Weight-variant Latent Causal Models

• URL: http://arxiv.org/abs/2208.14153v1
• Date: Tue, 30 Aug 2022 11:12:59 GMT
• Title: Weight-variant Latent Causal Models
• Authors: Yuhang Liu, Zhen Zhang, Dong Gong, Mingming Gong, Biwei Huang, Anton van den Hengel, Kun Zhang, Javen Qinfeng Shi
• Abstract summary: Causal representation learning exposes latent high-level causal variables behind low-level observations. In this work we focus on identifying latent causal variables. We show that the transitivity severely hinders the identifiability of latent causal variables. We propose a novel method, termed Structural caUsAl Variational autoEncoder, which directly learns latent causal variables.
• Score: 79.79711624326299
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Causal representation learning exposes latent high-level causal variables behind low-level observations, which has enormous potential for a set of downstream tasks of interest. Despite this, identifying the true latent causal representation from observed data is a great challenge. In this work we focus on identifying latent causal variables. To this end, we analysis three intrinsic properties in latent space, including transitivity, permutation and scaling. We show that the transitivity severely hinders the identifiability of latent causal variables, while permutation and scaling guide the direction of identifying latent causal variable. To break the transitivity, we assume the underlying latent causal relations to be linear Gaussian models, in which the weights, mean and variance of Gaussian noise are modulated by an additionally observed variable. Under these assumptions we theoretically show that the latent causal variables can be identifiable up to trivial permutation and scaling. Built on this theoretical result, we propose a novel method, termed Structural caUsAl Variational autoEncoder, which directly learns latent causal variables, together with the mapping from the latent causal variables to the observed ones. Experimental results on synthetic and real data demonstrate the identifiable result and the ability of the proposed method for learning latent causal variables.

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