12,208 research outputs found
Integrated Pre-Processing for Bayesian Nonlinear System Identification with Gaussian Processes
We introduce GP-FNARX: a new model for nonlinear system identification based
on a nonlinear autoregressive exogenous model (NARX) with filtered regressors
(F) where the nonlinear regression problem is tackled using sparse Gaussian
processes (GP). We integrate data pre-processing with system identification
into a fully automated procedure that goes from raw data to an identified
model. Both pre-processing parameters and GP hyper-parameters are tuned by
maximizing the marginal likelihood of the probabilistic model. We obtain a
Bayesian model of the system's dynamics which is able to report its uncertainty
in regions where the data is scarce. The automated approach, the modeling of
uncertainty and its relatively low computational cost make of GP-FNARX a good
candidate for applications in robotics and adaptive control.Comment: Proceedings of the 52th IEEE International Conference on Decision and
Control (CDC), Firenze, Italy, December 201
A new kernel-based approach for overparameterized Hammerstein system identification
In this paper we propose a new identification scheme for Hammerstein systems,
which are dynamic systems consisting of a static nonlinearity and a linear
time-invariant dynamic system in cascade. We assume that the nonlinear function
can be described as a linear combination of basis functions. We reconstruct
the coefficients of the nonlinearity together with the first samples of
the impulse response of the linear system by estimating an -dimensional
overparameterized vector, which contains all the combinations of the unknown
variables. To avoid high variance in these estimates, we adopt a regularized
kernel-based approach and, in particular, we introduce a new kernel tailored
for Hammerstein system identification. We show that the resulting scheme
provides an estimate of the overparameterized vector that can be uniquely
decomposed as the combination of an impulse response and coefficients of
the static nonlinearity. We also show, through several numerical experiments,
that the proposed method compares very favorably with two standard methods for
Hammerstein system identification.Comment: 17 pages, submitted to IEEE Conference on Decision and Control 201
Maximum entropy properties of discrete-time first-order stable spline kernel
The first order stable spline (SS-1) kernel is used extensively in
regularized system identification. In particular, the stable spline estimator
models the impulse response as a zero-mean Gaussian process whose covariance is
given by the SS-1 kernel. In this paper, we discuss the maximum entropy
properties of this prior. In particular, we formulate the exact maximum entropy
problem solved by the SS-1 kernel without Gaussian and uniform sampling
assumptions. Under general sampling schemes, we also explicitly derive the
special structure underlying the SS-1 kernel (e.g. characterizing the
tridiagonal nature of its inverse), also giving to it a maximum entropy
covariance completion interpretation. Along the way similar maximum entropy
properties of the Wiener kernel are also given
Machine Learning in Automated Text Categorization
The automated categorization (or classification) of texts into predefined
categories has witnessed a booming interest in the last ten years, due to the
increased availability of documents in digital form and the ensuing need to
organize them. In the research community the dominant approach to this problem
is based on machine learning techniques: a general inductive process
automatically builds a classifier by learning, from a set of preclassified
documents, the characteristics of the categories. The advantages of this
approach over the knowledge engineering approach (consisting in the manual
definition of a classifier by domain experts) are a very good effectiveness,
considerable savings in terms of expert manpower, and straightforward
portability to different domains. This survey discusses the main approaches to
text categorization that fall within the machine learning paradigm. We will
discuss in detail issues pertaining to three different problems, namely
document representation, classifier construction, and classifier evaluation.Comment: Accepted for publication on ACM Computing Survey
A new kernel-based approach to system identification with quantized output data
In this paper we introduce a novel method for linear system identification
with quantized output data. We model the impulse response as a zero-mean
Gaussian process whose covariance (kernel) is given by the recently proposed
stable spline kernel, which encodes information on regularity and exponential
stability. This serves as a starting point to cast our system identification
problem into a Bayesian framework. We employ Markov Chain Monte Carlo methods
to provide an estimate of the system. In particular, we design two methods
based on the so-called Gibbs sampler that allow also to estimate the kernel
hyperparameters by marginal likelihood maximization via the
expectation-maximization method. Numerical simulations show the effectiveness
of the proposed scheme, as compared to the state-of-the-art kernel-based
methods when these are employed in system identification with quantized data.Comment: 10 pages, 4 figure
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