计各向异性函数AI 解读

In nonparametric regression problems involving multiple predictors, there is typically interest in estimating an anisotropic multivariate regression surface in the important predictors while discarding the unimportant ones. Our focus is on defining a Bayesian procedure that leads to the minimax optimal rate of posterior contraction (up to a log factor) adapting to the unknown dimension and anisotropic smoothness of the true surface. We propose such an approach based on a…