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马尔可夫链混合模型中最优匹配聚类的一致性AI 解读

We study clustering of categorical sequences using the Optimal Matching (OM) distance under finite mixtures of finite-state Markov chains. We show that the normalized OM distance between two independent chains converges almost surely to a deterministic population quantity, concentrates exponentially around its finite-horizon mean, and admits an $O(\sqrt{\log n/n})$ convergence rate when the two chains have the same transition kernel. These population quantities yield a…

连接局部与总体因果效应：近端工具变量方法AI 解读

Instrumental variable (IV) methods address treatment endogeneity, but with non-compliance and heterogeneous treatment effects a binary instrument generally identifies the local average treatment effect (LATE) among compliers rather than the population average treatment effect (ATE). When treatment effects and compliance probabilities are heterogeneous and dependent through latent factors, the ATE need not be identified by IV variation alone. We develop a proximal…

目标函数平衡：利用策略性不平衡估计因果效应AI 解读

When estimating the average treatment effect of a binary intervention with weights, investigators are often burdened with how best to leave imbalance in the distributions of observed covariates. This requires that investigators proceed cautiously, as imbalance in key (nonlinear transformations of) covariates potentially introduces bias into the ultimate estimated effect. This paper introduces Targeted Function Balancing (TFB), a flexible covariate balancing weights approach…

随机特征方法与神经网络的平滑差异原则AI 解读

We study data-driven early stopping for spectral regularisation methods in the classical non-parametric regression setting. Building on the discrepancy principle, we propose a multi-scale stopping rule that applies to general kernel estimators and show that, unlike previous approaches, it achieves full adaptivity over all smoothness levels in the well-specified case. A key contribution of our work is an extension based on random feature approximations, which reduces…

时间序列中的条件独立检验AI 解读

We consider the problem of testing Granger causality in time series, specifically, whether the future outcome $Y_{t+1}$ and the exposure history $\bar X_t$ are conditionally independent given the history of $\bar Y_t$ and a set of confounding variables $\bar Z_t$ up to time $t$. This testing procedure distinguishes true causal effects from associations driven by common external processes, supporting reliable decision-makings in applications such as finance, neuroscience, and…

Lévy 噪声下广义朗之万方程的历史条件化记忆与随机驱动推断AI 解读

We consider the identification of memory and stochastic forcing in a one-dimensional generalized Langevin equation with state-dependent Brownian noise and optional additive symmetric $α$-stable jumps. A finite-dimensional Markov embedding provides Kramers--Moyal conditional moment relations that separate memory drift, Brownian diffusion, and jump contributions. From increment ensembles conditioned on the observed velocity history, truncated statistics estimate the stable…

超越线性：多值处理污染偏误的半参数解决方案AI 解读

We examine semiparametric solutions to contamination bias for nonbinary treatments. Deepening the discussion by Goldsmith-Pinkham et al. (2024), we detail how spline functions approximate conditional expectation and propensity score functions under weak functional-form assumptions. Reanalyzing 18 regressions across 11 studies, we compare standard linear regressions against parametric and semiparametric versions of three contamination-robust estimators. We document large…

向量值核岭回归的稳健误差界AI 解读

While kernel-based learning methods for scalar-valued functions have been extensively studied, comparatively little work considers nonlinear vector-valued operators. Such operators with vector-valued outputs, e.g., state vectors and trajectories, commonly arise in system identification problems. In this paper, we study the problem of learning a vector-valued operator under the framework of vector-valued kernel ridge regression. We assume that the outputs take values in an…

审查员工具变量设计的局部稳健半参数方法AI 解读

I propose a locally robust semiparametric framework for estimating causal effects using examiner IV designs when adjustment for many or continuous covariates makes saturation infeasible or produces sparse cells. The key ingredient of this approach is an orthogonal moment function that removes the first-order effect of estimation errors in the two treatment regressions defining the examiner IV. I derive the orthogonal moment function and show that it remains valid under…

生存治疗效应的有效迁移与推广AI 解读

Randomized controlled trials provide internally valid estimates of treatment effects, but their results may not directly apply to broader target populations due to differences in baseline covariate distributions, adherence to treatment or variations in outcome mechanisms. Under standard transport and time-to-event identifiability assumptions, we develop nonparametric, debiased machine learning estimators for transporting and generalizing causal survival treatment effect…

正则化似然反卷积与后验密度重构AI 解读

Density deconvolution is an ill-posed inverse problem because recovering the latent density amplifies high-frequency variation in the observed data. We propose a two-stage likelihood procedure. The first estimator maximizes the convolution likelihood over a regularized Gaussian-mixture sieve; the second treats this fit as an empirical prior and averages the fitted conditional latent densities. Under fixed-model misspecification, the estimators generally have different…

有限状态嵌套 Markov 模型的递归头几何与无序有效推断AI 解读

Exploiting the equality restrictions that nested Markov models encode requires their tangent-space geometry. For strictly positive finite-state models on arbitrary acyclic directed mixed graphs (ADMGs), we differentiate the recursive-head chart and prove that the range of its score map is the full tangent space. Intrinsic-set coordinate blocks form an algebraic direct sum, blocks of distinct districts are orthogonal, and the resulting Gram projection needs neither…

单调序贯随机缺失下的有效估计与完整案例粗化成本AI 解读

Complete-case coarsening discards observed confounder values from partially complete records. We study its consequences for average treatment effect estimation with two ordered, partially observed confounders under monotone sequential missing at random. We specialize the standard coarsening-at-random transformation to the causal influence function, establish the canonical gradient, and give an exact drift identity for a cross-fitted estimator with sequential multiple…

动态选择下的因果推断：时变协变量与潜在异质性AI 解读

I study dynamic treatment effects in panel data under staggered adoption when treatment timing depends jointly on unobserved time-invariant heterogeneity and time-varying pretreatment covariates, including lagged outcomes. Untreated potential outcomes follow a nonparametric dynamic panel model that allows flexible interactions between time-varying covariates and latent heterogeneity. I use pretreatment outcome histories to find individuals with similar time-invariant latent…

通过变换后的低秩分位数曲面发现因果方向AI 解读

We propose Low-Rank Quantile Surfaces (LRQS), a bivariate causal model in which, in the causal direction, an unknown monotone transformation of the conditional quantile surface admits a low-rank functional decomposition. LRQS subsumes location-scale noise models and post-nonlinear heteroscedastic noise models, while allowing multiple quantile bases to represent changes beyond location-scale effects. We prove generic identifiability of LRQS: the transformed quantile surface…

生成式人工智能辅助的非结构化数据动态因果推断AI 解读

A growing number of scholars seek to estimate causal effects of unstructured data such as text, images, and video. However, existing methods typically treat each object as a single, static observation. We develop a statistical framework for dynamic causal inference with unstructured data by leveraging generative artificial intelligence (GenAI) models. Our approach enables researchers to estimate the causal effects of sequences of treatment features, including their positions…

非参数贝叶斯政策学习AI 解读

I propose Nonparametric Bayesian Policy Learning (NBPL) as a framework for uncertainty-aware treatment choice. The key observation is that welfare is fully determined by a reduced-form distribution, so uncertainty about optimal policies entirely reflects uncertainty about this distribution. NBPL places a Dirichlet process prior on the reduced-form distribution and uses the resulting posterior for both traditional policy choice and inference on optimal welfare and optimal…

风险比较定理及其在扩散系数深度学习中的应用AI 解读

We investigate the nonparametric estimation of the diffusion matrix in stochastic differential equations featuring multidimensional, strong mixing covariate processes. We propose a flexible statistical framework based on general function classes that does not require a linear basis representation, rendering our results directly applicable to deep neural network estimators. Our approach employs a two-step estimation procedure: constructing a preliminary nonparametric…

非可分双边关系回归AI 解读

This paper studies a nonseparable model for dyadic outcomes, such as bilateral trade flows, in which the outcome depends on both agents' characteristics and on a scalar unobservable through an unknown function increasing in that unobservable. I establish identification of a normalized structural function and the error distribution, propose kernel plug-in estimators, and derive a two-regime central limit theory under dyadic dependence in which a shared-agent variance…

布尔超立方体上的可分辨傅里叶阶数与极小极大估计AI 解读

We study high-dimensional nonparametric regression on the Boolean hypercube \(\{0,1\}^d\), from a sample of size \(n\), under a Fourier--Sobolev budget, i.e., a bound \(B\) on the total quadratic influence of the regression function. The central object is the resolvable Fourier degree \(D^*(d,n)\), defined as the largest interaction order \(D\) such that the dimension of the degree-\(D\) Fourier--Walsh space does not exceed \(n\). We prove that the minimax risk over…

一般干扰下分位数暴露效应的设计型估计与推断AI 解读

Many applications in public health, environmental science, and economics feature spillovers across connected units, violating the Stable Unit Treatment Value Assumption (SUTVA) underlying classical quantile treatment effect methods. We develop a general framework for defining, estimating, and conducting inference for quantile exposure effects (QEEs) under network interference, encompassing quantile direct and spillover effects as leading cases. Studying QEEs under…

基于统计微分方案的抗噪声惩罚算子AI 解读

Classical approaches to penalized smoothing often rely on basis or kernel expansions, which constrain the estimator to a fixed span and may be restrictive for discretely observed data. We instead regularize a single noisy trajectory directly on its observation grid, using difference operators that remain genuine finite-difference approximations to derivatives while being statistically normalized and mutually decorrelated under a reference noise law. We extend this…

Banach 空间中含测量误差的非参数回归AI 解读

We consider nonparametric regression with a Banach-space-valued predictor where the covariate takes values in a general separable Banach space. Our primary objective is to develop a unified framework for estimating the regression operator without relying on an inner-product structure, thereby extending classical and functional nonparametric regression beyond Euclidean and Hilbert spaces in the presence of measurement error. We establish the fundamental properties of the…

超越平均处理效应的最优协变量调整：已处理人群与重叠加权目标AI 解读

Graphical causal inference supplies a complete theory of efficient covariate adjustment for the average treatment effect: one adjustment set, computable from the graph, is optimal under every compatible distribution. We show that this is a property of the average treatment effect's inverse-prevalence weights, not of causal estimands in general. For the average treatment effect on the treated we index the efficiency bound by the adjustment set and derive exact identities for…