G. Pillonetto

• University of Pavia

We address the problem of distributed unconstrained convex optimization under separability assumptions, i.e., the framework where each agent of a network is endowed with a local private multidimensional convex cost, is subject to communication constraints, and wants to collaborate to compute the minimizer of the sum of the local costs. We propose a...

System Identification has been developed, by and large, following the classical parametric approach. In this tutorial we shall discuss how Bayesian statistics and regularization theory can be employed to tackle the system identification problem from a nonparametric (or semi-parametric) point of view. The present paper provides an introduction to th...

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 in...

We consider estimation of network cardinality by distributed anonymous strategies relying on statistical inference methods. In particular, we focus on the relative Mean Square Error (MSE) of Maximum Likelihood (ML) estimators based on either the maximum or the average of $M$-dimensional vectors randomly generated at each node. In the case of contin...

A kernel-based regularization method to linear system identification was introduced and studied recently. Its novelty is that it finds a reliable way to tackle the bias-variance tradeoff via well-tuned regularization. Kernel design is a key issue for this method and several single kernels have been proposed. Very recently, we introduced and studied...

In the recent years several regularization strategies have been proposed to tackle linear system identification problems. One line of work has concentrated on designing and studying the properties of several Kernels for l2-type regularization in impulse response estimation; a second stream of work has proposed using Nuclear Norm type of penalties o...

This paper considers the classification problem using support vector (SV) machines and investigates how to maximally reduce the size of the training set without losing information. Under separable data set assumptions, we derive the exact conditions stating which observations can be discarded without diminishing the overall information content. For...

Model estimation and structure detection with short data records are two issues that receive increasing interests in System Identification. In this paper, a multiple kernel-based regularization method is proposed to handle those issues. Multiple kernels are conic combinations of fixed kernels suitable for impulse response estimation, and equip the...

We consider the convergence rates of two convex optimization strategies in the context of multi agent systems, namely the Newton-Raphson consensus optimization and a distributed Gradient-Descent opportunely derived from the first. To allow analytical derivations, the convergence analyses are performed under the simplificative assumption of quadrati...

We demonstrate that many robust, sparse and nonsmooth identification and Kalman smoothing problems can be studied using a unified statistical framework. This framework is built on a broad sub-class of log-concave densities, which we call PLQ densities, that include many popular models for regression and state estimation, e.g. ℓ1, ℓ2, Vapnik and Hub...

The paper considers the problem of reconstructing a probability density function from a finite set of samples independently drawn from it.We cast the problem in a Bayesian setting where the unknown density is modeled via a nonlinear transformation of a Bayesian prior placed on a Reproducing Kernel Hilbert Space. The learning of the unknown density...

This paper presents a novel method for the online estimation of variance parameters regulating the dynamics of a nonlinear dynamic system. The approach exploits and extends classical iterated Kalman filtering equations by propagating an approximation of the marginal posterior of the unknown variances over time. In addition to the theoretical founda...

In this work we consider a multidimensional distributed optimization technique that is suitable for multi-agents systems subject to limited communication connectivity. In particular, we consider a convex unconstrained additive problem, i.e. a case where the global convex unconstrained multidimensional cost function is given by the sum of local cost...

To maintain and organize distributed systems it is necessary to have a certain degree of knowledge of their status like the number of cooperating agents. The estimation of this number, usually referred as the network size, can pose challenging questions when agents' identification information cannot be disclosed, since the exchanged information can...

We introduce a new kernel-based nonparametric approach to estimate the second-order statistics of scalar and stationary stochastic processes. The correlations functions are assumed to be summable and are modeled as realizations of zero-mean Gaussian processes using the recently introduced Stable Spline kernel. In this way, information on the decay...

A client-server architecture to simultaneously solve multiple learning tasks from distributed datasets is described. In such architecture, each client corresponds to an individual learning task and the associated dataset of examples. The goal of the architecture is to perform information fusion from multiple datasets while preserving privacy of ind...

Identification of sparse high dimensional linear systems pose sever challenges to off-the-shelf techniques for system identification. This is particularly so when relatively small data sets, as compared to the number of inputs and outputs, have to be used. In this paper we introduce a new nonparametric technique which borrows ideas from a recently...

The distributed estimation of the number of active sensors in a network can be important for estimation and organization purposes. We propose a design methodology based on the following paradigm: some locally randomly generated values are exchanged among the various sensors and thus modified by known consensus-based strategies. Statistical analysis...

We present a moving horizon approach for estimating the state of a nonlinear dynamic system that may be subject to inequality constraints. The method takes advantage of a recent smoothing algorithm proposed in the literature based on interior point techniques. The approach exploits the same decomposition used for unconstrained Kalman-Bucy smoothers...

A new nonparametric paradigm to model identification has been recently introduced in the literature. Instead of adopting finite-dimensional models of the system transfer function, the system impulse response is searched for within an infinite dimensional space using regularization theory. The method exploits the so called stable spline kernels whic...

The paper considers the framework of distributed Bayesian linear estimation. We introduce some consensus-based estimation strategies that are equivalent to centralized ones pending knowledge of some parameters, e.g. number of agents in the network. If such parameters are not known, agents can estimate them locally or exploit prior knowledge. We sho...

We propose a novel nonparametric approach to ARMAX identification with missing data relying upon recent work on predictor estimation via Gaussian regression. The Bayesian setup allows one to compute explicitly an input-output marginal density where the model dependence has been integrated out. This turns out to be a key step in facilitating the imp...

In this paper we analyze the problem of estimating a function from different noisy data sets collected by spatially distributed sensors and subject to unknown temporal shifts. We propose a novel approach based on non-parametric Gaussian regression and reproducing kernel Hilbert space theory that exploit compact and accurate representations of funct...

An accurate characterization of tissue residue function R(t) in bolus-tracking magnetic resonance imaging is of crucial importance to quantify cerebral hemodynamics. R(t) estimation requires to solve a deconvolution problem. The most popular deconvolution method is singular value decomposition (SVD). However, SVD is known to bear some limitations,...

A novel nonparametric paradigm to model identification has been recently proposed where, in place of postulating finite-dimensional models of the system transfer function, the system impulse response is searched for within an infinite-dimensional space. In this paper, we extend such nonparametric approach to the design of optimal predictors by inte...

In this paper we propose a new nonparametric approach to identification of linear time invariant systems using subspace methods. The nonparametric paradigm to prediction of stationary stochastic processes, developed in a companion paper, is integrated into a recently proposed subspace method. Simulation results show that this approach significantly...

We consider a class of linear systems in state-space form whose parameters evolve in time according to a continuous-time Gauss-Markov process. Our problem is to identify the system from a finite set of noisy output measurements. We derive a connection between this problem and Tikhonov regularization in reproducing kernel Hilbert spaces. Relying upo...

This paper presents an experimental validation of an online estimation algorithm we recently investigated theoretically. One of the peculiar characteristics of the approach we propose is the ability to perform an online estimation of the variance parameters that regulate the dynamics of the nonlinear dynamical model used. The approach exploits and...

We are given a reliable parametric model of a system whose structure and parameter values can be obtained by an identification experiment. Often, one or more indices can be determined as a function of model parameters, i.e. an index is a function that maps the parameter space into the real line. The aim of these indices is to incorporate as much in...

We propose a new-kernel based approach for linear system identification. The impulse response is modeled as realization of a Gaussian process which includes information on smoothness and BIBO-stability. The corresponding minimum- variance estimate belongs to a Reproducing kernel Hilbert space which is given a spectral characterization and shown to...

Recently, standard single-task kernel methods have been extended to the case of multi-task learning under the framework of regularization. Experimental results have shown that such an approach can perform much better than single-task techniques, especially when few examples per task are available. However, a possible drawback may be computational c...

The multirobot localization problem is solved in this paper using an innovative approach related to Tikhonov regularization. We release the requirement that robots are equipped with sensors to estimate their own motion, as well as the requirement that covariance matrices describing system and measure noises are perfectly known. Robots are assumed t...

In the context of biomedical data analysis, population models are used to characterize the average and individual behavior of a population of subjects. When a mechanistic model is not available, one can resort to the nonparametric approach that describes the individual curves as realizations of Gaussian processes. In this paper, efficient algorithm...

Endogenous glucose production (EGP) after a glucose stimulus can be estimated by deconvolution of the endogenous component of glucose concentration, which is computed from noisy measurements. This study analyzes how measurement errors propagate to endogenous glucose and affect EGP reconstruction during intravenous (IVGTT) and oral (MEAL) glucose to...

The standard measures of insulin sensitivity, SI , obtained e.g. by clamp or minimal model (MM) techniques, do not account for how fast/slow insulin action reaches its plateau value. Recently, we have proposed a new dynamic insulin sensitivity index, S ID, that incorporates this information. We have shown that in normal subjects S ID offers, in com...

In this paper we investigate whether it is advantageous to merge some ideas formerly found in the randomized potential field planner with our recently introduced adaptive random walks planner. These aspects are biasing the generation of samples, an attractor for the samples generator, and the possibility to backtrack when the planner gets stuck whi...

Introduction. Bolus tracking MRI allows to quantify cerebral blood flow (CBF), volume (CBV) and mean transit time (MTT) by deconvolution from arterial input function, AIF(t), and tissue concentration, C(t), measures: C(t)=CBF٠[AIF(t)⊗R(t)] (eq.1), where R(t) is the tissue residue function. In particular, one obtains R*(t)=CBF·R(t) and estimates CBF...

We propose a novel single-shot motion-planning algorithm based on adaptive random walks. The proposed algorithm turns out to be simple to implement, and the solution it produces can be easily and efficiently optimized. Furthermore, the algorithm can incorporate adaptive components, so the developer is not required to specify all the parameters of t...

We propose a novel motion planning algorithm based on adaptive random walks. The proposed algorithm turns out to be easy to implement and the solution it produces can be easily and efficiently optimized. Furthermore the algorithm can incorporate adaptive components, so that the developer is not required to specify all the parameters of the random d...

Reconstructing insulin secretion rate (ISR) after a glucose stimulus by deconvolution is difficult because of its biphasic pattern, i.e., a rapid secretion peak is followed by a slower release. Here, we refine a recently proposed stochastic deconvolution method by modeling ISR as the multiple integration of a white noise process with time-varying s...

Wireless networks can easily provide temperature, humidity and solar radiation measurements from tens to hundreds of sensors, thus potentially providing a fine-grained spatial-temporal resolution. However such a wealth of data may render model identification rather difficult for state of the art methods, which may require enormous amount of data (i...