Papers by Alessandro Chiuso
Springer eBooks, 2019
System identification has been developed, by and large, following the classical parametric approa... more System identification has been developed, by and large, following the classical parametric approach. In this entry we discuss how regularization theory can be employed to tackle the system identification problem from a nonparametric (or semi-parametric) point of view. Both regularization for smoothness and regularization for sparseness are discussed, as flexible means to face the bias/variance dilemma and to perform model selection. These techniques have also advantages from the computational point of view, leading sometimes to convex optimization problems.
Linear system identification using the sequential stabilizing spline algorithm
Automatica, Apr 1, 2022
Tuning complexity in kernel-based linear system identification: The robustness of the marginal likelihood estimator
In recent works, a new regularized approach for linear system identification has been proposed. T... more In recent works, a new regularized approach for linear system identification has been proposed. The estimator solves a regularized least squares problem and admits also a Bayesian interpretation with the impulse response modeled as a zero-mean Gaussian vector. A possible choice for the covariance is the so called stable spline kernel. It encodes information on smoothness and exponential stability, and contains just two unknown parameters that can be determined from data via marginal likelihood (ML) optimization. Experimental evidence has shown that this new approach may outperform traditional system identification approaches, such as PEM and subspace techniques. This paper provides some new insights on the effectiveness of the stable spline estimator equipped with ML for hyperparameter estimation. We discuss the mean squared error properties of ML without assuming the correctness of the Bayesian prior on the impulse response. Our findings reveal that many criticisms on ML robustness are not well founded. ML is instead valuable for tuning model complexity in linear system identification also when impulse response description is affected by undermodeling.
逆動力学モデリングのためのオンライン半パラメトリック学習【Powered by NICT】
IEEE Conference Proceedings, 2016
The stable spline (SS) kernel and the diagonal correlated (DC) kernel are two kernels that have b... more The stable spline (SS) kernel and the diagonal correlated (DC) kernel are two kernels that have been applied and studied extensively for kernel-based regularized LTI system identification. In this note, we show that similar to the derivation of the SS kernel, the continuous-time DC kernel can be derived by applying the same "stable" coordinate change to a "generalized" first-order spline kernel, and thus can be interpreted as a stable generalized first-order spline kernel. This interpretation provides new facets to understand the properties of the DC kernel. In particular, we derive a new orthonormal basis expansion of the DC kernel, and the explicit expression of the norm of the RKHS associated with the DC kernel. Moreover, for the non-uniformly sampled DC kernel, we derive its maximum entropy property and show that its kernel matrix has tridiagonal inverse.
Estimating Effective Connectivity using Brain Partitioning
2021 60th IEEE Conference on Decision and Control (CDC), Dec 14, 2021
One of the main outstanding issues in the neuroscience is estimation of effective connectivity in... more One of the main outstanding issues in the neuroscience is estimation of effective connectivity in brain networks, which models the causal interactions among neuronal populations. Estimation of effective connectivity embraces two types of the challenges, such as estimation accuracy and computational complexity. In this paper, we consider resting-state (rs) fMRI data serving as an input for a stochastic linear DCM model. The model parameters are estimated through an EM (expectation maximization) iterative procedure. In this work, we propose the alternative scheme for the hyperparameters estimation aiming in reduction of computational burden of the original EM-algorithm. The simulation results demonstrate the viability of the proposed block-reweighting scheme and represents a promising research direction to be further investigated.
Non-iterative control-oriented regularization for linear system identification
In the context of regularization methods for linear system identification, we introduce a new ker... more In the context of regularization methods for linear system identification, we introduce a new kernel design procedure that accounts for control objectives. We consider a model-reference control setup and assume data from one experiment is available. Exploiting the frequency response of the reference model, we design a new kernel that is able to extract the least amount of information from the data to the purpose of matching the desired closed-loop, with particular attention to user-defined frequency bands. Unlike the recently proposed CoRe algorithm, the proposed method is non-iterative and does not require any preliminary controller estimation. Simulation results on a benchmark example show that, when the model is used for control design, the proposed regularization procedure outperforms traditional kernel-based techniques as well as bias-shaping through data prefiltering.
Observability Linear Hybrid Systems
ACM International Conference Hybrid Systems: Computation and Control, 2003
arXiv (Cornell University), Feb 26, 2013
The popular Lasso approach for sparse estimation can be derived via marginalization of a joint de... more The popular Lasso approach for sparse estimation can be derived via marginalization of a joint density associated with a particular stochastic model. A different marginalization of the same probabilistic model leads to a different non-convex estimator where hyperparameters are optimized. Extending these arguments to problems where groups of variables have to be estimated, we study a computational scheme for sparse estimation that differs from the Group Lasso. Although the underlying optimization problem defining this estimator is non-convex, an initialization strategy based on a univariate Bayesian forward selection scheme is presented. This also allows us to define an effective non-convex estimator where only one scalar variable is involved in the optimization process. Theoretical arguments, independent of the correctness of the priors entering the sparse model, are included to clarify the advantages of this non-convex technique in comparison with other convex estimators. Numerical experiments are also used to compare the performance of these approaches.
We introduce a novel approach to modeling the dynamics of human facial motion induced by the acti... more We introduce a novel approach to modeling the dynamics of human facial motion induced by the action of speech for the purpose of synthesis. We represent the trajectories of a number of salient features on the human face as the output of a dynamical system made up of two subsystems, one driven by the deterministic speech input, and a second driven by an unknown stochastic input. Inference of the model (learning) is performed automatically and involves an extension of independent component analysis to time-depentend data. Using a shapetexture decompositional representation for the face, we generate facial image sequences reconstructed from synthesized feature point positions.
IFAC Proceedings Volumes, Sep 1, 2003
In this paper we illustrate the use of identification-theoretic techniques in computer vision, an... more In this paper we illustrate the use of identification-theoretic techniques in computer vision, and hint at some open problems.
arXiv (Cornell University), Nov 27, 2014
Visual representations are defined in terms of minimal sufficient statistics of visual data, for ... more Visual representations are defined in terms of minimal sufficient statistics of visual data, for a class of tasks, that are also invariant to nuisance variability. Minimal sufficiency guarantees that we can store a representation in lieu of raw data with smallest complexity and no performance loss on the task at hand. Invariance guarantees that the statistic is constant with respect to uninformative transformations of the data. We derive analytical expressions for such representations and show they are related to feature descriptors commonly used in computer vision, as well as to convolutional neural networks. This link highlights the assumptions and approximations tacitly assumed by these methods and explains empirical practices such as clamping, pooling and joint normalization.
Data-Driven Control of Nonlinear Systems: Learning Koopman Operators for Policy Gradient
2021 60th IEEE Conference on Decision and Control (CDC), Dec 14, 2021
Data-driven control of nonlinear dynamical systems is a largely open problem. In this paper, buil... more Data-driven control of nonlinear dynamical systems is a largely open problem. In this paper, building upon the theory of Koopman operators and exploiting ideas from policy gradient methods in reinforcement learning, a novel approach for data-driven optimal control of unknown nonlinear dynamical systems is introduced.
3-D Motion and Structure Causally Integrated Over Time: Theory
IFAC-PapersOnLine, 2018
Stability of identified models can be achieved, in the framework of parametric Prediction Error M... more Stability of identified models can be achieved, in the framework of parametric Prediction Error Methods (PEM) by imposing nonlinear constraints on the parameter space. When using regularisation techniques with, for instance, stable spline kernels, stability of the predictor model is guaranteed; however this does not imply stability of the model, nor there is a trivial way to guarantee the identified model is stable. An important approach available in the literature to recover stability relies on linear matrix inequalities (LMI). In particular, by means of overparametrization, a convex optimization problem is formulated. Its solution has to balance adherence to a preliminarily obtained (unconstrained) estimate and system stability according to a design parameter δ that determines dominant poles location. In this paper we propose a new stabilization algorithm. Our approach is non convex but does not require overparametrization and embeds regularization through the use of Gaussian regression and stable spline kernels. It is implemented by a very efficient sequential convex optimization procedure, namely the sequential stabilizing spline (SSS) algorithm. In comparison with LMI, numerical experiments show that SSS can provide more predictive models with a computational time orders of magnitude faster.
Springer eBooks, 2007
In this paper we make a first attempt at understanding how to build an optimal approximate normal... more In this paper we make a first attempt at understanding how to build an optimal approximate normal factor analysis model. The criterion we have chosen to evaluate the distance between different models is the Idivergence between the corresponding normal laws. The algorithm that we propose for the construction of the best approximation is of an the alternating minimization kind.
IFAC-PapersOnLine, 2015
We discuss the linear system identification methods that are based on a regularized estimation pr... more We discuss the linear system identification methods that are based on a regularized estimation problem including a rank penalty (typically formulated in terms of nuclear norm). We provide a common framework, under which most of these procedures can be recast. Following the Bayesian approach to system identification, we also introduce a Gaussian prior inducing a rank penalty and we prove the effectiveness of this method through a Monte-Carlo experiment.
2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601), 2004
Many algorithms have been proposed in literature to deal with the tracking and data association p... more Many algorithms have been proposed in literature to deal with the tracking and data association problem. A common assumption made in the proposed algorithms is that the targets are independent. There are however many interesting applications in which targets exhibit some sort of coordination, they satisfy shape constraints. In the current work a general and well formalized method which allows to embed such constraints into data association filters is proposed. The resulting algorithm performs robustly in challenging scenarios.
Methods for solving multi target tracking and data association problems in presence of clutter an... more Methods for solving multi target tracking and data association problems in presence of clutter and occlusions are based on models that describe the target dynamics and the measurements statistics. Most often the dynamics of the targets are assumed to be independent from each other. In many applications, however, the motion of the targets may be coordinated. We introduce a statistical concept of shape, or coordination, in terms of invariants w.r.t. the motion of the targets. Assuming that the rules of coordination may slowly change over time, we study the interplay among the shape and the target dynamics.
Controlled Recognition Bounds for Scaling and Occlusion Channels
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Papers by Alessandro Chiuso