S. Joe Qin — Page 2

arXiv2023

Alternating minimization for simultaneous estimation of a latent variable and identification of a linear continuous-time dynamic system

We propose an optimization formulation for the simultaneous estimation of a latent variable and the identification of a linear continuous-time dynamic system, given a single input-output pair. We justify this approach based on Bayesian maximum a posteriori estimators. Our scheme takes the form of a convex alternating minimization, over the trajectories and the dynamic model respectively. We prove its convergence to a local minimum which verifies a two point-boundary problem for the (latent) state variable and a tensor product expression for the optimal dynamics.

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arXiv2020

On the Convergence of the Dynamic Inner PCA Algorithm

Dynamic inner principal component analysis (DiPCA) is a powerful method for the analysis of time-dependent multivariate data. DiPCA extracts dynamic latent variables that capture the most dominant temporal trends by solving a large-scale, dense, and nonconvex nonlinear program (NLP). A scalable decomposition algorithm has been recently proposed in the literature to solve these challenging NLPs. The decomposition algorithm performs well in practice but its convergence properties are not well understood. In this work, we show that this algorithm is a specialized variant of a coordinate maximization algorithm. This observation allows us to explain why the decomposition algorithm might work (or not) in practice and can guide improvements. We compare the performance of the decomposition strategies with that of the off-the-shelf solver Ipopt. The results show that decomposition is more scalable and, surprisingly, delivers higher quality solutions.

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