Estimates of causal parameters such as conditional average treatment effects
and conditional quantile treatment effects play an important role in real-world
decision making. Given this importance, one should ensure these estimators are
calibrated. While there is a rich literature on calibrating estimators of
non-causal parameters, very few methods have been derived for calibrating
estimators of causal parameters, or more generally estimators of quantities
involving nuisance parameters.
In this work, we provide a general framework for calibrating predictors
involving nuisance estimation. We consider a notion of calibration defined with
respect to an arbitrary, nuisance-dependent loss $\ell$, under which we say an
estimator $\theta$ is calibrated if its predictions cannot be changed on any
level set to decrease loss. We prove generic upper bounds on the calibration
error of any causal parameter estimate $\theta$ with respect to any loss $\ell$
using a concept called Neyman Orthogonality. Our bounds involve two decoupled
terms - one measuring the error in estimating the unknown nuisance parameters,
and the other representing the calibration error in a hypothetical world where
the learned nuisance estimates were true. We use our bound to analyze the
convergence of two sample splitting algorithms for causal calibration. One
algorithm, which applies to universally orthogonalizable loss functions,
transforms the data into generalized pseudo-outcomes and applies an
off-the-shelf calibration procedure. The other algorithm, which applies to
conditionally orthogonalizable loss functions, extends the classical uniform
mass binning algorithm to include nuisance estimation. Our results are
exceedingly general, showing that essentially any existing calibration
algorithm can be used in causal settings, with additional loss only arising
from errors in nuisance estimation.

本文提供了一个通用框架，用于校准涉及干扰估计的预测器，并使用所谓的 Neyman 正交概念证明了对于任意损失函数，任何因果参数估计的校准误差上界，进而分析了两种样本分割算法在因果校准中的收敛性。

正交因果校准

Orthogonal Causal Calibration

Linear structural equation models represent direct causal effects as directed
edges and confounding factors as bidirected edges. An open problem is to
identify the causal parameters from correlations between the nodes. We
investigate models, whose directed component forms a tree, and show that there,
besides classical instrumental variables, missing cycles of bidirected edges
can be used to identify the model. They can yield systems of quadratic
equations that we explicitly solve to obtain one or two solutions for the
causal parameters of adjacent directed edges. We show how multiple missing
cycles can be combined to obtain a unique solution. This results in an
algorithm that can identify instances that previously required approaches based
on Gröbner bases, which have doubly-exponential time complexity in the number
of structural parameters.

本文研究线性结构方程模型，提出一种利用缺失的双向边识别模型因果参数的算法，并展示了如何组合多个缺失的环来获得唯一解。

树形线性因果模型中的识别

Identification in Tree-shaped Linear Structural Causal Models

We consider the problem of predicting a response variable from a set of
covariates on a data set that differs in distribution from the training data.
Causal parameters are optimal in terms of predictive accuracy if in the new
distribution either many variables are affected by interventions or only some
variables are affected, but the perturbations are strong. If the training and
test distributions differ by a shift, causal parameters might be too
conservative to perform well on the above task. This motivates anchor
regression, a method that makes use of exogeneous variables to solve a
relaxation of the causal minimax problem by considering a modification of the
least-squares loss. The procedure naturally provides an interpolation between
the solutions of ordinary least squares and two-stage least squares. We prove
that the estimator satisfies predictive guarantees in terms of distributional
robustness against shifts in a linear class; these guarantees are valid even if
the instrumental variables assumptions are violated. If anchor regression and
least squares provide the same answer (anchor stability), we establish that OLS
parameters are invariant under certain distributional changes. Anchor
regression is shown empirically to improve replicability and protect against
distributional shifts.

本文研究了在训练数据与测试数据分布不同的情况下，利用 anchor regression 方法通过使用外生变量来预测响应变量，并提高其可复现性和分布鲁棒性。

锚定回归：异质数据迎接因果关系

Anchor regression: heterogeneous data meets causality

Most modern supervised statistical/machine learning (ML) methods are
explicitly designed to solve prediction problems very well. Achieving this goal
does not imply that these methods automatically deliver good estimators of
causal parameters. Examples of such parameters include individual regression
coefficients, average treatment effects, average lifts, and demand or supply
elasticities. In fact, estimates of such causal parameters obtained via naively
plugging ML estimators into estimating equations for such parameters can behave
very poorly due to the regularization bias. Fortunately, this regularization
bias can be removed by solving auxiliary prediction problems via ML tools.
Specifically, we can form an orthogonal score for the target low-dimensional
parameter by combining auxiliary and main ML predictions. The score is then
used to build a de-biased estimator of the target parameter which typically
will converge at the fastest possible 1/root(n) rate and be approximately
unbiased and normal, and from which valid confidence intervals for these
parameters of interest may be constructed. The resulting method thus could be
called a "double ML" method because it relies on estimating primary and
auxiliary predictive models. In order to avoid overfitting, our construction
also makes use of the K-fold sample splitting, which we call cross-fitting.
This allows us to use a very broad set of ML predictive methods in solving the
auxiliary and main prediction problems, such as random forest, lasso, ridge,
deep neural nets, boosted trees, as well as various hybrids and aggregators of
these methods.

本文提出了一种新方法，双重机器学习 (Double ML)，用于解决因变量的原因关系，利用多种主要和辅助机器学习预测模型解决辅助和主关键参数预测，通过 K 折采样交叉拟合解决过拟合问题。