From Identifiable Causal Representations to Controllable Counterfactual
  Generation: A Survey on Causal Generative Modeling
Aneesh Komanduri Xintao Wu Yongkai Wu Feng Chen
Deep generative models have shown tremendous success in data density
estimation and data generation from finite samples. While these models have
shown impressive performance by learning correlations among features in the
data, some fundamental shortcomings are their lack of explainability, the
tendency to induce spurious correlations, and poor out-of-distribution
extrapolation. In an effort to remedy such challenges, one can incorporate the
theory of causality in deep generative modeling. Structural causal models
(SCMs) describe data-generating processes and model complex causal
relationships and mechanisms among variables in a system. Thus, SCMs can
naturally be combined with deep generative models. Causal models offer several
beneficial properties to deep generative models, such as distribution shift
robustness, fairness, and interoperability. We provide a technical survey on
causal generative modeling categorized into causal representation learning and
controllable counterfactual generation methods. We focus on fundamental theory,
formulations, drawbacks, datasets, metrics, and applications of causal
generative models in fairness, privacy, out-of-distribution generalization, and
precision medicine. We also discuss open problems and fruitful research
directions for future work in the field.