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基于多元谱积分 Frobenius 范数的模型识别AI 解读

Abstract We study the integral of the Frobenius norm as a measure of the discrepancy between two multivariate spectra. Such a measure can be used to fit time series models, and ensures proximity between model and process at all frequencies of the spectral density. We develop new asymptotic results for linear and quadratic functionals of the periodogram, and apply the integrated Frobenius norm to fit time series models and test whether model residuals are white noise. The…

利用时变工具变量估计与改进动态治疗方案AI 解读

Abstract Estimating dynamic treatment regimes (DTRs) from retrospective observational data is challenging as some degree of unmeasured confounding is often expected. In this work, we develop a framework of estimating properly defined ‘optimal’ DTRs with a time-varying instrumental variable (IV) when unmeasured covariates confound the treatment and outcome, rendering the potential outcome distributions only partially identified. We derive a novel Bellman equation under…

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…

以分布函数为结果的因果推断AI 解读

Abstract Understanding causal relationships is one of the most important goals of modern science. So far, the causal inference literature has focused almost exclusively on outcomes coming from the Euclidean space Rp. However, it is increasingly common that complex datasets are best summarized as data points in nonlinear spaces. In this paper, we present a novel framework of causal effects for outcomes from the Wasserstein space of cumulative distribution functions, which in…

利用外部数据估计未来临床试验中协变量调整的效率增益AI 解读

Abstract We present a framework for using existing external data to identify and estimate the relative efficiency of a covariate-adjusted estimator compared to an unadjusted estimator in a future randomized trial. Under conditions, these relative efficiencies approximate the ratio of sample sizes needed to achieve a desired power. We develop semiparametrically efficient estimators of the relative efficiencies for several treatment effect estimands of interest with either…

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…

异方差与相关误差线性模型的去偏及阈值化岭回归AI 解读

Abstract High-dimensional linear models with independent errors have been well-studied. However, statistical inference on a high-dimensional linear model with heteroskedastic, dependent (and possibly nonstationary) errors is still a novel topic. Under such complex assumptions, the paper at hand introduces a debiased and thresholded ridge regression estimator that is consistent, and is able to recover the model sparsity. Moreover, we derive a Gaussian approximation theorem…

通过曲率分析识别网络模型的潜在空间几何AI 解读

Abstract A common approach to modelling networks assigns each node to a position on a low-dimensional manifold where distance is inversely proportional to connection likelihood. More positive manifold curvature encourages more and tighter communities; negative curvature induces repulsion. We consistently estimate manifold type, dimension, and curvature from simply connected, complete Riemannian manifolds of constant curvature. We represent the graph as a noisy distance…

利用因果生存森林估计右删失数据中的异质性处理效应AI 解读

Abstract Forest-based methods have recently gained in popularity for non-parametric treatment effect estimation. Building on this line of work, we introduce causal survival forests, which can be used to estimate heterogeneous treatment effects in survival and observational setting where outcomes may be right-censored. Our approach relies on orthogonal estimating equations to robustly adjust for both censoring and selection effects under unconfoundedness. In our experiments,…

用于检测回归模型异方差的实验设计AI 解读

Abstract We consider the problem of designing experiments to detect the presence of a specified heteroscedastity in Gaussian regression models. We study the relationship of the Ds- and KL-criteria with the noncentrality parameter of the asymptotic chi-squared distribution of a likelihood-based test, for local alternatives. We found that, when the heteroscedastity depends on one parameter, the two criteria coincide asymptotically and that the D1-criterion is proportional to…

用于小区域估计的高维参数嵌套误差回归模型AI 解读

Abstract In this paper, we propose a flexible nested error regression small area model with high-dimensional parameter that incorporates heterogeneity in regression coefficients and variance components. We develop a new robust small area-specific estimating equations method that allows appropriate pooling of a large number of areas in estimating small area-specific model parameters. We propose a parametric bootstrap and jackknife method to estimate not only the mean squared…

高维回归中的推断AI 解读

Abstract This paper develops an approach to inference in a linear regression model when the number of potential explanatory variables is larger than the sample size. The approach treats each regression coefficient in turn as the interest parameter, the remaining coefficients being nuisance parameters, and seeks an optimal interest-respecting transformation, inducing sparsity on the relevant blocks of the notional Fisher information matrix. The induced sparsity is exploited…

用于神经网络贝叶斯学习与 MCMC 的迹类高斯先验AI 解读

Abstract This paper introduces a new neural network based prior for real valued functions. Each weight and bias of the neural network has an independent Gaussian prior, with the key novelty that the variances decrease in the width of the network in such a way that the resulting function is well defined in the limit of an infinite width network. We show that the induced posterior over functions is amenable to Monte Carlo sampling using Hilbert space Markov chain Monte Carlo…

贝叶斯融合：可扩展地统一分布式统计分析AI 解读

Abstract There has been considerable interest in addressing the problem of unifying distributed analyses into a single coherent inference, which arises in big-data settings, when working under privacy constraints, and in Bayesian model choice. Most existing approaches relied upon approximations of the distributed analyses, which have significant shortcomings—the quality of the inference can degrade rapidly with the number of analyses being unified, and can be substantially…

保形化生存分析AI 解读

Abstract In this paper, we develop an inferential method based on conformal prediction, which can wrap around any survival prediction algorithm to produce calibrated, covariate-dependent lower predictive bounds on survival times. In the Type I right-censoring setting, when the censoring times are completely exogenous, the lower predictive bounds have guaranteed coverage in finite samples without any assumptions other than that of operating on independent and identically…

多处理臂及可能包含析因结构的实验中的协变量调整AI 解读

Abstract Randomized experiments are the gold standard for causal inference and enable unbiased estimation of treatment effects. Regression adjustment provides a convenient way to incorporate covariate information for additional efficiency. This article provides a unified account of its utility for improving estimation efficiency in multiarmed experiments. We start with the commonly used additive and fully interacted models for regression adjustment in estimating average…

缺失数据的偏样本经验似然加权：逆概率加权的替代方法AI 解读

Abstract Inverse probability weighting (IPW) is widely used in many areas when data are subject to unrepresentativeness, missingness, or selection bias. An inevitable challenge with the use of IPW is that the IPW estimator can be remarkably unstable if some probabilities are very close to zero. To overcome this problem, at least three remedies have been developed in the literature: stabilizing, thresholding, and trimming. However, the final estimators are still IPW-type…

基于张量 CP 分解的矩阵时间序列建模AI 解读

Abstract We consider to model matrix time series based on a tensor canonical polyadic (CP)-decomposition. Instead of using an iterative algorithm which is the standard practice for estimating CP-decompositions, we propose a new and one-pass estimation procedure based on a generalized eigenanalysis constructed from the serial dependence structure of the underlying process. To overcome the intricacy of solving a rank-reduced generalized eigenequation, we propose a further…

复杂网络中的信息核心识别AI 解读

Abstract In a complex network, the core component with interesting structures is usually hidden within noninformative connections. The noises and bias introduced by the noninformative component can obscure the salient structure and limit many network modeling procedures’ effectiveness. This paper introduces a novel core–periphery model for the noninformative periphery structure of networks without imposing a specific form of the core. We propose spectral algorithms for core…

时空数据的因果推断：估计伊拉克空袭对叛乱暴力的影响AI 解读

Abstract Many causal processes have spatial and temporal dimensions. Yet the classic causal inference framework is not directly applicable when the treatment and outcome variables are generated by spatio-temporal point processes. We extend the potential outcomes framework to these settings by formulating the treatment point process as a stochastic intervention. Our causal estimands include the expected number of outcome events in a specified area under a particular…

拒绝潜在因子模型结构解释的统计检验AI 解读

Abstract Factor analysis is often used to assess whether a single univariate latent variable is sufficient to explain most of the covariance among a set of indicators for some underlying construct. When evidence suggests that a single factor is adequate, research often proceeds by using a univariate summary of the indicators in subsequent research. Implicit in such practices is the assumption that it is the underlying latent, rather than the indicators, that is causally…

异质缺失下的高维主成分分析AI 解读

Abstract We study the problem of high-dimensional Principal Component Analysis (PCA) with missing observations. In a simple, homogeneous observation model, we show that an existing observed-proportion weighted (OPW) estimator of the leading principal components can (nearly) attain the minimax optimal rate of convergence, which exhibits an interesting phase transition. However, deeper investigation reveals that, particularly in more realistic settings where the observation…

函数均值的经验似然推断及其可穿戴设备数据应用AI 解读

Abstract This paper develops a nonparametric inference framework that is applicable to occupation time curves derived from wearable device data. These curves consider all activity levels within the range of device readings, which is preferable to the practice of classifying activity into discrete categories. Motivated by certain features of these curves, we introduce a powerful likelihood ratio approach to construct confidence bands and compare functional means. Notably, our…

含噪网络关联数据的线性回归与推断AI 解读

Abstract Linear regression on network-linked observations has been an essential tool in modelling the relationship between response and covariates with additional network structures. Previous methods either lack inference tools or rely on restrictive assumptions on social effects and usually assume that networks are observed without errors. This paper proposes a regression model with non-parametric network effects. The model does not assume that the relational data or…