Exploring Statistical Learning in Multi-View Deep Joint Subspace Analysis

Pradipta Maji

http://www.isical.ac.in/~pmaji/  

pmaji@isical.ac.in

Abstract: Multi-view data analysis is an important machine learning paradigm, which explores the consistency and complementary properties of multiple views to discover patterns hidden in data. One of the important issues associated with real-life high-dimensional multi-view data is how to integrate relevant and complementary information from multiple views, while generating discriminative joint subspaces for analysis. Although the integration of multi-view data is expected to provide an intrinsically more powerful model than its single-view counterpart, it poses its own set of challenges. The most important problems associated with multi-view data analysis are the handling heterogeneous nature of different views and high-dimension low-sample size nature of individual views, selection of relevant and complementary views while generating discriminative joint subspaces for analysis, and capturing the lower dimensional non-linear geometry of each view. In a multi-view scenario, it is expected that the joint subspace should be learned in such a way that the similarity in the latent space implies the similarity in the corresponding concepts. The joint subspace should also reflect the intrinsic properties of each of the individual views and should efficiently capture the non-linear correlated structures across different views. In this regard, some novel deep learning algorithms will be discussed, which are developed based on the theory of statistical learning. The theory of canonical correlation analysis is judiciously integrated with the learning objective of the multimodal discriminative deep Boltzmann machine to learn a joint subspace from the maximally correlated subspaces, while the concept of Hilbert-Schmidt independence criterion helps to encapsulate the cross-view dependency in terms of consensus and/or complementary knowledge from the input pairs of views. Based on the Bayes error analysis, an upper bound on the error probability of the novel deep models is estimated, which facilitates determining the optimal architectures of the models.

Biography: Pradipta Maji received the bachelor degree in Physics, the master degree in Electronics Science, and the PhD degree in Science, all from Jadavpur University, Kolkata, India. Currently, he is a Professor with the Machine Intelligence Unit, Indian Statistical Institute, Kolkata, India. His research interests include machine learning, deep learning, medical imaging, and bioinformatics. He has published more than 150 papers in international journals and conferences. He is a Fellow of the National Academy of Sciences, India, and a recipient of the Young Scientist/Associate Awards of all three science academies of India. He also received the 2015 Young Faculty Research Fellowship from the Ministry of Electronics and Information Technology, Government of India.