491 research outputs found
Distributed multi-agent Gaussian regression via finite-dimensional approximations
We consider the problem of distributedly estimating Gaussian processes in
multi-agent frameworks. Each agent collects few measurements and aims to
collaboratively reconstruct a common estimate based on all data. Agents are
assumed with limited computational and communication capabilities and to gather
noisy measurements in total on input locations independently drawn from a
known common probability density. The optimal solution would require agents to
exchange all the input locations and measurements and then invert an matrix, a non-scalable task. Differently, we propose two suboptimal
approaches using the first orthonormal eigenfunctions obtained from the
\ac{KL} expansion of the chosen kernel, where typically . The benefits
are that the computation and communication complexities scale with and not
with , and computing the required statistics can be performed via standard
average consensus algorithms. We obtain probabilistic non-asymptotic bounds
that determine a priori the desired level of estimation accuracy, and new
distributed strategies relying on Stein's unbiased risk estimate (SURE)
paradigms for tuning the regularization parameters and applicable to generic
basis functions (thus not necessarily kernel eigenfunctions) and that can again
be implemented via average consensus. The proposed estimators and bounds are
finally tested on both synthetic and real field data
Identification of stable models via nonparametric prediction error methods
A new Bayesian approach to linear system identification has been proposed in
a series of recent papers. The main idea is to frame linear system
identification as predictor estimation in an infinite dimensional space, with
the aid of regularization/Bayesian techniques. This approach guarantees the
identification of stable predictors based on the prediction error minimization.
Unluckily, the stability of the predictors does not guarantee the stability of
the impulse response of the system. In this paper we propose and compare
various techniques to address this issue. Simulations results comparing these
techniques will be provided.Comment: number of pages = 6, number of figures =
Bayesian kernel-based 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 (MCMC)
methods to provide an estimate of the system. In particular, we show how to
design a Gibbs sampler which quickly converges to the target distribution.
Numerical simulations show a substantial improvement in the accuracy of the
estimates over state-of-the-art kernel-based methods when employed in
identification of systems with quantized data.Comment: Submitted to IFAC SysId 201
Bayesian and regularization approaches to multivariable linear system identification: the role of rank penalties
Recent developments in linear system identification have proposed the use of
non-parameteric methods, relying on regularization strategies, to handle the
so-called bias/variance trade-off. This paper introduces an impulse response
estimator which relies on an -type regularization including a
rank-penalty derived using the log-det heuristic as a smooth approximation to
the rank function. This allows to account for different properties of the
estimated impulse response (e.g. smoothness and stability) while also
penalizing high-complexity models. This also allows to account and enforce
coupling between different input-output channels in MIMO systems. According to
the Bayesian paradigm, the parameters defining the relative weight of the two
regularization terms as well as the structure of the rank penalty are estimated
optimizing the marginal likelihood. Once these hyperameters have been
estimated, the impulse response estimate is available in closed form.
Experiments show that the proposed method is superior to the estimator relying
on the "classic" -regularization alone as well as those based in atomic
and nuclear norm.Comment: to appear in IEEE Conference on Decision and Control, 201
Maximum Entropy Vector Kernels for MIMO system identification
Recent contributions have framed linear system identification as a
nonparametric regularized inverse problem. Relying on -type
regularization which accounts for the stability and smoothness of the impulse
response to be estimated, these approaches have been shown to be competitive
w.r.t classical parametric methods. In this paper, adopting Maximum Entropy
arguments, we derive a new penalty deriving from a vector-valued
kernel; to do so we exploit the structure of the Hankel matrix, thus
controlling at the same time complexity, measured by the McMillan degree,
stability and smoothness of the identified models. As a special case we recover
the nuclear norm penalty on the squared block Hankel matrix. In contrast with
previous literature on reweighted nuclear norm penalties, our kernel is
described by a small number of hyper-parameters, which are iteratively updated
through marginal likelihood maximization; constraining the structure of the
kernel acts as a (hyper)regularizer which helps controlling the effective
degrees of freedom of our estimator. To optimize the marginal likelihood we
adapt a Scaled Gradient Projection (SGP) algorithm which is proved to be
significantly computationally cheaper than other first and second order
off-the-shelf optimization methods. The paper also contains an extensive
comparison with many state-of-the-art methods on several Monte-Carlo studies,
which confirms the effectiveness of our procedure
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
Nonparametric Bayesian Mixed-effect Model: a Sparse Gaussian Process Approach
Multi-task learning models using Gaussian processes (GP) have been developed
and successfully applied in various applications. The main difficulty with this
approach is the computational cost of inference using the union of examples
from all tasks. Therefore sparse solutions, that avoid using the entire data
directly and instead use a set of informative "representatives" are desirable.
The paper investigates this problem for the grouped mixed-effect GP model where
each individual response is given by a fixed-effect, taken from one of a set of
unknown groups, plus a random individual effect function that captures
variations among individuals. Such models have been widely used in previous
work but no sparse solutions have been developed. The paper presents the first
sparse solution for such problems, showing how the sparse approximation can be
obtained by maximizing a variational lower bound on the marginal likelihood,
generalizing ideas from single-task Gaussian processes to handle the
mixed-effect model as well as grouping. Experiments using artificial and real
data validate the approach showing that it can recover the performance of
inference with the full sample, that it outperforms baseline methods, and that
it outperforms state of the art sparse solutions for other multi-task GP
formulations.Comment: Preliminary version appeared in ECML201
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