Multi-view Matrix Factorization for Linear Dynamical System Estimation
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. 
However, I do not understand why the paper tell the story from a two-view aspect. In LDS, we can construct x_t from two ways. One is from \phi_t and the other is from \phi_{t-1}. Eq.4 is minimizing the reconstruction error for x_t constructed in both ways, with regularization on \Phi, C and A. This is a general framework, which is a reconstruction loss plus regularization, widely used in many classical machine learning algorithms. I do not see much novelty in the proposed learning objective Eq.4, and I cannot tell the merit of stating the old story from a two-view direction.
Lemma 1 proposes a method to transform the nonconvex problem into a convex one. However, I cannot see any benefit of transforming Eq.4 into a convex problem. The new learning objective Z in Lemma 1 is just a de-noised version of x_t. The original low-dimensional latent space estimation problem now becomes the problem directly estimating the de-noised high-rank observed state. Thus all merits from low-dimensional assumption are not available now. Since the proposed model is still non-convex, what is its merit compared to classical non-convex matrix factorization style algorithms in LDS?