Deep learning applied to system identification : A probabilistic approach

Abstract: Machine learning has been applied to sequential data for a long time in the field of system identification. As deep learning grew under the late 00's machine learning was again applied to sequential data but from a new angle, not utilizing much of the knowledge from system identification. Likewise, the field of system identification has yet to adopt many of the recent advancements in deep learning. This thesis is a response to that. It introduces the field of deep learning in a probabilistic machine learning setting for problems known from system identification.Our goal for sequential modeling within the scope of this thesis is to obtain a model with good predictive and/or generative capabilities. The motivation behind this is that such a model can then be used in other areas, such as control or reinforcement learning. The model could also be used as a stepping stone for machine learning problems or for pure recreational purposes.Paper I and Paper II focus on how to apply deep learning to common system identification problems. Paper I introduces a novel way of regularizing the impulse response estimator for a system. In contrast to previous methods using Gaussian processes for this regularization we propose to parameterize the regularization with a neural network and train this using a large dataset. Paper II introduces deep learning and many of its core concepts for a system identification audience. In the paper we also evaluate several contemporary deep learning models on standard system identification benchmarks. Paper III is the odd fish in the collection in that it focuses on the mathematical formulation and evaluation of calibration in classification especially for deep neural network. The paper proposes a new formalized notation for calibration and some novel ideas for evaluation of calibration. It also provides some experimental results on calibration evaluation.