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高维有向无环图模型及其等价类的贝叶斯学习复杂度AI 解读

Structure learning via MCMC sampling is known to be very challenging because of the enormous search space and the existence of Markov equivalent DAGs. Theoretical results on the mixing behavior are lacking. In this work, we prove the rapid mixing of a random walk Metropolis–Hastings algorithm, which reveals that the complexity of Bayesian learning of sparse equivalence classes grows only polynomially in n and p, under some high-dimensional assumptions. A series of…

清晰与模糊断点回归设计的非参数贝叶斯分析AI 解读

We develop a nonparametric Bayesian analysis of regression discontinuity (RD) designs, allowing for covariates, in which we model and estimate the unknown functions of the forcing variable by basis expansion methods. In a departure from current methods, we use the entire data on the forcing variable, but we emphasize the data near the threshold by placing some knots at and near the threshold, a technique we refer to as soft-windowing. To handle the nonequally spaced knots…

共轭贝叶斯向量自回归中的子空间收缩AI 解读

Summary Macroeconomists using large datasets often face the choice of working with either a large vector autoregression (VAR) or a factor model. In this paper, we develop a conjugate Bayesian VAR with a subspace shrinkage prior that combines the two. This prior shrinks towards the subspace which is defined by a factor model. Our approach allows for estimating the strength of the shrinkage and the number of factors. After establishing the theoretical properties of our prior,…

深度分布时间序列模型与日内电价概率预测AI 解读

Summary Recurrent neural networks (RNNs) with rich feature vectors of past values can provide accurate point forecasts for series that exhibit complex serial dependence. We propose two approaches to constructing deep time series probabilistic models based on a variant of RNN called an echo state network (ESN). The first is where the output layer of the ESN has stochastic disturbances and a Bayesian prior for regularization. The second employs the implicit copula of an ESN…

基于含噪边际似然估计的贝叶斯超参数优化AI 解读

Summary Bayesian models often involve a small set of hyperparameters determined by maximizing the marginal likelihood. Bayesian optimization is an iterative method where a Gaussian process posterior of the underlying function is sequentially updated by new function evaluations. We propose a novel Bayesian optimization framework for situations where the user controls the computational effort and therefore the precision of the function evaluations. This is a common situation…

Dirichlet 过程混合模型的聚类一致性AI 解读

Summary Dirichlet process mixtures are flexible nonparametric models, particularly suited to density estimation and probabilistic clustering. In this work we study the posterior distribution induced by Dirichlet process mixtures as the sample size increases, and more specifically focus on consistency for the unknown number of clusters when the observed data are generated from a finite mixture. Crucially, we consider the situation where a prior is placed on the concentration…

用后验因果效应评估既有结果的成因AI 解读

Summary For the case with a single causal variable, Dawid et al. (2014) defined the probability of causation, and Pearl (2000) defined the probability of necessity to assess the causes of effects. For a case with multiple causes that could affect each other, this paper defines the posterior total and direct causal effects based on the evidence observed for post-treatment variables, which could be viewed as measurements of causes of effects. Posterior causal effects involve…

Hug 与 Hop：离散时间非可逆马尔可夫链蒙特卡洛算法AI 解读

Summary This article introduces the hug and hop Markov chain Monte Carlo algorithm for estimating expectations with respect to an intractable distribution. The algorithm alternates between two kernels, referred to as hug and hop. Hug is a nonreversible kernel that repeatedly applies the bounce mechanism from the recently proposed bouncy particle sampler to produce a proposal point that is far from the current position yet on almost the same contour of the target density,…

Summary We propose new ways to compare two latent distributions when only ordinal data are available, and without imposing parametric assumptions on the underlying continuous distributions. First, we contribute identification results. We show how certain ordinal conditions provide evidence of between-group inequality, quantified by particular quantiles being higher in one latent distribution than in the other. We also show how other ordinal conditions provide evidence of…

多因素条件下的单调响应曲面：估计与贝叶斯分类器AI 解读

Abstract We formulate the estimation of monotone response surface of multiple factors as the inverse of an iteration of partially ordered classifier ensembles. Each ensemble (called product-of-independent-probability-escalation (PIPE)-classifiers) is a projection of Bayes classifiers on the constrained space. We prove that the inverse of PIPE-classifiers (iPIPE) exists, and propose algorithms to efficiently compute iPIPE by reducing the space over which optimisation is…

贝叶斯金字塔：离散数据的可识别多层离散潜结构模型AI 解读

Abstract High-dimensional categorical data are routinely collected in biomedical and social sciences. It is of great importance to build interpretable parsimonious models that perform dimension reduction and uncover meaningful latent structures from such discrete data. Identifiability is a fundamental requirement for valid modeling and inference in such scenarios, yet is challenging to address when there are complex latent structures. In this article, we propose a class of…

通过幂后验与重要性抽样改进边际似然估计AI 解读

Power posteriors have become popular in estimating the marginal likelihood of a Bayesian model. A power posterior is referred to as the posterior distribution that is proportional to the likelihood raised to a power b∈[0,1]. Important power-posterior-based algorithms include thermodynamic integration (TI) of Friel and Pettitt (2008) and steppingstone sampling (SS) of Xie et al. (2011). In this paper, it is shown that the Bernstein–von Mises (BvM) theorem holds for power…

摘要暂缺

Probit、Tobit、多项 Probit 及扩展模型的贝叶斯共轭性：综述与新结果AI 解读

A broad class of models that routinely appear in several fields can be expressed as partially or fully discretized Gaussian linear regressions. Besides including classical Gaussian response settings, this class also encompasses probit, multinomial probit and tobit regression, among others, thereby yielding one of the most widely-implemented families of models in routine applications. The relevance of such representations has stimulated decades of research in the Bayesian…

费城犯罪趋势：结合粒子优化的贝叶斯聚类AI 解读

Accurate estimation of the change in crime over time is a critical first step toward better understanding of public safety in large urban environments. Bayesian hierarchical modeling is a natural way to study spatial variation in urban crime dynamics at the neighborhood level, since it facilitates principled "sharing of information" between spatially adjacent neighborhoods. Typically, however, cities contain many physical and social boundaries that may manifest as spatial…

加速稀疏高斯图模型的贝叶斯结构学习AI 解读

Bayesian structure learning in Gaussian graphical models is often done by search algorithms over the graph space.The conjugate prior for the precision matrix satisfying graphical constraints is the well-known G-Wishart.With this prior, the transition probabilities in the search algorithms necessitate evaluating the ratios of the prior normalizing constants of G-Wishart.In moderate to high-dimensions, this ratio is often approximated by using sampling-based methods as…

哈密顿辅助 Metropolis 抽样AI 解读

Various Markov chain Monte Carlo (MCMC) methods are studied to improve upon random walk Metropolis sampling, for simulation from complex distributions. Examples include Metropolis-adjusted Langevin algorithms, Hamiltonian Monte Carlo, and other algorithms related to underdamped Langevin dynamics. We propose a broad class of irreversible sampling algorithms, called Hamiltonian-assisted Metropolis sampling (HAMS), and develop two specific algorithms with appropriate tuning and…

利用重复数据的次序统计量回归进行非参数误差下的经验贝叶斯均值估计AI 解读

We study empirical Bayes estimation of the effect sizes of $N$ units from $K$ noisy observations on each unit. We show that it is possible to achieve near-Bayes optimal mean squared error, without any assumptions or knowledge about the effect size distribution or the noise. The noise distribution can be heteroskedastic and vary arbitrarily from unit to unit. Our proposal, which we call Aurora, leverages the replication inherent in the $K$ observations per unit and recasts…

计算机模型函数校准的再生核希尔伯特空间方法AI 解读

This article develops a frequentist solution to the functional calibration problem, where the value of a calibration parameter in a computer model is allowed to vary with the value of control variables in the physical system. The need of functional calibration is motivated by engineering applications where using a constant calibration parameter results in a significant mismatch between outputs from the computer model and the physical experiment. Reproducing kernel Hilbert…

协作式多标签分类AI 解读

In multilabel classification, strong label dependence is present for exploiting, particularly for word-to-word dependence defined by semantic labels. In such a situation, we develop a collaborative-learning framework to predict class labels based on label-predictor pairs and label-only data. For example, in image categorization and recognition, language expressions describe the content of an image together with a large number of words and phrases without associated images.…

有技能共同基金的筛选：依赖情形下的错误发现控制AI 解读

Selecting skilled mutual funds through the multiple testing framework has received increasing attention from finance researchers and statisticians. The intercept α of Carhart four-factor model is commonly used to measure the true performance of mutual funds, and positive α’s are considered as skilled. We observe that the standardized ordinary least-square estimates of α’s across the funds possess strong dependence and nonnormality structures, indicating that the conventional…

美国月度国内生产总值的协调估计AI 解读

In the United States, income and expenditure-side estimates of gross domestic product (GDP) (GDPI and GDPE) measure “true” GDP with error and are available at a quarterly frequency. Methods exist for using these proxies to produce reconciled quarterly estimates of true GDP. In this paper, we extend these methods to provide reconciled historical true GDP estimates at a monthly frequency. We do this using a Bayesian mixed frequency vector autoregression (MF-VAR) involving…

贝叶斯动态张量回归AI 解读

High- and multi-dimensional array data are becoming increasingly available. They admit a natural representation as tensors and call for appropriate statistical tools. We propose a new linear autoregressive tensor process (ART) for tensor-valued data, that encompasses some well-known time series models as special cases. We study its properties and derive the associated impulse response function. We exploit the PARAFAC low-rank decomposition for providing a parsimonious…

面板数据模型中的密度预测：半参数贝叶斯视角AI 解读

This article constructs individual-specific density forecasts for a panel of firms or households using a dynamic linear model with common and heterogeneous coefficients as well as cross-sectional heteroscedasticity. The panel considered in this article features a large cross-sectional dimension N but short time series T. Due to the short T, traditional methods have difficulty in disentangling the heterogeneous parameters from the shocks, which contaminates the estimates of…