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Instrumental Variables in Causal Inference and Machine Learning: A Survey

因果推断与机器学习中的工具变量:综述

Causal inference is the process of using assumptions, study designs, and estimation strategies to draw conclusions about the causal relationships between variables based on data. This allows researchers to better understand the underlying mechanisms at work in complex systems and make more informed decisions. In many settings, we may not fully observe all the confounders that affect both the treatment and outcome variables, complicating the estimation of causal effects. To…

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Hybrid Censored Quantile Regression Forest to Assess the Heterogeneous Effects

用于评估异质性效应的混合删失分位数回归森林

In many applications, heterogeneous treatment effects on a censored response variable are of primary interest, and it is natural to evaluate the effects at different quantiles (e.g., median). The large number of potential effect modifiers, the unknown structure of the treatment effects, and the presence of right censoring pose significant challenges. In this paper, we develop a hybrid forest approach called Hybrid Censored Quantile Regression Forest (HCQRF) to assess the…

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Double Robustness for Complier Parameters and a Semiparametric Test for Complier Characteristics

服从者参数的双重稳健性与服从者特征的半参数检验

We propose a semiparametric test to evaluate (i) whether different instruments induce subpopulations of compliers with the same observable characteristics on average, and (ii) whether compliers have observable characteristics that are the same as the full population on average. The test is a flexible robustness check for the external validity of instruments. We use it to reinterpret the difference in LATE estimates that Angrist and Evans (1998) obtain when using different…

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Robust Inference in High Dimensional Linear Model with Cluster Dependence

聚类依赖下高维线性模型的稳健推断

Cluster standard error (Liang and Zeger, 1986) is widely used by empirical researchers to account for cluster dependence in linear model. It is well known that this standard error is biased. We show that the bias does not vanish under high dimensional asymptotics by revisiting Chesher and Jewitt (1987)'s approach. An alternative leave-cluster-out crossfit (LCOC) estimator that is unbiased, consistent and robust to cluster dependence is provided under high dimensional setting…

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Estimation and Inference on Heterogeneous Treatment Effects in High-Dimensional Dynamic Panels under Weak Dependence

弱依赖下高维动态面板异质处理效应的估计与推断

This paper provides estimation and inference methods for a conditional average treatment effects (CATE) characterized by a high-dimensional parameter in both homogeneous cross-sectional and unit-heterogeneous dynamic panel data settings. In our leading example, we model CATE by interacting the base treatment variable with explanatory variables. The first step of our procedure is orthogonalization, where we partial out the controls and unit effects from the outcome and the…

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What Makes A Good Fisherman? Linear Regression under Self-Selection Bias

怎样才算好渔夫?自选择偏差下的线性回归

In the classical setting of self-selection, the goal is to learn $k$ models, simultaneously from observations $(x^{(i)}, y^{(i)})$ where $y^{(i)}$ is the output of one of $k$ underlying models on input $x^{(i)}$. In contrast to mixture models, where we observe the output of a randomly selected model, here the observed model depends on the outputs themselves, and is determined by some known selection criterion. For example, we might observe the highest output, the smallest…

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Estimation and Application of the Convergence Bounds for Nonlinear Markov Chains

非线性马尔可夫链收敛界的估计与应用

Nonlinear Markov Chains (nMC) are regarded as the original (linear) Markov Chains with nonlinear small perturbations. It fits real-world data better, but its associated properties are difficult to describe. A new approach is proposed to analyze the ergodicity and even estimate the convergence bounds of nMC, which is more precise than existing results. In the new method, Coupling Markov about homogeneous Markov chains is applied to reconstitute the relationship between…

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Individual causal effects from observational longitudinal studies with time-varying exposures

时变暴露观测性纵向研究中的个体因果效应

Causal effects may vary among individuals and can even be of opposite signs. When significant effect heterogeneity exists, the population average causal effect might be uninformative for an individual. Due to the fundamental problem of causality, individual causal effects (ICEs) cannot be retrieved from cross-sectional data. However, in crossover studies, it is accepted that ICEs can be estimated under the assumptions of no carryover effects and time invariance of potential…

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Power and Sample Size Calculations for Rerandomization

再随机化实验的功效与样本量计算

Power analyses are an important aspect of experimental design, because they help determine how experiments are implemented in practice. It is common to specify a desired level of power and compute the sample size necessary to obtain that power. Such calculations are well-known for completely randomized experiments, but there can be many benefits to using other experimental designs. For example, it has recently been established that rerandomization, where subjects are…

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Optimal Model Selection in RDD and Related Settings Using Placebo Zones

利用安慰剂区域优化断点回归及相关方法的模型选择

We propose a new model-selection algorithm for Regression Discontinuity Design, Regression Kink Design, and related IV estimators. Candidate models are assessed within a 'placebo zone' of the running variable, where the true effects are known to be zero. The approach yields an optimal combination of bandwidth, polynomial, and any other choice parameters. It can also inform choices between classes of models (e.g. RDD versus cohort-IV) and any other choices, such as…

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Semiparametric Distribution Regression with Instruments and Monotonicity

带工具变量与单调性约束的半参数分布回归

This paper proposes IV-based estimators for the semiparametric distribution regression model in the presence of an endogenous regressor, which are based on an extension of IV probit estimators. We discuss the causal interpretation of the estimators and two methods (monotone rearrangement and isotonic regression) to ensure a monotonically increasing distribution function. Asymptotic properties and simulation evidence are provided. An application to wage equations reveals…

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A Residuals-Based Nonparametric Variance Ratio Test for Cointegration

基于残差的非参数协整方差比检验

This paper derives asymptotic theory for Breitung's (2002, Journal of Econometrics 108, 343-363) nonparameteric variance ratio unit root test when applied to regression residuals. The test requires neither the specification of the correlation structure in the data nor the choice of tuning parameters. Compared with popular residuals-based no-cointegration tests, the variance ratio test is less prone to size distortions but has smaller local asymptotic power. However, this…

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Learning Instrumental Variable from Data Fusion for Treatment Effect Estimation

从数据融合中学习工具变量以估计处理效应

The advent of the big data era brought new opportunities and challenges to draw treatment effect in data fusion, that is, a mixed dataset collected from multiple sources (each source with an independent treatment assignment mechanism). Due to possibly omitted source labels and unmeasured confounders, traditional methods cannot estimate individual treatment assignment probability and infer treatment effect effectively. Therefore, we propose to reconstruct the source label and…

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A Gentle Introduction to Conformal Prediction and Distribution-Free Uncertainty Quantification

共形预测与无分布不确定性量化入门

Black-box machine learning models are now routinely used in high-risk settings, like medical diagnostics, which demand uncertainty quantification to avoid consequential model failures. Conformal prediction is a user-friendly paradigm for creating statistically rigorous uncertainty sets/intervals for the predictions of such models. Critically, the sets are valid in a distribution-free sense: they possess explicit, non-asymptotic guarantees even without distributional…

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Robust Orthogonal Machine Learning of Treatment Effects

处理效应的稳健正交机器学习

Causal learning is the key to obtaining stable predictions and answering \textit{what if} problems in decision-makings. In causal learning, it is central to seek methods to estimate the average treatment effect (ATE) from observational data. The Double/Debiased Machine Learning (DML) is one of the prevalent methods to estimate ATE. However, the DML estimators can suffer from an \textit{error-compounding issue} and even give extreme estimates when the propensity scores are…

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Local Quadratic Spectral and Covariance Matrix Estimation

局部二次谱密度矩阵与协方差矩阵估计

The problem of estimating the spectral density matrix $f(w)$ of a multivariate time series is revisited with special focus on the frequencies $w=0$ and $w=π$. Recognizing that the entries of the spectral density matrix at these two boundary points are real-valued, we propose a new estimator constructed from a local polynomial regression of the real portion of the multivariate periodogram. The case $w=0$ is of particular importance, since $f(0)$ is associated with the…

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Auxiliary Quantile Forecasting with Linear Networks

利用线性网络进行辅助分位数预测

We propose a novel multi-task method for quantile forecasting with shared Linear layers. Our method is based on the Implicit quantile learning approach, where samples from the Uniform distribution $\mathcal{U}(0, 1)$ are reparameterized to quantile values of the target distribution. We combine the implicit quantile and input time series representations to directly forecast multiple quantile estimations for multiple horizons jointly. Prior works have adopted a Linear layer…

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A Data Fusion Approach for Ride-sourcing Demand Estimation: A Discrete Choice Model with Sampling and Endogeneity Corrections

网约车需求估计的数据融合方法:带抽样和内生性校正的离散选择模型

Ride-sourcing services offered by companies like Uber and Didi have grown rapidly in the last decade. Understanding the demand for these services is essential for planning and managing modern transportation systems. Existing studies develop statistical models for ride-sourcing demand estimation at an aggregate level due to limited data availability. These models lack foundations in microeconomic theory, ignore competition of ride-sourcing with other travel modes, and cannot…

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Generalized Varying Coefficient Mediation Models

广义变系数中介模型

Motivated by an analysis of causal mechanism from economic stress to entrepreneurial withdrawals through depressed affect, we develop a two-layer generalized varying coefficient mediation model. This model captures the bridging effects of mediators that may vary with another variable, by treating them as smooth functions of this variable. It also allows various response types by introducing the generalized varying coefficient model in the first layer. The varying direct and…

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Nonparametric Group Variable Selection with Multivariate Response for Connectome-Based Modeling of Cognitive Scores

用于脑连接组认知评分建模的多元响应非参数组变量选择

In this article, we study association between the structural connectome and cognitive profiles using a multi-response nonparametric regression model.The cognitive profiles are measured in terms of seven age-adjusted cognitive test scores. The structural connectomes are represented by undirected graphs. The connectivity properties of these graphs are available in terms of the nodal attributes. A collection of nodal centralities together can encode different patterns of…

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Sentiment Analysis on Inflation after Covid-19

新冠疫情后的通胀情绪分析

We implement traditional machine learning and deep learning methods for global tweets from 2017-2022 to build a high-frequency measure of the public's sentiment index on inflation and analyze its correlation with other online data sources such as google trend and market-oriented inflation index. We use manually labeled trigrams to test the prediction performance of several machine learning models(logistic regression,random forest etc.) and choose Bert model for final…

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Predictive Quantile Regression with Mixed Roots and Increasing Dimensions: The ALQR Approach

混合根与维度增长下的预测分位数回归:ALQR 方法

In this paper we propose the adaptive lasso for predictive quantile regression (ALQR). Reflecting empirical findings, we allow predictors to have various degrees of persistence and exhibit different signal strengths. The number of predictors is allowed to grow with the sample size. We study regularity conditions under which stationary, local unit root, and cointegrated predictors are present simultaneously. We next show the convergence rates, model selection consistency, and…

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Variable elimination, graph reduction and efficient g-formula

变量消除、图约简与有效率的 g 公式

We study efficient estimation of an interventional mean associated with a point exposure treatment under a causal graphical model represented by a directed acyclic graph without hidden variables. Under such a model, it may happen that a subset of the variables are uninformative in that failure to measure them neither precludes identification of the interventional mean nor changes the semiparametric variance bound for regular estimators of it. We develop a set of graphical…

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Estimating Time-Varying Direct and Indirect Causal Excursion Effects with Longitudinal Binary Outcomes

纵向二元结局的时变直接与间接因果偏离效应估计

Construction of just-in-time adaptive interventions, such as prompts delivered by mobile apps to promote and maintain behavioral change, requires knowledge about time-varying moderated effects to inform when and how we deliver intervention options. Micro-randomized trials (MRT) have emerged as a sequentially randomized design to gather requisite data for effect estimation. The existing literature (Qian et al., 2020; Boruvka et al., 2018; Dempsey et al., 2020) has defined a…

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