### Thursday, June 20

8:20 - 8:30 | Welcome |

8:30 - 9:30 |
Lennart Ljung (Linköping University) Some Classical and Some New Ideas in System Identification Abstract: This presentation gives an overview of state-of-the art in System Identification. The focus is on classical parameter estimation in carefully selected model structures. The most common structures will be reviewed as well as the basic, classical asymptotic properties in terms of bias and variance. The advantages as well as the disadvantages of the common identification practice will be mentioned. Recent developments inspired by machine learning will then be discussed and also how they relate to the classical approaches by the introduction of well-known, but carefully tuned regularization techniques. |

9:30 - 10:15 |
Lieven Vandenberghe (University of California, Los Angeles) Graphical models of autoregressive time series Abstract: In a graphical model of a Gaussian random variable the sparsity pattern of the inverse covariance matrix determines the conditional independence relations and the topology of the graph. A popular method for estimating the sparse inverse covariance matrix is based on a penalized maximum likelihood formulation with 1-norm penalty. This requires the solution of a convex optimization problem for which several efficient algorithms have recently been proposed. In this talk we will discuss extensions of this sparse inverse covariance problem to autoregressive models of multivariate time series. We will present maximum likelihood formulations with convex penalties and constraints, and discuss first-order algorithms for solving them. |

10:15 - 10:30 | Coffee break |

10:30 - 11:15 |
Giuseppe De Nicolao (University of Pavia) Bayesian linear system identification with stable spline priors Abstract: The issue of linear system identification is revisited as a Bayesian learning problem related to the reconstruction of an unknown function. As such, the estimator is specified by the choice of the prior distribution for the unknown impulse response, regarded as the realization of a stochastic process. Under gaussianity assumptions, the prior is specified by an autocovariance function, whose choice is the key ingredient for developing a successful system identification scheme. Classical choices used in the field of Gaussian Processes do not prove adequate as they are not tailored to the specific features of linear system identification. The introduction of the so-called stable-spline prior brings definite advantages as it guarantees asymptotic stability in addition to standard smoothness properties. The probabilistic framework offers a further advantage as the tuning of the hyperparameters can be restated as the problem of maximizing a marginal likelihood, overcoming some shortcomings of classical model order selection procedures largely employed in parametric identification of linear dynamic systems. |

11:15 - 12:00 |
Alessandro Chiuso (University of Padova) Smoothness priors, Shrinkage and Sparsity in System Identification: Bayesian procedures from a classical perspective Abstract: |

12:00 - 14:00 | Lunch break |

14:00 - 14:45 |
Byron Boots (University of Washington) Spectral Approaches to Learning Dynamical Systems Abstract: In this talk I will give an overview of spectral algorithms for learning compact, accurate, predictive models of partially observable dynamical systems directly from sequences of observations. I will discuss several related approaches with a focus on spectral methods for classical models like Kalman filters and hidden Markov models. I will also briefly discuss variations of these algorithms including batch and online algorithms, and kernel-based algorithms for learning models in high- and infinite-dimensional feature spaces. All of these approaches share a common framework: the model's belief space is represented as predictions of observable quantities and an eigen-decomosition is applied as a key step for learning the model parameters. Unlike the popular EM algorithm, spectral learning algorithms are statistically consistent, computationally efficient, and easy to implement using established matrix-algebra techniques. |

14:45 - 15:30 |
Mario Sznaier (Northeastern University) Hankel Based Maximum Margin Classifiers: A Connection Between Machine Learning and Nonlinear Systems Identification Abstract: Finding low dimensional parsimonious non-linear representations of high dimensional correlated data is a classical problem in machine learning and a large number of solutions are available. However, while these methods have proved very efficient in handling static data, most do not exploit dynamical information, encapsulated in the temporal ordering of the data. Thus, the resulting embeddings may not be suitable for problems such as tracking, anomaly detection or time-series classification, that critically hinge on capturing the underlying temporal dynamics. Alternatively, from a control perspective, the problem of finding low dimensional embeddings that respect the temporal dynamics can be recast as a Wiener system (the cascade of a linear system and a static nonlinearity) identification problem. Here the linear dynamics account for the temporal evolution in the embedding manifold, while the nonlinearity models the mapping from this manifold to the original (high dimensional) data. Identification of Wiener systems has been the subject of recent intense research in the control community, leading to large number of approaches, which can be roughly classified into statistical and set membership. A salient feature of these approaches is that the dimension of the state space of the system is assumed to be known. However, in the case of interest here (embedding of dynamic data) this information is not a-priori available and must also be identified from the experimental data, a situation that cannot be handled by existing techniques. This talk presents a rapprochement between systems identification and machine learning techniques. Our goal is, starting from experimental input output data, to find an embedding manifold such that the data can indeed be explained as a trajectory of a Wiener system, and to identify its linear and non-linear portions, as well as the dimensions of both the embedding manifold and the dynamics there. A salient feature of the proposed approach (common in machine learning, but to the best of our knowledge hitherto not used in the identification community), is its ability to use of both positive and negative samples, that is experimental data generated both by the system to be identified and by other systems. This is a situation commonly encountered in applications such as activity classification, where sample clips of different activities are available, or in tracking, where often a segmentation separating the target of interest from other targets and the background is known. The main result of the talk shows that in this context, the problem of jointly finding the embedding manifold and the linear dynamics can be recast into a convex optimization over a semi-algebraic set (a set defined by a collection of polynomial inequalities). In turn, the use of recent results from polynomial optimization allows for relaxing this problem to a tractable convex optimization. Further, as in kernel based methods, the proposed algorithm uses only information about the covariance matrix of the observed data (as opposed to the data itself). Thus, it can comfortably handle cases such as those arising in computer vision applications where the dimension of the output space is very large (since each data point is a frame from a video sequence with thousands of pixels). These results will be illustrated with both academic examples and practical ones involving human activity classification from video clips. |

15:30 - 17:00 | Poster Session |

17:00 - 17:45 |
Thomas Schön (Linköping University) Nonlinear system identification enabled via sequential Monte Carlo Abstract: Sequential Monte Carlo (SMC) methods are computational methods primarily used to deal with the state inference problem in nonlinear state space models. The particle filters and the particle smoothers are the most popular SMC methods. These methods open up for nonlinear system identification (both maximum likelihood and Bayesian solutions) in a systematic way. As we will see it is not a matter of directly applying the SMC algorithms, but there are several ways in which they enter as a natural part of the solution. The use of SMC for nonlinear system identification is a relatively recent development and the aim here is to first provide a brief overview of how SMC can be used in solving challenging nonlinear system identification problems by sketching both maximum likelihood and Bayesian solutions. We will then introduce a recent powerful class of algorithms collectively referred to as Particle Markov Chain Monte Carlo (PMCMC) targeting the Bayesian problem. PMCMC provides a systematic way of combining SMC and MCMC, where SMC is used to construct the high-dimensional proposal density for the MCMC sampler. The first results emerged in 2010 and since then we have witnessed a steadily increasing activity within this area. We focus on our new PMCMC method "Particle Gibbs with ancestor sampling" and show its use in computing the posterior distribution for a general Wiener model (i.e. identifying a Bayesian Wiener model). |