Flexible and scalable decentralized learning solutions are fundamentally important in the application of multi-agent systems. While several recent approaches introduce (ensembles of) kernel machines in the distributed setting, Bayesian solutions are much more limited. We introduce a fully decentralized, asymptotically exact solution to computing the random feature approximation of Gaussian processes. We further address the choice of hyperparameters by introducing an ensembling scheme for Bayesian multiple kernel learning based on online Bayesian model averaging. The resulting algorithm is tested against Bayesian and frequentist methods on simulated and real-world datasets.

Bayesian Optimization (BO) is a popular black-box optimization method consisting of a surrogate model, typically a probabilistic model such as a Gaussian Process (GP) and an Acquisition function (AF). Effective selection of these functions has a strong impact on the optimization process. Existing ensemble-based methods for AF selection operate under the assumption that an "optimal" AF exists in the pool of considered AFs, and the method attempts to find the best AF. In this work, we operate in an agnostic setting and consider the optimal AF to be one which minimizes joint risk over all AFs considered. This allows us to treat the joint risk as a random process and perform Bayesian inference on the posterior. We empirically demonstrate the effectiveness of this method and provide theoretical bounds on the regret.

Bayesian optimization (BO) is a popular approach to optimizing costly, black-box functions that rely on a statistical surrogate model of the function to select new query points, balancing exploration and exploitation of the parameter space. Most of the work on BO has focused on the time-invariant setting where the function does not change over time. Recently, the time-varying BO (TV-BO) framework has been introduced to handle non-stationary functions. In this work, we explore TV-BO with the use of dynamic random feature-based Gaussian processes (DRF-GPs). These processes capture the nonstationarity of the unknown functions by evolving the parameter vector of a linear model. We propose an evolution mechanism that results in an acquisition function with sensible exploitation-exploration trade-offs over time. We compare the resulting algorithm with the TV-BO baseline algorithms on a toy example and a localization problem with synthetic data.

In the last decade, soundscapes have become one of the most active topics in Acoustics, providing a holistic approach to the acoustic environment, which involves human perception and context. Soundscapes-elicited emotions are central and substantially subtle and unnoticed (compared to speech or music). Currently, soundscape emotion recognition is a very active topic in the literature. We provide an exhaustive variable selection study (i.e., a selection of the soundscapes indicators) to a well-known dataset (emo-soundscapes). We consider linear soundscape emotion models for two soundscapes descriptors: arousal and valence. Several ranking schemes and procedures for selecting the number of variables are applied. We have also performed an alternating optimization scheme for obtaining the best sequences keeping fixed a certain number of features. Furthermore, we have designed a novel technique based on Gibbs sampling, which provides a more complete and clear view of the relevance of each variable. Finally, we have also compared our results with the analysis obtained by the classical methods based on p-values. As a result of our study, we suggest two simple and parsimonious linear models of only 7 and 16 variables (within the 122 possible features) for the two outputs (arousal and valence), respectively. The suggested linear models provide very good and competitive performance, with$R^{2}>0.86$and$R^{2}>0.63$(values obtained after a cross-validation procedure), respectively.

Bayesian methods and their implementations by means of sophisticated Monte Carlo techniques, such as Markov chain Monte Carlo (MCMC) and particle filters, have become very popular in signal processing over the last years. In this letter, we present a novel interacting parallel MCMC scheme, called parallel Metropolis-Hastings coupler (PMHC), where the information provided by different parallel MCMC chains is properly combined by the use of another advanced MCMC method, called normal kernel coupler (NKC). The NKC employs a mixture of densities as proposal density, which is updated according to a population of states. The PMHC is particularly efficient in multimodal scenarios, since it obtains a faster exploration of the state space with respect to other benchmark techniques. Several numerical simulations are provided showing the efficiency and robustness of the proposed method.