Deconvolution of mixing time series on a graph

Area of Science:

• Statistics
• Time Series Analysis
• Network Science

Background:

• Many applications require inferring latent time series from indirect, aggregated, or mixed measurements.
• These problems often involve solving a series of ill-posed inverse problems where the mixing matrix (A) is key.
• Examples include positron emission tomography, super-resolution, and network traffic monitoring.

Purpose of the Study:

• To develop an efficient inference method for multilevel state-space models of mixing time series.
• To address challenges posed by bursty and sparse time series mixed on a graph.
• To improve the estimation of point-to-point traffic flows from aggregate network measurements.

Main Methods:

• Developed a multilevel state-space model specifically for mixing time series.
• Implemented an efficient inference approach using a two-stage strategy.
• Utilized a simple model to calibrate regularization parameters for efficient inference.

Main Results:

• The proposed method effectively handles inference from indirect measurements in mixed time series.
• The approach demonstrates superior performance in estimating network traffic flows compared to existing methods.
• The two-stage inference strategy proves efficient for complex multilevel models.

Conclusions:

• The developed multilevel state-space model and inference method offer a robust solution for analyzing mixed time series.
• This work provides a significant advancement in network traffic flow estimation.
• The proposed inference strategy is applicable to various multilevel models of multivariate time series.