Learning Discrete Latent Models from Discrete Observations

Yi Han, Yujia Zheng, Haoyue Dai, Kun Zhang

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

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Submission Number: 12650