Public research · 2022
Improvements for Nonlinear Filtering Algorithms
Sequential Monte Carlo, Gaussian processes, and online hyperparameter inference for noisy streaming data.
- Problem
- How can filtering algorithms remain accurate and computationally efficient when observations are noisy, incomplete, and arrive sequentially?
- Method
- Studied the Kalman filter, particle filter, and Gaussian processes with Hamiltonian Monte Carlo for hyperparameter inference, then re-cast the inference as a Sequential Monte Carlo problem over streaming data.
- Demonstrates
- Probabilistic inference, mathematical modeling, and reasoning about algorithmic behavior under online and resource-constrained conditions.
This project investigates filtering and online inference for noisy sequential data, from the foundations of the Kalman and particle filters through Gaussian process hyperparameter inference.
A central contribution is treating Gaussian process hyperparameter inference as a sequential problem and comparing Hamiltonian Monte Carlo against Sequential Monte Carlo (SMC) with jittered resampling. The empirical results show SMC offers meaningful efficiency gains over HMC for incremental data, at the cost of recomputing covariance terms — a trade-off favorable in many online settings.
The work emphasizes that filtering quality is inseparable from computational behavior: an algorithm is only useful if it converges quickly enough to be wrong about the next observation, not just the last one.