# Likelihood-Free Overcomplete ICA and Applications in Causal Discovery

arXiv: https://arxiv.org/abs/1909.01525 · HTML: https://mlsanity.com/paper/1909.01525/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Sep 2019.

## Built on by (most cited first, 2 of 2)

- [I-CAM-UV: Integrating Causal Graphs over Non-Identical Variable Sets Using Causal Additive Models with Unobserved Variables](https://mlsanity.com/paper/2603.03207/) (2026)
- [On the Identifiability of Causal Graphs with the Invariance Principle](https://mlsanity.com/paper/2510.13583/) (2025)

## Abstract (arXiv)

Causal discovery witnessed significant progress over the past decades. In particular, many recent causal discovery methods make use of independent, non-Gaussian noise to achieve identifiability of the causal models. Existence of hidden direct common causes, or confounders, generally makes causal discovery more difficult; whenever they are present, the corresponding causal discovery algorithms can be seen as extensions of overcomplete independent component analysis (OICA). However, existing OICA algorithms usually make strong parametric assumptions on the distribution of independent components, which may be violated on real data, leading to sub-optimal or even wrong solutions. In addition, existing OICA algorithms rely on the Expectation Maximization (EM) procedure that requires computationally expensive inference of the posterior distribution of independent components. To tackle these problems, we present a Likelihood-Free Overcomplete ICA algorithm (LFOICA) that estimates the mixing matrix directly by back-propagation without any explicit assumptions on the density function of independent components. Thanks to its computational efficiency, the proposed method makes a number of causal discovery procedures much more practically feasible. For illustrative purposes, we demonstrate the computational efficiency and efficacy of our method in two causal discovery tasks on both synthetic and real data.