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观察性研究中用于因果推断的人工智能贝叶斯生成模型AI 解读

Causal inference in observational studies with high-dimensional covariates presents significant challenges. We introduce CausalBGM, an AI-powered Bayesian generative modeling approach that captures the causal relationship among covariates, treatment, and outcome. The core innovation is to estimate the individual treatment effect (ITE) by learning the individual-specific distribution of a low-dimensional latent feature set (e.g., latent confounders) that drives changes in…

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.…

基因扰动实验的强信号检测：具有功效保证与 FDR 控制的自适应方法AI 解读

The perturbation of a transcription factor should affect the expression levels of its direct targets. However, not all genes showing changes in expression are direct targets. To increase the chance of detecting direct targets, we propose a modified two-group model where the null group corresponds to genes which are not direct targets, but can have small nonzero effects. We model the behavior of genes from the null set by a Gaussian distribution with unknown variance τ 2 . To…

耦合可选 Pólya 树与两样本问题AI 解读

Testing and characterizing the difference between two data samples is of fundamental interest in statistics. Existing methods such as Kolmogorov–Smirnov and Cramer–von Mises tests do not scale well as the dimensionality increases and provide no easy way to characterize the difference should it exist. In this work, we propose a theoretical framework for inference that addresses these challenges in the form of a prior for Bayesian nonparametric analysis. The new prior is…

从实验数据学习因果贝叶斯网络结构AI 解读

We propose a method for the computational inference of directed acyclic graphical structures given data from experimental interventions. Order-space Markov chain Monte Carlo, equi-energy sampling, importance weighting, and stream-based computation are combined to create a fast algorithm for learning causal Bayesian network structures.

等能量采样器及其在统计推断与统计力学中的应用AI 解读

We introduce a new sampling algorithm, the equi-energy sampler, for efficient statistical sampling and estimation. Complementary to the widely used temperature-domain methods, the equi-energy sampler, utilizing the temperature–energy duality, targets the energy directly. The focus on the energy function not only facilitates efficient sampling, but also provides a powerful means for statistical estimation, for example, the calculation of the density of states and…

ψ学习研究AI 解读

The concept of large margins have been recognized as an important principle in analyzing learning methodologies, including boosting, neural networks, and support vector machines (SVMs). However, this concept alone is not adequate for learning in nonseparable cases. We propose a learning methodology, called ψ-learning, that is derived from a direct consideration of generalization errors. We provide a theory for ψ-learning and show that it essentially attains the optimal rates…

实参数进化蒙特卡洛及其在贝叶斯混合模型中的应用AI 解读

We propose an evolutionary Monte Carlo algorithm to sample from a target distribution with real-valued parameters. The attractive features of the algorithm include the ability to learn from the samples obtained in previous steps and the ability to improve the mixing of a system by sampling along a temperature ladder. The effectiveness of the algorithm is examined through three multimodal examples and Bayesian neural networks. The numerical results confirm that the real-coded…

蒙特卡洛计算中动态加权的理论AI 解读

This article provides a first theoretical analysis of a new Monte Carlo approach, the dynamic weighting algorithm, proposed recently by Wong and Liang. In dynamic weighting Monte Carlo, one augments the original state space of interest by a weighting factor, which allows the resulting Markov chain to move more freely and to escape from local modes. It uses a new invariance principle to guide the construction of transition rules. We analyze the behavior of the weights…

Metropolis 抽样中的多重尝试方法与局部优化AI 解读

This article describes a new Metropolis-like transition rule, the multiple-try Metropolis, for Markov chain Monte Carlo (MCMC) simulations. By using this transition rule together with adaptive direction sampling, we propose a novel method for incorporating local optimization steps into a MCMC sampler in continuous state-space. Numerical studies show that the new method performs significantly better than the traditional Metropolis-Hastings (M-H) sampler. With minor tailoring…

随机筛似然与一般回归模型AI 解读

Consider a semiparametric regression model Y = f(θ, X, ϵ), where f is a known function, θ is an unknown vector, ϵ consists of a random error and possibly of some unobserved variables, and the distribution F(·) of (ϵ, X) is unspecified. This article introduces, in a general setting, new methodology for estimating θ and F(·). The proposed method constructs a profile likelihood defined on random-level sets (a random sieve). The proposed method is related to empirical likelihood…

拒绝控制与序贯重要性抽样AI 解读

We discuss ways of combining rejection sampling and importance sampling methods in Monte Carlo computations and demonstrate their usefulness in updating dynamic systems. Specifically, we propose the rejection controlled sequential importance sampling (RC-SIS) algorithm, which is designed to simultaneously reduce Monte Carlo variation and retain independent samples in sequential importance sampling. The proposed method is demonstrated by three examples taken from…

似然比的概率不等式与筛最大似然估计的收敛率AI 解读

Let $Y_1,\ldots, Y_n$ be independent identically distributed with density $p_0$ and let $\mathscr{F}$ be a space of densities. We show that the supremum of the likelihood ratios $\prod^n_{i=1} p(Y_i)/p_0(Y_i)$, where the supremum is over $p \in \mathscr{F}$ with $\|p^{1/2} - p^{1/2}_0\|_2 \geq \varepsilon$, is exponentially small with probability exponentially close to 1. The exponent is proportional to $n\varepsilon^2$. The only condition required for this to hold is that $\varepsilon$…

筛估计的收敛速度AI 解读

In this paper, we develop a general theory for the convergence rate of sieve estimates, maximum likelihood estimates (MLE's) and related estimates obtained by optimizing certain empirical criteria in general parameter spaces. In many cases, especially when the parameter space is infinite dimensional, maximization over the whole parameter space is undesirable. In such cases, one has to perform maximization over an approximating space (sieve) of the original parameter space…

序贯插补与贝叶斯缺失数据问题AI 解读

For missing data problems, Tanner and Wong have described a data augmentation procedure that approximates the actual posterior distribution of the parameter vector by a mixture of complete data posteriors. Their method of constructing the complete data sets is closely related to the Gibbs sampler. Both required iterations, and, similar to the EM algorithm, convergence can be slow. We introduce in this article an alternative procedure that involves imputing the missing data…

Gibbs 抽样的协方差结构：估计量与数据增广方案的比较AI 解读

We study the covariance structure of a Markov chain generated by the Gibbs sampler, with emphasis on data augmentation. When applied to a Bayesian missing data problem, the Gibbs sampler produces two natural approximations for the posterior distribution of the parameter vector: the empirical distribution based on the sampled values of the parameter vector, and a mixture of complete data posteriors. We prove that Rao-Blackwellization causes a one-lag delay for the…

剖面似然与条件参数模型AI 解读

In this paper, we outline a general approach to estimating the parametric component of a semiparametric model. For the case of a scalar parametric component, the method is based on the idea of first estimating a one-dimensional subproblem of the original problem that is least favorable in the sense of Stein. The likelihood function for the scalar parameter along this estimated subproblem may be viewed as a generalization of the profile likelihood for the problem. The scalar…

参数非线性函数后验密度的拉普拉斯展开AI 解读

An asymptotic expansion for marginal posterior densities of nonlinear functions of parameters is derived. The density in question is proportional to an integral over a lower dimensional manifold with the integrand including an appropriate change-in-volume term, Laplace's method is applied to obtain the expansion. Avoiding the difficult step of the explicit parameterization of the manifold, we carry out the expansion via an implicit and local parameterization, and the…

参数非线性函数后验密度的拉普拉斯展开AI 解读

SUMMARY An asymptotic expansion for marginal posterior densities of nonlinear functions of parameters is derived. The density in question is proportional to an integral over a lower dimensional manifold with the integrand including an appropriate change-in-volume term, Laplace's method is applied to obtain the expansion. Avoiding the difficult step of the explicit parameterization of the manifold, we carry out the expansion via an implicit and local parameterization, and the…

无限维参数空间中的最大似然估计AI 解读

An approximate maximum likelihood estimate is known to be consistent under some compactness and integrability conditions. In this paper we study its convergence rate and its asymptotic efficiency in estimating smooth functionals of the parameter. We provide conditions under which the rate of convergence can be established. This rate is essentially governed by the size of the space of score functions as measured by an entropy index. We also show that, for a large class of…

含时变离散协变量的非参数风险函数估计AI 解读

The traditional one-sample nonparametric estimator of the cumulative hazard function is extended to allow for time-varying discrete covariates. A proof for the consistency and asymptotic normality of the estimator, as well as a derivation of the asymptotic standard error, is provided. Numerical results show that the estimator performs reasonably well.

通过数据增广计算后验分布AI 解读

The idea of data augmentation arises naturally in missing value problems, as exemplified by the standard ways of filling in missing cells in balanced two-way tables. Thus data augmentation refers to a scheme of augmenting the observed data so as to make it more easy to analyze. This device is used to great advantage by the EM algorithm (Dempster, Laird, and Rubin 1977) in solving maximum likelihood problems. In situations when the likelihood cannot be approximated closely by…

部分似然理论AI 解读

A general asymptotic theory is developed for the maximum likelihood estimator based on a partial likelihood. Conditions are given for consistency and asymptotic normality, and a method is provided for the calculation of the asymptotic efficiency of the estimator. The implications of the general theory are examined in special cases such as inference in stochastic processes, Cox regression models, and AR processes with missing segments.

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