Bayesian Tensor Train Decomposition for Streaming Data Recovery

Concepts de base

The author introduces the SPTT algorithm, a Bayesian tensor train decomposition method, to recover streaming data efficiently by estimating the posterior of TT format.

Résumé

Streaming data recovery through Bayesian tensor train decomposition is explored in this paper. The proposed SPTT algorithm excels in recovering high-order, incomplete, and noisy streaming data. Experiments on synthetic and real-world datasets demonstrate the accuracy of the method compared to existing Bayesian tensor decomposition methods.

The paper discusses the challenges of processing streaming data with traditional tensor decomposition methods designed for static data. It introduces a novel approach based on TT decomposition and a Gaussian prior tailored for streaming data analysis. The SPTT algorithm aims to estimate the latent structure online based on current observed elements and recover missing elements using this structure.

By leveraging a probabilistic model of TT decomposition and applying the SVB method, SPTT provides an effective solution for streaming tensor train decomposition. The algorithm updates the posterior distribution of TT-cores and noise precision iteratively as new data batches are received.

Experimental results show that SPTT outperforms existing methods in terms of predictive performance on both synthetic and real-world datasets. The running relative error analysis demonstrates the effectiveness of SPTT over time as more data batches are processed.

Stats

SNR = 10 log (var(AAA) / σ^2)
Batch sizes: {28, 29, 210, 211}
Rank values: {3, 4, 5, 6}

Citations

"We introduce SPTT, a Streaming Probabilistic Tensor Train decomposition approach."
"Numerical experiments show that our SPTT algorithm can produce accurate predictions on synthetic and real-world streaming data."

Idées clés tirées de

Streaming data recovery via Bayesian tensor train decomposition

by Yunyu Huang,... à arxiv.org 02-29-2024

https://arxiv.org/pdf/2302.12148.pdf

Questions plus approfondies

How does the proposed SPTT algorithm address challenges faced by traditional tensor decomposition methods in processing streaming data

The proposed SPTT algorithm addresses challenges faced by traditional tensor decomposition methods in processing streaming data by introducing a Bayesian tensor train (TT) decomposition approach. Unlike traditional methods that require access to the entire observed data at each iteration step, SPTT is designed to update the latent structure online based on the current observed elements without revisiting previously generated data. This capability is crucial for scenarios where only partial observed elements are available due to constraints on database capacity and privacy concerns. By formulating posteriors of TT cores using a Gaussian prior tailored for streaming data, SPTT excels in recovering high-order, incomplete, and noisy properties of streaming data.

What are potential applications beyond streaming data recovery where Bayesian tensor train decomposition could be beneficial

Beyond streaming data recovery, Bayesian tensor train decomposition could be beneficial in various applications across different domains. One potential application is anomaly detection in complex systems such as network traffic monitoring or cybersecurity. By leveraging the probabilistic nature of Bayesian inference and incorporating uncertainty estimates into the latent structure, the algorithm can effectively identify anomalies or unusual patterns within high-dimensional datasets. Additionally, Bayesian tensor train decomposition could be applied in image and video analysis tasks like object recognition or motion tracking where capturing uncertainties in the underlying structures is essential for robust performance.

How might incorporating uncertainty estimates into the latent structure impact the overall performance of the SPTT algorithm

Incorporating uncertainty estimates into the latent structure can have a significant impact on the overall performance of the SPTT algorithm. By considering uncertainties associated with each slice of TT-cores during posterior inference, SPTT becomes more robust to variations and noise present in streaming data. This enhanced modeling of uncertainties allows for more accurate predictions and better generalization capabilities when dealing with incomplete or noisy observations. Furthermore, by quantifying uncertainties within the latent structure estimation process, SPTT can provide valuable insights into confidence levels associated with recovered values, leading to more reliable decision-making processes based on streaming tensor data analysis.