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关系数据的非参数贝叶斯动态建模AI 解读

Symmetric binary matrices representing relations are collected in many areas. Our focus is on dynamically evolving binary relational matrices, with interest being on inference on the relationship structure and prediction. We propose a nonparametric Bayesian dynamic model, which reduces dimensionality in characterizing the binary matrix through a lower-dimensional latent space representation, with the latent coordinates evolving in continuous time via Gaussian processes. By…

用于密度估计的潜在因子模型AI 解读

Abstract: Although discrete mixture modeling has formed the backbone of the literature on Bayesian density estimation, there are some well known disadvantages. We propose an alternative class of priors based on random nonlinear functions of a uniform latent variable with an additive residual. The induced prior for the density is shown to have desirable properties including ease of centering on an initial guess for the density, large support, posterior consistency and…

利用高斯过程投影的贝叶斯单调回归AI 解读

Shape-constrained regression analysis has applications in dose-response modelling, environmental risk assessment, disease screening and many other areas. Incorporating the shape constraints can improve estimation efficiency and avoid implausible results. We propose a novel method, focusing on monotone curve and surface estimation, which uses Gaussian process projections. Our inference is based on projecting posterior samples from the Gaussian process. We develop theory on…

计数过程的非参数贝叶斯建模AI 解读

Data on count processes arise in a variety of applications, including longitudinal, spatial and imaging studies measuring count responses. The literature on statistical models for dependent count data is dominated by models built from hierarchical Poisson components. The Poisson assumption is not warranted in many applied contexts, and hierarchical Poisson models make restrictive assumptions about overdispersion in marginal distributions. In this article we propose a class…

收缩先验下线性模型的后验一致性AI 解读

We investigate the asymptotic behaviour of posterior distributions of regression coefficients in high-dimensional linear models as the number of dimensions grows with the number of observations. We show that the posterior distribution concentrates in neighbourhoods of the true parameter under simple sufficient conditions. These conditions hold under popular shrinkage priors given some sparsity assumptions.

大规模数据的高效高斯过程回归AI 解读

Gaussian processes are widely used in nonparametric regression, classification and spatiotemporal modelling, facilitated in part by a rich literature on their theoretical properties. However, one of their practical limitations is expensive computation, typically on the order of n3 where n is the number of data points, in performing the necessary matrix inversions. For large datasets, storage and processing also lead to computational bottlenecks, and numerical stability of…

贝叶斯保序密度回归AI 解读

Density regression models allow the conditional distribution of the response given predictors to change flexibly over the predictor space. Such models are much more flexible than nonparametric mean regression models with nonparametric residual distributions, and are well supported in many applications. A rich variety of Bayesian methods have been proposed for density regression, but it is not clear whether such priors have full support so that any true data-generating model…

稀疏贝叶斯无限因子模型AI 解读

We focus on sparse modelling of high-dimensional covariance matrices using Bayesian latent factor models. We propose a multiplicative gamma process shrinkage prior on the factor loadings which allows introduction of infinitely many factors, with the loadings increasingly shrunk towards zero as the column index increases. We use our prior on a parameter-expanded loading matrix to avoid the order dependence typical in factor analysis models and develop an efficient Gibbs…

流形上的非参数贝叶斯密度估计及平面形状应用AI 解读

Statistical analysis on landmark-based shape spaces has diverse applications in morphometrics, medical diagnostics, machine vision and other areas. These shape spaces are non-Euclidean quotient manifolds. To conduct nonparametric inferences, one may define notions of centre and spread on this manifold and work with their estimates. However, it is useful to consider full likelihood-based methods, which allow nonparametric estimation of the probability density. This article…

随机效应的非参数贝叶斯局部分割模型AI 解读

This paper focuses on the problem of choosing a prior for an unknown random effects distribution within a Bayesian hierarchical model. The goal is to obtain a sparse representation by allowing a combination of global and local borrowing of information. A local partition process prior is proposed, which induces dependent local clustering. Subjects can be clustered together for a subset of their parameters, and one learns about similarities between subjects increasingly as…

通过密度估计开展贝叶斯非参数函数型数据分析AI 解读

In many modern experimental settings, observations are obtained in the form of functions, and interest focuses on inferences on a collection of such functions. We propose a hierarchical model that allows us to simultaneously estimate multiple curves nonparametrically by using dependent Dirichlet Process mixtures of Gaussians to characterize the joint distribution of predictors and outcomes. Function estimates are then induced through the conditional distribution of the…

随机序约束下的贝叶斯非参数推断AI 解读

This article considers Bayesian inference about collections of unknown distributions subject to a partial stochastic ordering. To address problems in testing of equalities between groups and estimation of group-specific distributions, we propose classes of restricted dependent Dirichlet process priors. These priors have full support in the space of stochastically ordered distributions, and can be used for collections of unknown mixture distributions to obtain a flexible…

核折棒过程AI 解读

We propose a class of kernel stick-breaking processes for uncountable collections of dependent random probability measures. The process is constructed by first introducing an infinite sequence of random locations. Independent random probability measures and beta-distributed random weights are assigned to each location. Predictor-dependent random probability measures are then constructed by mixing over the locations, with stick-breaking probabilities expressed as a kernel…