Streaming Variational Monte Carlo.

Area of Science:

• Dynamical systems analysis
• Machine learning
• Statistical inference

Background:

• Nonlinear state-space models are crucial for analyzing complex time series data.
• Online inference of states and nonlinear dynamics in streaming data presents significant practical challenges.

Purpose of the Study:

• To develop a novel online learning framework for flexible and accurate Bayesian joint filtering.
• To enable simultaneous inference of states and nonlinear dynamics in a streaming setting.

Main Methods:

• Leveraging variational inference and sequential Monte Carlo methods.
• Approximating the filtering posterior using sparse Gaussian processes for interpretable dynamics.
• Implementing a framework with constant time complexity per sample.

Main Results:

• The proposed method achieves flexible and accurate Bayesian joint filtering.
• It provides an approximation of the filtering posterior arbitrarily close to the true distribution.
• Efficient approximation of dynamics posterior using sparse Gaussian processes.

Conclusions:

• The framework is suitable for online learning scenarios and real-time applications.
• It offers an interpretable model of latent dynamics.
• Enables efficient and accurate processing of streaming data for complex dynamical systems.