Structured state-space models are deep Wiener models

The goal of this paper is to provide a system identification-friendly introduction to the Structured State-space Models (SSMs). These models have become recently popular in the machine learning community since, owing to their parallelizability, they can be efficiently and scalably trained to tackle extremely-long sequence classification and regression problems. Interestingly, SSMs appear as an effective way to learn deep Wiener models, which allows to reframe SSMs as an extension of a model class commonly used in system identification. In order to stimulate a fruitful exchange of ideas between the machine learning and system identification communities, we deem it useful to summarize the recent contributions on the topic in a structured and accessible form. At last, we highlight future research directions for which this community could provide impactful contributions.

Deep Convolutional Networks in System Identification

Recent developments within deep learning are relevant for nonlinear system identification problems. In this paper, we establish connections between the deep learning and the system identification communities. It has recently been shown that convolutional architectures are at least as capable as recurrent architectures when it comes to sequence modeling tasks. Inspired by these results we explore the explicit relationships between the recently proposed temporal convolutional network (TCN) and two classic system identification model structures; Volterra series and block-oriented models. We end the paper with an experimental study where we provide results on two real-world problems, the well-known Silverbox dataset and a newer dataset originating from ground vibration experiments on an F-16 fighter aircraft.

Evaluating model calibration in classification

Probabilistic classifiers output a probability distribution on target classes rather than just a class prediction. Besides providing a clear separation of prediction and decision making, the main advantage of probabilistic models is their ability to represent uncertainty about predictions. In safety-critical applications, it is pivotal for a model to possess an adequate sense of uncertainty, which for probabilistic classifiers translates into outputting probability distributions that are consistent with the empirical frequencies observed from realized outcomes. A classifier with such a property is called calibrated. In this work, we develop a general theoretical calibration evaluation framework grounded in probability theory, and point out subtleties present in model calibration evaluation that lead to refined interpretations of existing evaluation techniques. Lastly, we propose new ways to quantify and visualize miscalibration in probabilistic classification, including novel multidimensional reliability diagrams.

Data-Driven Impulse Response Regularization via Deep Learning

We consider the problem of impulse response estimation of stable linear single-input single-output systems. It is a well-studied problem where flexible non-parametric models recently offered a leap in performance compared to the classical finite-dimensional model structures. Inspired by this development and the success of deep learning we propose a new flexible data-driven model. Our experiments indicate that the new model is capable of exploiting even more of the hidden patterns that are present in the input-output data as compared to the non-parametric models.