Learning Discrete Latent Models from Discrete Observations

ICLR 2025 Conference Submission12650 Authors

Keywords: Latent Variable Identification, Nonlinear Independent Component Analysis (ICA)

Abstract: A central challenge in machine learning is discovering meaningful representations of high-dimensional data, commonly referred to as representation learning. However, many existing methods lack a theoretical foundation, leading to unreliable representations and limited inferential capabilities. In approaches where certain uniqueness of representation is guaranteed, such as nonlinear ICA, variables are typically assumed to be continuous. While recent work has extended identifiability to binarized observed variables, no principled method has been developed for scenarios involving discrete latent variables. In this paper, we show how multi-domain information can be leveraged to achieve identifiability when both latent and observed variables are discrete. We propose general identification conditions that do not depend on specific data distributional assumptions or parametric model forms. The effectiveness of our approach is validated through experiments on both simulated and real-world datasets.

Primary Area: unsupervised, self-supervised, semi-supervised, and supervised representation learning

Code Of Ethics: I acknowledge that I and all co-authors of this work have read and commit to adhering to the ICLR Code of Ethics.

Submission Guidelines: I certify that this submission complies with the submission instructions as described on https://iclr.cc/Conferences/2025/AuthorGuide.

Reciprocal Reviewing: I understand the reciprocal reviewing requirement as described on https://iclr.cc/Conferences/2025/CallForPapers. If none of the authors are registered as a reviewer, it may result in a desk rejection at the discretion of the program chairs. To request an exception, please complete this form at https://forms.gle/Huojr6VjkFxiQsUp6.

Anonymous Url: I certify that there is no URL (e.g., github page) that could be used to find authors’ identity.

No Acknowledgement Section: I certify that there is no acknowledgement section in this submission for double blind review.

Submission Number: 12650