Accurate Kernel Learning for Linear Gaussian Markov Processes using a Scalable Likelihood Computation
This work addresses computational bottlenecks in kernel learning for time series analysis, offering incremental improvements in efficiency and accuracy for domain-specific applications like climate data.
The authors tackled the problem of scalable likelihood computation for Linear Gaussian Markov processes, achieving better scaling for complex models and sparsely sampled signals. They found that the posterior mean with a reference prior is more accurate for such cases, while maximum likelihood is efficient for denser sampling and lower-order models, as confirmed in simulation and speleothem data experiments.
We report an exact likelihood computation for Linear Gaussian Markov processes that is more scalable than existing algorithms for complex models and sparsely sampled signals. Better scaling is achieved through elimination of repeated computations in the Kalman likelihood, and by using the diagonalized form of the state transition equation. Using this efficient computation, we study the accuracy of kernel learning using maximum likelihood and the posterior mean in a simulation experiment. The posterior mean with a reference prior is more accurate for complex models and sparse sampling. Because of its lower computation load, the maximum likelihood estimator is an attractive option for more densely sampled signals and lower order models. We confirm estimator behavior in experimental data through their application to speleothem data.