Gaussian Process priors with uncertain inputs? Application to multiple-step ahead time series forecasting

We consider the problem of multi-step ahead prediction in time series analysis using the non-parametric Gaussian process model. k-step ahead forecasting of a discrete-time non-linear dynamic system can be performed by doing repeated one-step ahead predictions. For a state-space model of the form y t = f(Yt-1 ,..., Yt-L ), the prediction of y at time t + k is based on the point estimates of the previous outputs. In this paper, we show how, using an analytical Gaussian approximation, we can formally incorporate the uncertainty about intermediate regressor values, thus updating the uncertainty on the current prediction

LMI-based design of distributed energy-dissipation systems for vibration control of large multi-story structures

In this paper, we present an advanced computational procedure that allows obtaining distributed energy-dissipation systems for large multi-story structures. The proposed methodology is based on a decentralized velocity-feedback energy-to-componentwise-peak (ECWP) controller design approach and can be formulated as a linear matrix inequality (LMI) optimization problem with structure constraints. To demonstrate the effectiveness of the proposed design methodology, a passive damping system is computed for the seismic protection of a 20-story building equipped with a complete set of interstory viscous dampers. The high-performance characteristics of the obtained passive ECWP control system are clearly evidenced by the numerical simulation results. Also, the computational effectiveness of the proposed design procedure is confirmed by the low computation time of the associated LMI optimization problem.Peer ReviewedPostprint (published version

Propagation of Uncertainty in Bayesian Kernel Models - Application to Multiple-Step Ahead Forecasting

The object of Bayesian modelling is the predictive distribution, which in a forecasting scenario enables improved estimates of forecasted values and their uncertainties. In this paper we focus on reliably estimating the predictive mean and variance of forecasted values using Bayesian kernel based models such as the Gaussian Process and the Relevance Vector Machine. We derive novel analytic expressions for the predictive mean and variance for Gaussian kernel shapes under the assumption of a Gaussian input distribution in the static case, and of a recursive Gaussian predictive density in iterative forecasting. The capability of the method is demonstrated for forecasting of time-series and compared to approximate methods

Presència del bivalve invasor Sinanodonta woodiana (Lea, 1834) al delta del Llobregat (Baix Llobregat)

El delta del Llobregat és una de les zones humides més importants de Catalunya. Disposa d’una malacofauna força diversa, encara que amenaçada a causa de la proximitat a l’àrea urbana de Barcelona i al fet d’estar envoltada per grans infraestructures. Aquest article registra per primera vegada la presència i distribució en aquest espai natural d’un bivalve invasor, la nàiade asiàtica Sinanodonta woodiana, del qual se n’han trobat nombrosos exemplars i que presenta una població ben establerta.Presence of the invasive bivalve Sinanodonta woodiana (Lea, 1834) in the Llobregat delta (Baix Llobregat)The Llobregat delta is among the most important wetlands in Catalonia. The diverse  malacofauna of the area is threatened, however,  by the large infrastructures surrounding the delta  and the area´s  close proximity to the urban centre  of Barcelona. Here we present the first report on  invasive bivalves in the delta  following  findings of a well-established population  of the Chinese pond mussel, Sinanodonta woodiana. The  distribution of the species in  this natural area is also discussed.Presencia del bivalvo invasor Sinanodonta woodiana (Lea, 1834) en el delta del Llobregat (Baix Llobregat) El delta del Llobregat es una de las zonas húmedas más importantes de Cataluña. Dispone de una malacofauna muy diversa, aunque amenazada debido a su proximidad al área urbana de Barcelona y a que está rodeada por grandes infraestructuras. Este artículo registra por primera vez la presencia y distribución en este espacio natural de un bivalvo invasor, la almeja china del cieno Sinanodonta woodiana, del que se han encontrado numerosos ejemplares y presenta una población bien establecida

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

Probabilistic movement modeling for intention inference in human-robot interaction.

Intention inference can be an essential step toward efficient humanrobot interaction. For this purpose, we propose the Intention-Driven Dynamics Model (IDDM) to probabilistically model the generative process of movements that are directed by the intention. The IDDM allows to infer the intention from observed movements using Bayes ’ theorem. The IDDM simultaneously finds a latent state representation of noisy and highdimensional observations, and models the intention-driven dynamics in the latent states. As most robotics applications are subject to real-time constraints, we develop an efficient online algorithm that allows for real-time intention inference. Two human-robot interaction scenarios, i.e., target prediction for robot table tennis and action recognition for interactive humanoid robots, are used to evaluate the performance of our inference algorithm. In both intention inference tasks, the proposed algorithm achieves substantial improvements over support vector machines and Gaussian processes.

Fast methods for training Gaussian processes on large data sets

Gaussian process regression (GPR) is a non-parametric Bayesian technique for interpolating or fitting data. The main barrier to further uptake of this powerful tool rests in the computational costs associated with the matrices which arise when dealing with large data sets. Here, we derive some simple results which we have found useful for speeding up the learning stage in the GPR algorithm, and especially for performing Bayesian model comparison between different covariance functions. We apply our techniques to both synthetic and real data and quantify the speed-up relative to using nested sampling to numerically evaluate model evidences.Comment: Fixed missing reference

CAR-Net: Clairvoyant Attentive Recurrent Network

We present an interpretable framework for path prediction that leverages dependencies between agents' behaviors and their spatial navigation environment. We exploit two sources of information: the past motion trajectory of the agent of interest and a wide top-view image of the navigation scene. We propose a Clairvoyant Attentive Recurrent Network (CAR-Net) that learns where to look in a large image of the scene when solving the path prediction task. Our method can attend to any area, or combination of areas, within the raw image (e.g., road intersections) when predicting the trajectory of the agent. This allows us to visualize fine-grained semantic elements of navigation scenes that influence the prediction of trajectories. To study the impact of space on agents' trajectories, we build a new dataset made of top-view images of hundreds of scenes (Formula One racing tracks) where agents' behaviors are heavily influenced by known areas in the images (e.g., upcoming turns). CAR-Net successfully attends to these salient regions. Additionally, CAR-Net reaches state-of-the-art accuracy on the standard trajectory forecasting benchmark, Stanford Drone Dataset (SDD). Finally, we show CAR-Net's ability to generalize to unseen scenes.Comment: The 2nd and 3rd authors contributed equall

Knot selection in sparse Gaussian processes with a variational objective function

Sparse, knot‐based Gaussian processes have enjoyed considerable success as scalable approximations of full Gaussian processes. Certain sparse models can be derived through specific variational approximations to the true posterior, and knots can be selected to minimize the Kullback‐Leibler divergence between the approximate and true posterior. While this has been a successful approach, simultaneous optimization of knots can be slow due to the number of parameters being optimized. Furthermore, there have been few proposed methods for selecting the number of knots, and no experimental results exist in the literature. We propose using a one‐at‐a‐time knot selection algorithm based on Bayesian optimization to select the number and locations of knots. We showcase the competitive performance of this method relative to optimization of knots simultaneously on three benchmark datasets, but at a fraction of the computational cost