Md Musfiqur Rahman

Md Musfiqur Rahman, Ziwei Jiang, Hilaf Hasson et al.

Causal inference from observational data provides strong evidence for the best action in decision-making without performing expensive randomized trials. The effect of an action is usually not identifiable under unobserved confounding, even with an infinite amount of data. Recent work uses neural networks to obtain practical bounds to such causal effects, which is often an intractable problem. However, these approaches may overfit to the dataset and be overconfident in their causal effect estimates. Moreover, there is currently no systematic approach to disentangle how much of the width of causal effect bounds is due to fundamental non-identifiability versus how much is due to finite-sample limitations. We propose a novel framework to address this problem by considering a confidence set around the empirical observational distribution and obtaining the intersection of causal effect bounds for all distributions in this confidence set. This allows us to distinguish the part of the interval that can be reduced by collecting more samples, which we call sample uncertainty, from the part that can only be reduced by observing more variables, such as latent confounders or instrumental variables, but not with more data, which we call non-ID uncertainty. The upper and lower bounds to this intersection are obtained by solving min-max and max-min problems with neural causal models by searching over all distributions that the dataset might have been sampled from, and all SCMs that entail the corresponding distribution. We demonstrate via extensive experiments on synthetic and real-world datasets that our algorithm can determine when collecting more samples will not help determine the best action. This can guide practitioners to collect more variables or lean towards a randomized study for best action identification.

Md Musfiqur Rahman, Murat Kocaoglu

Sound and complete algorithms have been proposed to compute identifiable causal queries using the causal structure and data. However, most of these algorithms assume accurate estimation of the data distribution, which is impractical for high-dimensional variables such as images. On the other hand, modern deep generative architectures can be trained to sample from high-dimensional distributions. However, training these networks are typically very costly. Thus, it is desirable to leverage pre-trained models to answer causal queries using such high-dimensional data. To address this, we propose modular training of deep causal generative models that not only makes learning more efficient, but also allows us to utilize large, pre-trained conditional generative models. To the best of our knowledge, our algorithm, Modular-DCM is the first algorithm that, given the causal structure, uses adversarial training to learn the network weights, and can make use of pre-trained models to provably sample from any identifiable causal query in the presence of latent confounders. With extensive experiments on the Colored-MNIST dataset, we demonstrate that our algorithm outperforms the baselines. We also show our algorithm's convergence on the COVIDx dataset and its utility with a causal invariant prediction problem on CelebA-HQ.

Md Musfiqur Rahman, Matt Jordan, Murat Kocaoglu

Causal inference from observational data plays critical role in many applications in trustworthy machine learning. While sound and complete algorithms exist to compute causal effects, many of them assume access to conditional likelihoods, which is difficult to estimate for high-dimensional (particularly image) data. Researchers have alleviated this issue by simulating causal relations with neural models. However, when we have high-dimensional variables in the causal graph along with some unobserved confounders, no existing work can effectively sample from the un/conditional interventional distributions. In this work, we show how to sample from any identifiable interventional distribution given an arbitrary causal graph through a sequence of push-forward computations of conditional generative models, such as diffusion models. Our proposed algorithm follows the recursive steps of the existing likelihood-based identification algorithms to train a set of feed-forward models, and connect them in a specific way to sample from the desired distribution. We conduct experiments on a Colored MNIST dataset having both the treatment ($X$) and the target variables ($Y$) as images and sample from $P(y|do(x))$. Our algorithm also enables us to conduct a causal analysis to evaluate spurious correlations among input features of generative models pre-trained on the CelebA dataset. Finally, we generate high-dimensional interventional samples from the MIMIC-CXR dataset involving text and image variables.