Robust parameter estimation with the EM algorithm

Investigate whether the Expectation-Maximization algorithm can robustly estimate the expectation step and ensure convergence when estimating the latent covariance matrices and gamma-distribution shape parameter in the state-space heartbeat dynamics model.

Background

The model requires estimation of parameters including latent covariance matrices and the gamma-emission shape parameter, both of which can substantially affect model fit. The authors identify Expectation-Maximization as a possible estimation procedure but report that its application did not provide robust expectation-step estimation or convergence guarantees in their setting.

The unresolved issue is therefore whether EM, potentially with an improved implementation or formulation, can be made reliable for parameter estimation in this non-Gaussian state-space heartbeat model.

References

While the Expectation-Maximization (EM) algorithm is one procedure that has been described to estimate parameters such as the latent covariance matrices and the shape parameter, which can heavily influence model fit, we found that its usage was unable to robustly estimate the expectation step and ensure convergence.

— Efficient Convex Optimization Methods for State-Space Heartbeat Dynamics Models with Gamma Generalized Linear Models  (2610.00884 - Liu et al., 1 Oct 2026) in Section 6, Discussion, paragraph beginning “There are a few limitations of our method.”