Nonparametric tensor ring decomposition with scalable amortized inference.

Area of Science:

• Machine Learning
• Data Science
• Artificial Intelligence

Background:

• Multi-dimensional data analysis is crucial in fields like video processing and time series analysis.
• Traditional tensor decomposition (TD) methods are limited by assumptions of multi-linearity and scalability to large datasets.

Purpose of the Study:

• To develop a nonparametric tensor decomposition (TD) method that overcomes the limitations of traditional approaches.
• To enhance the expressive power of TD by modeling complex latent structures and enabling application to massive datasets.

Main Methods:

• Proposed a non-linear extension of tensor ring decomposition using neural networks.
• Incorporated a matrix Gaussian process (GP) prior to model cross-sample correlations and physical structures.
• Developed a Variational Autoencoder (VAE)-like amortized inference network for efficient posterior inference in large-scale datasets.

Main Results:

• The proposed method effectively models complex latent structures beyond multi-linearity.
• Amortized inference enables the application of TD to datasets with massive samples.
• Demonstrated advantages through data imputation tasks on the Healing MNIST dataset and multivariate time series data.

Conclusions:

• The nonparametric TD with amortized inference offers a powerful and scalable approach for analyzing complex multi-dimensional data.
• This method enhances the expressiveness of TD by capturing hidden tensor structures, outperforming traditional techniques.