BS-CP: Efficient streaming Bayesian tensor decomposition method via assumed density filtering.

Area of Science:

• Data Science
• Machine Learning
• Numerical Analysis

Background:

• Tensor data is prevalent in applications like recommendation systems but often suffers from sparsity, noise, and high production rates.
• Bayesian tensor decomposition offers advantages for handling data imperfections but faces computational challenges, especially with streaming data.

Purpose of the Study:

• To develop an efficient and accurate method for dynamically updating the posterior of latent factors in Bayesian tensor decomposition for streaming data.
• To address the computational challenges of Bayesian CP (CANDECOMP/PARAFAC) decomposition with fast-produced data streams.

Main Methods:

• Proposed BS-CP, a novel structure for dynamic posterior updates.
• Introduced BS-CP1, an efficient implementation utilizing assumed density filtering (ADF).
• Developed BS-CP2, employing Gauss-Laguerre quadrature for improved noise integration and empirical results.

Main Results:

• BS-CP1 and BS-CP2 demonstrated significant Root Mean Square Error (RMSE) improvements on recommendation system datasets (e.g., 31.8% and 33.3% on MovieLens-1m and Fit Record).
• The proposed methods showed over 10% improvement compared to state-of-the-art methods, with superior stability.
• Empirical results indicate BS-CP algorithms are well-suited for large datasets and real-world scenarios.

Conclusions:

• BS-CP provides a computationally efficient and accurate approach for Bayesian tensor decomposition of streaming data.
• The proposed algorithms effectively handle sparse and noisy tensor data, outperforming existing methods in accuracy and stability.
• BS-CP is a promising solution for real-time applications involving dynamic tensor factorization.