UMBREON: Unbiased Moment-Based RecursivE InitializatiON

Abstract

Initialization is a primary bottleneck in the practical performance of the expectation–maximization (EM) algorithm for latent variable models. In linear Gaussian state space models, standard strategies—random restarts, grid search, or ad hoc choices—are computationally inefficient and often lead to slow convergence or poor local optima. We introduce UMBREON (short for Unbiased Moment-Based RecursivE InitializatiON), a deterministic, closed-form initialization method that recovers high-quality starting values directly from the second-order moment structure of observed input–output data. UMBREON combines autoregressive modeling of exogenous inputs, lagged cross-covariance regression, and recursive moment inversion, while enforcing structural stationarity constraints by construction. The resulting procedure runs in linear time, requires no tuning parameters, and produces feasible initializations without restarts. Empirically, UMBREON reduces EM iteration counts by up to 36% and consistently improves parameter recovery across Monte Carlo simulations. These results demonstrate that principled moment-based initialization can substantially improve both the efficiency and reliability of EM in structured state space models.