A Constraint Generation Approach toLearning Stable Linear Dynamical Systems

1 Introduction Many problems in machine learning involve sequences of real-valued multivariate observations.To model the statistical properties of such data, it is often sensible to assume each observation to be correlated to the value of an underlying latent variable, or state, that is evolving over the course of thesequence. In the case where the state is real-valued and the noise terms are assumed to be Gaussian, the resulting model is called a linear dynamical system (LDS), also known as a Kalman Filter [3].LDSs are an important tool for modeling time series in engineering, controls and economics as well as the physical and social sciences. Let {y"i(M)}Mi=1 denote the eigenvalues of a square matrix M in decreasing order of magnitude,