20 research outputs found
Fitting Jump Models
We describe a new framework for fitting jump models to a sequence of data.
The key idea is to alternate between minimizing a loss function to fit multiple
model parameters, and minimizing a discrete loss function to determine which
set of model parameters is active at each data point. The framework is quite
general and encompasses popular classes of models, such as hidden Markov models
and piecewise affine models. The shape of the chosen loss functions to minimize
determine the shape of the resulting jump model.Comment: Accepted for publication in Automatic
A learning-based approach to multi-agent decision-making
We propose a learning-based methodology to reconstruct private information
held by a population of interacting agents in order to predict an exact outcome
of the underlying multi-agent interaction process, here identified as a
stationary action profile. We envision a scenario where an external observer,
endowed with a learning procedure, is allowed to make queries and observe the
agents' reactions through private action-reaction mappings, whose collective
fixed point corresponds to a stationary profile. By adopting a smart query
process to iteratively collect sensible data and update parametric estimates,
we establish sufficient conditions to assess the asymptotic properties of the
proposed learning-based methodology so that, if convergence happens, it can
only be towards a stationary action profile. This fact yields two main
consequences: i) learning locally-exact surrogates of the action-reaction
mappings allows the external observer to succeed in its prediction task, and
ii) working with assumptions so general that a stationary profile is not even
guaranteed to exist, the established sufficient conditions hence act also as
certificates for the existence of such a desirable profile. Extensive numerical
simulations involving typical competitive multi-agent control and decision
making problems illustrate the practical effectiveness of the proposed
learning-based approach
Supervised classification and mathematical optimization
Data Mining techniques often ask for the resolution of optimization problems. Supervised Classification, and, in particular, Support Vector Machines, can be seen as a paradigmatic instance. In this paper, some links between Mathematical Optimization methods and Supervised Classification are emphasized. It is shown that many different areas of Mathematical Optimization play a central role in off-the-shelf Supervised Classification methods. Moreover, Mathematical Optimization turns out to be extremely
useful to address important issues in Classification, such as identifying relevant variables, improving the interpretability of classifiers or dealing with vagueness/noise in the data.Ministerio de Ciencia e Innovaci贸nJunta de Andaluc铆
Supervised Classification and Mathematical Optimization
Data Mining techniques often ask for the resolution of optimization problems. Supervised Classification, and, in particular, Support Vector Machines, can be seen as a paradigmatic instance. In this paper, some links between Mathematical Optimization methods and Supervised Classification are emphasized. It is shown that many different areas of Mathematical Optimization play a central role in off-the-shelf Supervised Classification methods. Moreover, Mathematical Optimization turns out to be extremely useful to address important issues in Classification, such as identifying relevant variables, improving the interpretability of classifiers or dealing with vagueness/noise in the data
Identification of piecewise-linear mechanical oscillators via Bayesian model selection and parameter estimation
The problem of identifying single degree-of-freedom (SDOF) nonlinear mechanical oscillators with piecewise-linear (PWL) restoring forces is considered. PWL nonlinear systems are a class of models that specify or approximate nonlinear systems via a set of locally-linear maps, each defined over different operating regions. They are useful in modelling hybrid phenomena common in practical situations, such as, systems with different modes of operation, or systems whose dynamics change because of physical limits or thresholds. However, identifying PWL models can be a challenging task when the number of operating regions and their partitions are unknown. This paper formulates the identification of oscillators with PWL restoring forces as a task of concurrent model selection and parameter estimation, where the selection of the number of linear regions is treated as a model selection task and identifying the associated system parameters as a task of parameter estimation. In this study, PWL maps in restoring forces with up to four regions are considered, and the task of model selection and parameter estimation task is addressed in a Bayesian framework. A likelihood-free Approximate Bayesian Computation (ABC) scheme is followed, which is easy to implement and provides a simplified way of doing model selection. The proposed approach has been demonstrated using two numerical examples and an experimental study, where ABC has been used to select models and identify parameters from among four SDOF PWL systems with different number of PWL regions. The results demonstrate the flexibility of using the proposed Bayesian approach for identifying the correct model and parameters of PWL systems, in addition to furnishing uncertainty estimates of the identified parameters