每日简报

核模型中的特征学习理论AI 解读

We study feature learning in a compositional variant of kernel ridge regression in which the predictor is applied to a learnable linear transformation of the input. When the response depends on the input only through a low-dimensional predictive subspace, we show that all global minimizers of the population objective for the linear transformation annihilate directions orthogonal to this subspace, and in certain regimes, exactly identify the subspace. Moreover, we show that…

扰动双重机器学习：超越参数化长度的非标准推断AI 解读

We study inference on a low-dimensional functional $β$ in the presence of infinite-dimensional nuisance parameters. Classical inferential methods are typically based on Wald intervals, whose large-sample validity rests on asymptotic negligibility of nuisance error; for example, influence-curve based estimators (Double/Debiased Machine Learning, DML) are asymptotically Gaussian when nuisance estimators converge faster than $n^{-1/4}$. Although such negligibility can hold even…

变量选择错误发现率的估计AI 解读

We introduce a generic estimator for the false discovery rate of any model selection procedure, in common statistical modeling settings including the Gaussian linear model, Gaussian graphical model, and model-X setting. We prove that our method has a conservative (non-negative) bias in finite samples under standard statistical assumptions, and provide a bootstrap method for assessing its standard error. For methods like the Lasso, forward-stepwise regression, and the…

高维线性回归中的参数化平均场经验贝叶斯AI 解读

In this paper, we consider the problem of parametric empirical Bayes estimation of an i.i.d. prior in high-dimensional Bayesian linear regression, with random design. We obtain the asymptotic distribution of the variational Empirical Bayes (vEB) estimator, which approximately maximizes a variational lower bound of the intractable marginal likelihood. We characterize a sharp phase transition behavior for the vEB estimator -- namely that it is information theoretically optimal…

面向 f-散度正则化上下文赌博机的离线策略学习精确分析AI 解读

Many offline reinforcement learning algorithms are underpinned by $f$-divergence regularization, but their sample complexity *defined with respect to regularized objectives* still lacks tight analyses, especially in terms of concrete data coverage conditions. In this paper, we study the exact concentrability requirements to achieve the $\tildeΘ(ε^{-1})$ sample complexity for offline $f$-divergence-regularized contextual bandits. For reverse Kullback-Leibler (KL) divergence,…

Jacobi 先验：一种替代性的贝叶斯监督学习方法AI 解读

The Jacobi prior offers an alternative Bayesian framework, designed to achieve superior computational efficiency without compromising predictive performance. Compared to widely used methods such as Lasso, Ridge, Elastic Net, uniLasso, the MCMC-based Horseshoe prior, and non-Bayesian machine learning methods including Support Vector Machines (SVM), Random Forests, and Extreme Gradient Boosting (XGBoost), the Jacobi prior achieves competitive or better accuracy with…

平滑样条 ANOVA 模型中导数的估计与假设检验AI 解读

Within the framework of smoothing spline ANOVA, we propose a plug-in kernel ridge regression estimator to estimate the derivatives of the underlying multivariate regression function. We first establish an $L_\infty$ convergence rate of the proposed estimator under general random designs. When the covariates are uniformly distributed, we provide a in-depth analysis that includes a sharp upper bound and the minimax lower bound of the $L_2$ convergence rate. Additionally,…

数据驱动的误差估计：无需输入函数类复杂度的超额风险界AI 解读

Constructing confidence intervals that are simultaneously valid across a class of estimates is central to tasks such as multiple mean estimation, generalization guarantees, and adaptive experimental design. We frame this as an ``error estimation problem," where the goal is to determine a high-probability upper bound on the maximum error for a class of estimates. We propose an entirely data-driven approach that derives such bounds for both finite and infinite class settings,…

面板数据的反事实预测AI 解读

We address the challenge of forecasting counterfactual outcomes in a panel data with missing entries and temporally dependent latent factors -- a common scenario in causal inference, where estimating unobserved potential outcomes ahead of time is essential. We propose Forecasting Counterfactuals under Stochastic Dynamics (FOCUS), a method that extends traditional matrix completion methods by leveraging time series dynamics of the factors, thereby enhancing the prediction…

差异性死亡或退出下既往事件率比方法的表现AI 解读

Purpose: Prior event rate ratio (PERR) method was proposed to control for measured or unmeasured confounders in real-world evaluation of effectiveness and safety of medical treatments using electronic medical records data. A widely cited simulation study showed that PERR estimate of treatment effect was biased in the presence of differential morality/dropout. However, the study only considered one specific PERR estimator of treatment effect and one specific scenario of…

事件时间过程中校准缩放干预的因果推断AI 解读

This work develops a flexible inferential framework for nonparametric causal inference in time-to-event settings, based on stochastic interventions defined through multiplicative scaling of the intensity governing an intermediate event process. These interventions induce a family of estimands indexed by a scalar parameter α, representing effects of modifying event rates while preserving the temporal and covariate-dependent structure of the observed data generating mechanism.…

有限混合模型的偏差缩减估计及面板潜在组结构应用AI 解读

Finite mixture models are widely used in econometric analyses to capture unobserved heterogeneity. This paper shows that maximum likelihood estimation of finite mixtures of parametric densities can suffer from substantial finite-sample bias in all parameters under mild regularity conditions. The bias arises from the influence of outliers in component densities with unbounded or large support and increases with the degree of overlap among mixture components. I show that…

依赖时间序列的条件极值估计AI 解读

We study the consistency and weak convergence of the conditional tail function and conditional Hill estimators under broad dependence assumptions for a heavy-tailed response sequence and a covariate sequence. Consistency is established under $α$-mixing, while asymptotic normality follows from $β$-mixing and second-order conditions. A key aspect of our approach is its versatile functional formulation in terms of the conditional tail process. Simulations demonstrate its…

弱因子究竟有多弱？信号加噪声模型中信号强度的统一推断AI 解读

The paper analyzes four classical signal-plus-noise models: the factor model, spiked sample covariance matrices, the sum of a Wigner matrix and a low-rank perturbation, and canonical correlation analysis with low-rank dependencies. The objective is to construct confidence intervals for the signal strength that are uniformly valid across all regimes - strong, weak, and critical signals. We demonstrate that traditional Gaussian approximations fail in the critical regime.…

理性预期下具有异质同伴效应的计数数据模型AI 解读

This paper develops a peer effect model for count responses under rational expectations. The model accounts for heterogeneity in peer effects across groups based on observed characteristics. Identification is based on the linear model condition that requires the presence of friends of friends who are not direct friends. I show that this identification condition extends to a broad class of nonlinear models. Parameters are estimated using a nested pseudo-likelihood approach.…

基于张量数据的扩散指数预测AI 解读

In this paper, we consider diffusion index forecasting with both tensor and non-tensor predictors, where the tensor structure is preserved with a Canonical Polyadic (CP) tensor factor model. When the number of non-tensor predictors is small, we study the asymptotic properties of the least squares estimator in this tensor factor-augmented regression, allowing for factors with different strengths. We derive an analytical formula for prediction intervals that accounts for the…

适用于名义尺度随机变量的相关系数AI 解读

This paper develops an intuitive concept of perfect dependence between two variables of which at least one has a nominal scale. Perfect dependence is attainable for all marginal distributions. It furthermore proposes a set of dependence measures that are 1 if and only if this perfect dependence is satisfied. The advantages of these dependence measures relative to classical dependence measures like contingency coefficients, Goodman-Kruskal's lambda and tau and the so-called…

带业务约束的增量效应定向：营销策略的因果优化框架AI 解读

This paper introduces a marketing decision framework that optimizes customer targeting by integrating heterogeneous treatment effect estimation with explicit business guardrails. The objective is to maximize revenue and retention while adhering to constraints such as budget, revenue protection, and customer experience. The framework first estimates Conditional Average Treatment Effects (CATE) using uplift learners, then solves a constrained allocation problem to decide whom…

比较敏感性参数的公理化方法AI 解读

Many methods are available for assessing the importance of omitted variables in linear regression. These methods typically make different, non-falsifiable assumptions. Hence the data alone cannot tell us which method is most appropriate. Since it is unreasonable to expect results to be robust against all possible robustness checks, researchers often use methods deemed ``interpretable,'' a subjective criterion with no formal definition. In contrast, we develop the first…

利用有效工具变量与机器学习推断异质处理效应AI 解读

We introduce a new instrumental variable (IV) estimator for heterogeneous treatment effects in the presence of endogeneity. Our estimator is based on double/debiased machine learning (DML) and uses efficient machine learning instruments (MLIV) and kernel smoothing. We prove consistency and asymptotic normality of our estimator and also construct confidence sets that are more robust towards weak IV. Along the way, we also provide an accessible discussion of the corresponding…

因果推断中的分布平衡：基于特征函数距离的统一框架AI 解读

Weighting methods are essential tools for estimating causal effects in observational studies, with the goal of balancing pre-treatment covariates across treatment groups. Traditional approaches pursue this objective indirectly, for example, via inverse propensity score weighting or by matching a finite number of covariate moments, and therefore do not guarantee balance of the full joint covariate distributions. Recently, distributional balancing methods have emerged as…

面板数据中集约边际效应的估计AI 解读

Many policies operate through two different channels: the extensive margin (e.g., the decision to participate) and the intensive margin (e.g., the intensity of the response among participants). This paper develops a novel identification strategy to estimate the intensive margin effect in panel data settings. I adapt the Horowitz-Manski-Lee bounds to the Changes-in-Changes framework to partially identify both the average and quantile intensive margin treatment effects.…

缺少干预前时期的面板数据因果融合AI 解读

Traditional panel-data causal inference frameworks, such as difference-in-differences and synthetic control methods, rely on pre-intervention data to estimate counterfactual means. However, such data may be unavailable in real-world settings when interventions are implemented in response to sudden events, such as public health crises or epidemiological shocks. In this paper, we introduce two data-fusion methods for causal inference from panel data in scenarios where…

一般工具变量下因果效应的识别与去偏学习AI 解读

Instrumental variable methods are fundamental to causal inference when treatment assignment is confounded by unobserved variables. In this article, we develop a general nonparametric causal framework for identification and learning with multi-categorical or continuous instrumental variables. Specifically, the mean potential outcomes and the average treatment effect can be identified via a regular weighting function derived from the proposed framework. Leveraging…