Model learning from data: from centralized multi-model regression to distributed cloud-aided single-model estimation

This thesis presents a collection of methods for learning modelsfrom data, looking at this problem from two perspectives:learning multiple models from a single data source and howto switch among them, and learning a single model from datacollected from multiple sources.Regarding the first, to describe complex phenomena with simplebut yet complete models, we propose a computationallyefficient method for Piecewise Affine (PWA) regression. Thisapproach relies on the combined use (i) multi-model RecursiveLeast-Squares (RLS) and (ii) piecewise linear multi- categorydiscrimination, and shows good performances whenused for the identification of Piecewise Affine dynamical systemswith eXogenous inputs (PWARX) and Linear ParameterVarying (LPV) models. The technique for PWA regression isthen extended to handle the problem of black-box identificationof Discrete Hybrid Automata (DHA) from input/outputobservations, with hidden operating modes. The method forDHA identification is based on multi-model RLS and multicategorydiscrimination and it can approximate both the continuousaffine dynamics and the Finite State Machine (FSM)governing the logical dynamics of the DHA. Two more approachesare presented to tackle the problem of learning modelsthat jump over time. While the technique designed tolearn Rarely Jump Models (RJMs) from data relies on the combinedsolution of a convex optimization problem and the useof Dynamic Programming, the method proposed for MarkovJump Models (MJMs) learning is based on the joint use ofclustering plus multi-model RLS and a probabilistic clusteringtechnique. The results of the tests performed on the method for RJMs learning have motivated the design of two techniquesfor Non-Intrusive Load Monitoring, i.e., to estimatethe power consumed by the appliances in an household fromaggregated measurements, which are also presented in thethesis. In particular, methods based on (i) the optimization ofa least-square error cost function, modified to account for thechanges in the appliances operating regime, and relying on(ii) multi-model Kalman filters are proposed.Regarding the second perspective, we propose methods forcloud-aided consensus-based parameter estimation over a multitudeof similar devices (such as a mass production). In particular,we focus on the design of RLS-based estimators, whichallow to handle (i) linear and (ii) nonlinear consensus constraintsand (iii) multi-class estimation.