Sufficient and Disentangled Representation Learning

Jian Huang, Yuling Jiao, Xu Liao, Jin Liu, Zhou Yu

Keywords: Conditional independence, f-divergence, rotation invariant, neural network, statistical guarantee

Abstract: We propose a novel approach to representation learning called sufficient and disentangled representation learning (SDRL). With SDRL, we seek a data representation that maps the input data to a lower-dimensional space with two properties: sufficiency and disentanglement. First, the representation is sufficient in the sense that the original input data is conditionally independent of the response or label given the representation. Second, the representation is maximally disentangled with mutually independent components and rotation invariant in distribution. We show that such a representation always exists under mild conditions on the input data distribution based on optimal transport theory. We formulate an objective function characterizing conditional independence and disentanglement. This objective function is then used to train a sufficient and disentangled representation with deep neural networks. We provide strong statistical guarantees for the learned representation by establishing an upper bound on the excess error of the objective function and show that it reaches the nonparametric minimax rate under mild conditions. We also validate the proposed method via numerical experiments and real data analysis.

One-sentence Summary: This paper proposes a sufficient and disentangled representation learning approach in the context of supervised 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

Reviewed Version (pdf): https://openreview.net/references/pdf?id=VYs_1ZoFQ1