Sparse Learning in State Space Models – University of Copenhagen

Sparse Learning in State Space Models

Specialeforsvar ved Lasse Petersen

Titel: Sparse Learning in State Space Models 


Abstract: The contribution of this thesis is the development of algorithms for performing sparse parameter estimation in linear Gaussian state space models. First we describe the theory of chain graph models and show how the linear Gaussian state space models can be interpreted in this framework. This is used to derive two different penalization schemes of the model parameters using sparsity inducing penalty functions. Since estimation in state space models can be viewed as a missing data problem, the EM algorithm is used for carrying out the estimation. We deduce an E-step and two different M-steps corresponding to the two different penalization approaches. Here we rely on existing methods from the field of high dimensional statistics. We conclude the thesis by carrying out a simulation study that assesses the performance of the proposed estimation algorithms 



Vejleder:  Niels Richard Hansen
Censor:    Morten Frydenberg, Aarhus Universitet