We consider maximum likelihood estimation of linear dynamical systems with generalized-linear observation models. Maximum likelihood is typically considered to be hard in this setting since latent states and transition parameters must be inferred jointly. Given that expectation-maximization does not scale and is prone to local minima, moment-matching approaches from the subspace identification literature have become standard, despite known statistical efficiency issues. In this paper, we instead reconsider likelihood maximization and develop an optimization based strategy for recovering the latent states and transition parameters. Key to the approach is a two-view reformulation of maximum likelihood estimation for linear dynamical systems that enables the use of global optimization algorithms for matrix factorization. We show that the proposed estimation strategy outperforms widely-used identification algorithms such as subspace identification methods, both in terms of accuracy and runtime.

This paper proposes an efficient maximum likelihood algorithm for parameter estimation in linear dynamical systems. The problem is reformulated as a two-view generative model with a shared latent factor, and approximated as a matrix factorization problem. The paper then proposes a novel proximal update. Experiments validate the effectiveness of the proposed method. The paper realizes that maximum likelihood style algorithms have some merit over classical moment-matching algorithms in LDS, and wants to solve the efficiency problem of existing maximum likelihood algorithms. Then the paper proposes a theoretical guaranteed proximal update to solve the optimization problem.

We introduce the federated multi-view matrix factorization method that extends the federated learning framework to matrix factorization with multiple data sources. Our method is able to learn the multi-view model without transferring the user's personal data to a central server. As far as we are aware this is the first federated model to provide recommendations using multi-view matrix factorization. The model is rigorously evaluated on three datasets on production settings. Empirical validation confirms that federated multi-view matrix factorization outperforms simpler methods that do not take into account the multi-view structure of the data, in addition, it demonstrates the usefulness of the proposed method for the challenging prediction tasks of cold-start federated recommendations.

We consider maximum likelihood estimation of linear dynamical systems with generalized-linear observation models. Maximum likelihood is typically considered to be hard in this setting since latent states and transition parameters must be inferred jointly. Given that expectation-maximization does not scale and is prone to local minima, moment-matching approaches from the subspace identification literature have become standard, despite known statistical efficiency issues. In this paper, we instead reconsider likelihood maximization and develop an optimization based strategy for recovering the latent states and transition parameters. Key to the approach is a two-view reformulation of maximum likelihood estimation for linear dynamical systems that enables the use of global optimization algorithms for matrix factorization.