论文检索

高维投影独立性检验：难题与改进AI 解读

Summary Testing independence between high-dimensional random vectors is fundamentally different from testing independence between univariate random variables. Taking the projection correlation as an example, it suffers from at least three problems. First, it has a high computational complexity of O{n3(p+q)}, where n, p and q are the sample size and dimensions of the random vectors; this limits its usefulness substantially when n is extremely large. Second, the asymptotic…

分离数据下高维 Logistic 回归模型的推断AI 解读

Summary Direct use of the likelihood function typically produces severely biased estimates when the dimension of the parameter vector is large relative to the effective sample size. With linearly separable data generated from a logistic regression model, the loglikelihood function asymptotes and the maximum likelihood estimator does not exist. We show that an exact analysis for each regression coefficient produces half-infinite confidence sets for some parameters when the…

重刊：因子模型结构变化的似然比检验AI 解读

A factor model with a break in its factor loadings is observationally equivalent to a model without changes in the loadings but with a change in the variance of its factors. This approach effectively transforms a high-dimensional structural change problem into a low-dimensional problem. This paper considers the likelihood ratio (LR) test for a variance change in the estimated factors. The LR test implicitly explores a special feature of the estimated factors: the pre-break…

目标主成分分析：高维面板数据的迁移学习AI 解读

This paper develops a novel method to estimate a latent factor model for a large target panel with missing observations by optimally using the information from auxiliary panel data sets. We refer to our estimator as target-PCA. Transfer learning from auxiliary panel data allows us to deal with a large fraction of missing observations and weak signals in the target panel. We show that our estimator is more efficient and can consistently estimate weak factors, which are not…

兼职补贴与母亲再就业：双重差分分析的证据AI 解读

Summary Employment interruptions of mothers are still one of the main causes for different labour market outcomes between women and men. Employment subsidies can incentivise mothers to shorten employment interruptions after childbirth. We examine a German parental leave reform incentivising an early return to part‐time work. Exploiting the exogenous variation defined by the child's birthday, we apply unconditional difference‐in‐differences (DiD) estimation using…

This paper investigates the stability of deep ReLU neural networks for nonparametric regression under the assumption that the noise has only a finite p-th moment. We unveil how the optimal rate of convergence depends on p, the degree of smoothness and the intrinsic dimension in a class of nonparametric regression functions with hierarchical composition structure when both the adaptive Huber loss and deep ReLU neural networks are used. This optimal rate of convergence cannot…

预印本版本摘要 · 查看来源

一般数据集偏移下的高效且多重稳健风险估计AI 解读

. Despite extensive literature on dataset shift, limited works address how to efficiently use the auxiliary populations to improve the accuracy of risk evaluation for a given machine learning task in the target population. In this paper, we study the general problem of efficiently estimating target population risk under various dataset shift conditions, leveraging semiparametric efficiency theory. We consider a general class of dataset shift conditions, which includes three…

高维加性回归的高效函数型 Lasso 核平滑AI 解读

Smooth backfitting has been proposed and proved as a powerful nonparametric estimation technique for additive regression models in various settings. Existing studies are restricted to cases with a moderate number of covariates and are not directly applicable to high dimensional settings. In this paper, we develop new kernel estimators based on the idea of smooth backfitting for high dimensional additive models. We introduce a novel penalization scheme, combining the idea of…

Gromov–Wasserstein距离：熵正则化、对偶与样本复杂度AI 解读

The Gromov–Wasserstein (GW) distance, rooted in optimal transport (OT) theory, quantifies dissimilarity between metric measure spaces and provides a framework for aligning heterogeneous datasets. While computational aspects of the GW problem have been widely studied, a duality theory and fundamental statistical questions concerning empirical convergence rates remained obscure. This work closes these gaps for the quadratic GW distance over Euclidean spaces of different…

可微 Hilbert 空间值参数的一步估计AI 解读

rate estimators and corresponding confidence sets. These estimators correspond to generalizations of cross-fitted one-step estimators based on Hilbert-valued efficient influence functions. We give theoretical guarantees even when arbitrary estimators of nuisance functions are used, including those based on machine learning techniques. We show that these results naturally extend to Hilbert spaces that lack a reproducing kernel, as long as the parameter has an efficient…

长宽比发散时低秩矩阵估计的基本极限AI 解读

We consider the problem of estimating the factors of a low-rank n×d matrix, when this is corrupted by additive Gaussian noise. A special example of our setting corresponds to clustering mixtures of Gaussians with equal (known) covariances. Simple spectral methods do not take into account the distribution of the entries of these factors and are therefore often suboptimal. Here, we characterize the asymptotics of the minimum estimation error under the assumption that the…

高斯变分推断的近似精度AI 解读

The main computational challenge in Bayesian inference is to compute integrals against a high-dimensional posterior distribution. In the past decades, variational inference (VI) has emerged as a tractable approximation to these integrals, and a viable alternative to the more established paradigm of Markov chain Monte Carlo. However, little is known about the approximation accuracy of VI. In this work, we bound the TV error and the mean and covariance approximation error of…

高维函数型时间序列中结构突变的检测与估计AI 解读

We consider detecting and estimating breaks in heterogenous mean functions of high-dimensional functional time series which are allowed to be cross-sectionally correlated. A new test statistic combining the functional CUSUM statistic and power enhancement component is proposed with asymptotic null distribution comparable to the conventional CUSUM theory derived for a single functional time series. In particular, the extra power enhancement component enlarges the region where…

多值处理效应的高维模型辅助推断AI 解读

Consider estimation of average treatment effects with multi-valued treatments using augmented inverse probability weighted (IPW) estimators, depending on outcome regression and propensity score models in high-dimensional settings. These regression models are often fitted by regularized likelihood-based estimation, while ignoring how the fitted functions are used in the subsequent inference about the treatment parameters. Such separate estimation can be associated with known…

样本选择下的异质处理效应界：社交媒体与政治极化应用AI 解读

We propose a method for estimation and inference for bounds for heterogeneous causal effect parameters in general sample selection models where the treatment can affect whether an outcome is observed and no exclusion restrictions are available. The method provides conditional effect bounds as functions of policy relevant pre-treatment variables. It allows for conducting valid statistical inference on the unidentified conditional effects. We use a flexible debiased/double…

高维面板数据模型的 GMM 估计AI 解读

In this paper, we study a class of high dimensional moment restriction panel data models with interactive effects, where the factors are unobserved and these factor loadings are nonparametrically unknown smooth functions of individual characteristic variables. We allow the dimension of the parameter vector and the number of moment conditions to diverge with the sample size. This is a very general framework and is closely related to many existing linear and nonlinear panel…

马丁努森对《因果模型的参数化与模拟》的讨论AI 解读

I congratulate the authors on an interesting and useful contribution to the literature on causal inference. The authors propose a nice way of generating data so that a given causal structure of interest is preserved. This is a handy tool to have when for instance one needs to generate data to investigate small sample performance of a new inference procedure. I find it less attractive to use the suggested procedure for estimation purposes as is also alluded to in the paper…

摘要暂缺

电子健康记录中的树引导稀有特征选择与逻辑聚合AI 解读

Statistical learning with a large number of rare binary features is commonly encountered in analyzing electronic health records (EHR) data, especially in the modeling of disease onset with prior medical diagnoses and procedures. Dealing with the resulting highly sparse and large-scale binary feature matrix is notoriously challenging as conventional methods may suffer from a lack of power in testing and inconsistency in model fitting, while machine learning methods may suffer…

复杂振荡时间序列的频率检测与变点估计AI 解读

We consider detecting the evolutionary oscillatory pattern of a signal when it is contaminated by nonstationary noises with complexly time-varying data generating mechanism. A high-dimensional dense progressive periodogram test is proposed to accurately detect all oscillatory frequencies. A further phase-adjusted local change point detection algorithm is applied in the frequency domain to detect the locations at which the oscillatory pattern changes. Our method is shown to…

高维数据的渐近分布无关独立性检验AI 解读

Test of independence is of fundamental importance in modern data analysis, with broad applications in variable selection, graphical models, and causal inference. When the data is high dimensional and the potential dependence signal is sparse, independence testing becomes very challenging without distributional or structural assumptions. In this paper, we propose a general framework for independence testing by first fitting a classifier that distinguishes the joint and…

理想的贝叶斯局部自适应AI 解读

Many real-life applications involve estimation of curves that exhibit complicated shapes including jumps or varying-frequency oscillations. Practical methods have been devised that can adapt to a locally varying complexity of an unknown function (e.g. variable-knot splines, sparse wavelet reconstructions, kernel methods or trees/forests). However, the overwhelming majority of existing asymptotic minimaxity theory is predicated on homogeneous smoothness assumptions. Focusing…

密度估计的平滑惩罚反卷积方法AI 解读

This article addresses the deconvolution problem of estimating a square-integrable probability density from observations contaminated with additive measurement errors having a known density. The estimator begins with a density estimate of the contaminated observations and minimizes a reconstruction error penalized by an integrated squared mth derivative. Theory for deconvolution has mainly focused on kernel- or wavelet-based techniques, but other methods including…

高维贝叶斯模型的稳健留一交叉验证AI 解读

Leave-one-out cross-validation (LOO-CV) is a popular method for estimating out-of-sample predictive accuracy. However, computing LOO-CV criteria can be computationally expensive due to the need to fit the model multiple times. In the Bayesian context, importance sampling provides a possible solution but classical approaches can easily produce estimators whose asymptotic variance is infinite, making them potentially unreliable. Here we propose and analyze a novel mixture…