Finite-Sample Analysis of Deep CCA-Based Unsupervised Post-Nonlinear Multimodal Learning.

Area of Science:

• Machine Learning
• Statistical Analysis
• Data Science

Background:

• Canonical Correlation Analysis (CCA) is vital for unsupervised multimodal latent representation learning and data fusion.
• Deep neural networks combined with CCA (Deep CCA) enhance performance but lack theoretical support.
• Previous work by Lyu and Fu (2020) offered theoretical guarantees under an unlimited data assumption.

Purpose of the Study:

• To provide a finite-sample analysis for the Deep CCA method proposed by Lyu and Fu (2020).
• To address the unrealistic assumption of unlimited data in prior theoretical analyses of Deep CCA.
• To establish theoretical guarantees for Deep CCA performance with a finite number of samples.

Main Methods:

• Finite-sample analysis of the Deep CCA criterion.
• Integration of statistical learning, numerical differentiation, and robust system identification.
• Theoretical examination of Deep CCA under a postnonlinear generative model.

Main Results:

• The finite-sample version of Deep CCA can accurately estimate shared information.
• Guaranteed accuracy is achieved when the number of samples is sufficiently large.
• The analytical approach demonstrates robustness beyond Deep CCA.

Conclusions:

• Deep CCA is theoretically sound even with a finite number of samples, provided the sample size is adequate.
• The analytical framework developed may benefit other unsupervised learning paradigms.
• This work bridges the gap between theoretical Deep CCA and practical applications with limited data.