Causal inference from observational data has recently found many applications
in machine learning. While sound and complete algorithms exist to compute
causal effects, many of these algorithms require explicit access to conditional
likelihoods over the observational distribution, which is difficult to estimate
in the high-dimensional regime, such as with images. To alleviate this issue,
researchers have approached the problem by simulating causal relations with
neural models and obtained impressive results. However, none of these existing
approaches can be applied to generic scenarios such as causal graphs on image
data with latent confounders, or obtain conditional interventional samples. In
this paper, we show that any identifiable causal effect given an arbitrary
causal graph can be computed through push-forward computations of conditional
generative models. Based on this result, we devise a diffusion-based approach
to sample from any (conditional) interventional distribution on image data. To
showcase our algorithm's performance, we conduct experiments on a Colored MNIST
dataset having both the treatment ($X$) and the target variables ($Y$) as
images and obtain interventional samples from $P(y|do(x))$. As an application
of our algorithm, we evaluate two large conditional generative models that are
pre-trained on the CelebA dataset by analyzing the strength of spurious
correlations and the level of disentanglement they achieve.

通过条件生成模型的向前推导计算，我们展示了对于任意可识别因果效应的计算。基于此结果，我们设计了一种扩散基础的方法，在图像数据上从任意（条件）干预分布中采样。作为算法的应用，我们通过分析虚假相关性的强度和解耦的水平，对预先在 CelebA 数据集上训练的两个大型条件生成模型进行了评估。

条件生成模型足以从任何因果效应估计中进行抽样

Conditional Generative Models are Sufficient to Sample from Any Causal  Effect Estimand

We study the problem of efficiently estimating the effect of an intervention
on a single variable (atomic interventions) using observational samples in a
causal Bayesian network. Our goal is to give algorithms that are efficient in
both time and sample complexity in a non-parametric setting.
Tian and Pearl (AAAI `02) have exactly characterized the class of causal
graphs for which causal effects of atomic interventions can be identified from
observational data. We make their result quantitative. Suppose P is a causal
model on a set $\vec{V}$ of n observable variables with respect to a given
causal graph G with observable distribution $P$. Let $P_x$ denote the
interventional distribution over the observables with respect to an
intervention of a designated variable X with x. Assuming that $G$ has bounded
in-degree, bounded c-components ($k$), and that the observational distribution
is identifiable and satisfies certain strong positivity condition, we give an
algorithm that takes $m=\tilde{O}(n\epsilon^{-2})$ samples from $P$ and $O(mn)$
time, and outputs with high probability a description of a distribution
$\hat{P}$ such that $d_{\mathrm{TV}}(P_x, \hat{P}) \leq \epsilon$, and:
1. [Evaluation] the description can return in $O(n)$ time the probability
$\hat{P}(\vec{v})$ for any assignment $\vec{v}$ to $\vec{V}$
2. [Generation] the description can return an iid sample from $\hat{P}$ in
$O(n)$ time.
We also show lower bounds for the sample complexity showing that our sample
complexity has an optimal dependence on the parameters $n$ and $\epsilon$, as
well as if $k=1$ on the strong positivity parameter.

本文研究使用因果贝叶斯网络中的观测样本有效估计单一变量干预效应的问题，并给出了高效的时间与样本复杂度算法。