Discovering influential factors in variational autoencoders. (April 2020)

• Record Type: Journal Article
• Authors: Liu, Shiqi; Liu, Jingxin; Zhao, Qian; Cao, Xiangyong; Li, Huibin; Meng, Deyu; Meng, Hongying; Liu, Sheng
• Is Part Of: Pattern recognition. Volume 100(2020:Apr.)
• Publication Date: 2020-04
• Subjects: Variational autoencoder -- Mutual information -- Generative model; Pattern perception -- Periodicals; Perception des structures -- Périodiques; Patroonherkenning; 006.4
• DOI: 10.1016/j.patcog.2019.107166
• Languages: English
• ISSNs: 0031-3203

Abstract

Highlights: This paper aims to study variational autoencoder, so as to discover its influential generating factors. It shows that the VAE objective inclines to induce mutual information sparsity in factor dimension over the data intrinsic dimension and therefore inclines to result in some non-influential factors whose function on data reconstruction could be ignored. We argue that the mutual information of the input and each learned factor of the representation plays a necessary indicator of discovering the influential factors. It show mutual information also influences the lower bound of VAEs reconstruction error and downstream classification task. Abstract: In the field of machine learning, it is still a critical issue to identify and supervise the learned representation without manually intervening or intuition assistance to extract useful knowledge or serve for the downstream tasks. In this work, we focus on supervising the influential factors extracted by the variational autoencoder (VAE). The VAE is proposed to learn independent low dimension representation while facing the problem that sometimes pre-set factors are ignored. We argue that the mutual information of the input and each learned factor of the representation plays a necessary indicator of discovering the influential factors. We find the VAE objective inclines to induce mutual information sparsity in factor dimension over the data intrinsic dimension and therefore result in some non-influential factors whose function on data reconstruction could be ignored. We show mutual information also influences the lower bound of VAE's reconstruction error and downstream classification task. To make such indicator applicable, we design an algorithm for calculating the mutual information for VAE and prove its consistency. Experimental results on MNIST, CelebA and DEAP datasets show that mutual information can help determine influential factors, of which some are interpretable and can be used to further generation and classification tasks, and help discover the variant that connects with emotion on DEAP dataset.