@article {omgp_pr,
	title = {Overlapping Mixtures of Gaussian Processes for the Data Association Problem},
	journal = {Pattern Recognition},
	volume = {45},
	number = {4},
	year = {2012},
	month = {April},
	pages = {1386{\textendash}1395},
	abstract = {In this work we introduce a mixture of GPs to address the data association problem, i.e. to label a group of observations according to the sources that generated them. Unlike several previously proposed GP mixtures, the novel mixture has the distinct characteristic of using no gating function to determine the association of samples and mixture components. Instead, all the GPs in the mixture are global and samples are clustered following {\textquotedblleft}trajectories{\textquotedblright} across input space. We use a non-standard variational Bayesian algorithm to efficiently recover sample labels and learn the hyperparameters. We show how multi-object tracking problems can be disambiguated and also explore the characteristics of the model in traditional regression settings.},
	issn = {0031-3203},
	author = {L{\'a}zaro-Gredilla, Miguel and Van Vaerenbergh, Steven and Lawrence, Neil D.}
}
@article {282,
	title = {Kernel Recursive Least-Squares Tracker for Time-Varying Regression},
	journal = {IEEE Transactions on Neural Networks and Learning Systems},
	volume = {23},
	year = {2012},
	month = {August},
	pages = {1313--1326},
	abstract = {In this paper, we introduce a kernel recursive least-squares (KRLS) algorithm that is able to track nonlinear, time-varying relationships in data. To this purpose, we first derive the standard KRLS equations from a Bayesian perspective (including a sensible approach to pruning) and then take advantage of this framework to incorporate forgetting in a consistent way, thus enabling the algorithm to perform tracking in nonstationary scenarios. The resulting method is the first kernel adaptive filtering algorithm that includes a forgetting factor in a principled and numerically stable manner. In addition to its tracking ability, it has a number of appealing properties. It is online, requires a fixed amount of memory and computation per time step, incorporates regularization in a natural manner and provides confidence intervals along with each prediction. We include experimental results that support the theory as well as illustrate the efficiency of the proposed algorithm.},
	keywords = {kernel adaptive filtering, KRLS},
	issn = {2162-237X},
	doi = {10.1109/TNNLS.2012.2200500},
	url = {http://ieeexplore.ieee.org/xpl/articleDetails.jsp?arnumber=6227361},
	author = {Van Vaerenbergh, Steven and L{\'a}zaro-Gredilla, Miguel and Santamar{\'\i}a, Ignacio}
}
@article {342,
	title = {Gaussian Processes for Nonlinear Signal Processing: An Overview of Recent Advances},
	journal = {IEEE Signal Processing Magazine},
	volume = {30},
	year = {2013},
	month = {July},
	pages = {40-50},
	abstract = {Gaussian processes (GPs) are versatile tools that have been successfully employed to solve nonlinear estimation problems in machine learning, but that are rarely used in signal processing. In this tutorial, we present GPs for regression as a natural nonlinear extension to optimal Wiener filtering. After establishing their basic formulation, we discuss several important aspects and extensions, including recursive and adaptive algorithms for dealing with non-stationarity, low-complexity solutions, non-Gaussian noise models and classification scenarios. Furthermore, we provide a selection of relevant applications to wireless digital communications.},
	keywords = {kernel adaptive filtering},
	issn = {1053-5888},
	doi = {10.1109/MSP.2013.2250352},
	url = {http://ieeexplore.ieee.org/xpl/articleDetails.jsp?arnumber=6530761},
	author = {P{\'e}rez-Cruz, Fernando and Van Vaerenbergh, Steven and Murillo-Fuentes, Juan Jos{\'e} and L{\'a}zaro-Gredilla, Miguel and Santamar{\'\i}a, Ignacio}
}
@article {378,
	title = {A Gaussian Process Model for Data Association and a Semi-Definite Programming Solution},
	journal = {IEEE Transactions on Neural Networks and Learning Systems},
	volume = {25},
	year = {2014},
	month = {November},
	pages = {1967-1979},
	abstract = {In this paper we propose a Bayesian model for the data association problem, in which trajectory smoothness is enforced through the use of Gaussian process priors. This model allows to score candidate associations by using the evidence framework, thus casting the data association problem into an optimization problem. Under some additional mild assumptions, this optimization problem is shown to be equivalent to a constrained Max K-Section problem. Furthermore, for K = 2, a MaxCut formulation is obtained, to which an approximate solution can be efficiently found using an SDP relaxation. Solving this MaxCut problem is equivalent to finding the optimal association out of the combinatorially many possibilities. The obtained clustering depends only on two hyperparameters, which can also be selected by maximum evidence.},
	issn = {2162-237X},
	doi = {10.1109/TNNLS.2014.2300701},
	author = {L{\'a}zaro-Gredilla, Miguel and Van Vaerenbergh, Steven}
}
@article {375,
	title = {A Bayesian Approach for Adaptive Multiantenna Sensing in Cognitive Radio Networks},
	journal = {Signal Processing},
	volume = {96},
	year = {2014},
	month = {March},
	pages = {240},
	chapter = {228},
	abstract = {Recent work on multiantenna spectrum sensing in cognitive radio (CR) networks has been based on generalized likelihood ratio test (GLRT) detectors, which lack the ability to learn from past decisions and to adapt to the continuously changing environment. To overcome this limitation, in this paper we propose a Bayesian detector capable of learning in an efficient way the posterior distributions under both hypotheses. Our Bayesian model places priors directly on the spatial covariance matrices under both hypotheses, as well as on the probability of channel occupancy. Specifically, we use inverse-gamma and complex inverse-Wishart distributions as conjugate priors for the null and alternative hypothesis, respectively; and a binomial distribution as the prior for channel occupancy. At each sensing period, Bayesian inference is applied and the posterior for the channel occupancy is thresholded for detection. After a suitable approximation, the posteriors are employed as priors for the next sensing frame, which forms the basis of the proposed Bayesian learning procedure. The performance of the Bayesian detector is evaluated by simulations and by means of a CR testbed composed of universal radio peripheral (USRP) nodes. Both the simulations and experimental measurements show that the Bayesian detector outperforms the GLRT in a variety of scenarios.
},
	doi = {10.1016/j.sigpro.2013.10.005},
	author = {Manco-V{\'a}squez, Julio and L{\'a}zaro-Gredilla, Miguel and Ram{\'\i}rez, David and V{\'\i}a, Javier and Santamar{\'\i}a, Ignacio}
}
@conference {205_vhgpr_icml,
	title = {Variational Heteroscedastic Gaussian Process Regression},
	booktitle = {The 28th International Conference on Machine Learning},
	year = {2011},
	month = {July},
	address = {Bellevue, Washington},
	author = {L{\'a}zaro-Gredilla, Miguel and Titsias, Michalis}
}
@conference {Icassp2011_Lazaro,
	title = {Tracking Performance of Adaptively Biased Adaptive Filters},
	booktitle = {IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP 2011)},
	year = {2011},
	month = {May},
	address = {Prague, Czech Republic},
	author = {Arenas-Garc{\'\i}a, J. and L{\'a}zaro-Gredilla, Miguel}
}
@conference {314,
	title = {Estimation of the Forgetting Factor in Kernel Recursive Least Squares},
	booktitle = {2012 IEEE International Workshop On Machine Learning For Signal Processing (MLSP)},
	year = {2012},
	month = {September},
	abstract = {In a recent work we proposed a kernel recursive least-squares tracker (KRLS-T) algorithm that is capable of tracking in non-stationary environments, thanks to a forgetting mechanism built on a Bayesian framework. In order to guarantee optimal performance its parameters need to be determined, specifically its kernel parameters, regularization and, most importantly in non-stationary environments, its forgetting factor. This is a common difficulty in adaptive filtering techniques and in signal processing algorithms in general. In this paper we demonstrate the equivalence between KRLS-T{\textquoteright}s recursive tracking solution and Gaussian process (GP) regression with a specific class of spatio-temporal covariance. This result allows to use standard hyperparameter estimation techniques from the Gaussian process framework to determine the parameters of the KRLS-T algorithm. Most notably, it allows to estimate the optimal forgetting factor in a principled manner. We include results on different benchmark data sets that offer interesting new insights.},
	keywords = {kernel adaptive filtering},
	author = {Van Vaerenbergh, Steven and Santamar{\'\i}a, Ignacio and L{\'a}zaro-Gredilla, Miguel}
}
@conference {310,
	title = {Bayesian Multiantenna Sensing for Cognitive Radio},
	booktitle = {7th IEEE Sensor Array and Multichannel Signal Processing Workshop},
	year = {2012},
	month = {June},
	address = {Hoboken, NJ, USA},
	abstract = {In this paper, the problem of multiantenna spectrum sensing in cognitive radio (CR) is addressed within a Bayesian framework. Unlike previous works, our Bayesian model places priors directly on the spatial covariance matrices under both hypotheses, as well as on the probability of channel occupancy. Specifically, we use inverse-gamma and complex inverse-Wishart distributions as conjugate priors for the null and alternative hypotheses, respectively; and a Bernoulli distribution as the prior for channel occupancy. At each sensing period, Bayesian inference is applied and the posterior of channel occupancy is thresholded for detection. After a suitable approximation, the posteriors are employed as priors for the next sensing frame, which can be beneficial in slowly time-varying environments. By means of simulations, the proposed detector is shown to outperform the Generalized Likelihood Ratio Test (GLRT) detector.},
	author = {Manco-V{\'a}squez, Julio and L{\'a}zaro-Gredilla, Miguel and Ram{\'\i}rez, David and V{\'\i}a, Javier and Santamar{\'\i}a, Ignacio}
}
@conference {Miguel_KRLS_MLSP2011,
	title = {A {Bayesian} Approach To Tracking With Kernel Recursive Least-Squares},
	booktitle = {IEEE International Workshop on Machine Learning for Signal Processing (MLSP 2011)},
	year = {2011},
	month = {September},
	address = {Beijing, China},
	abstract = {In this paper we introduce a kernel-based recursive least-squares (KRLS) algorithm that is able to track nonlinear, time-varying relationships in data. To this purpose we first derive the standard KRLS equations from a Bayesian perspective (including a principled approach to pruning) and then take advantage of this framework to incorporate forgetting in a consistent way, thus enabling the algorithm to perform tracking in non-stationary scenarios. In addition to this tracking ability, the resulting algorithm has a number of appealing properties: It is online, requires a fixed amount of memory and computation per time step and incorporates regularization in a natural manner. We include experimental results that support the theory as well as illustrate the efficiency of the proposed algorithm.},
	keywords = {kernel adaptive filtering, KRLS},
	author = {L{\'a}zaro-Gredilla, Miguel and Van Vaerenbergh, Steven and Santamar{\'\i}a, Ignacio}
}
