Data-driven methods for improving turbulence modeling in Reynolds-Averaged Navier-Stokes (RANS) simulations have gained significant interest in the computational fluid dynamics community. Modern machine learning models have opened up a new area of black-box turbulence models allowing for the tuning of RANS simulations to increase their predictive accuracy. While several data-driven turbulence models have been reported, the quantification of the uncertainties introduced has mostly been neglected. Uncertainty quantification for such data-driven models is essential since their predictive capability rapidly declines as they are tested for flow physics that deviate from that in the training data. In this work, we propose a novel data-driven framework that not only improves RANS predictions but also provides probabilistic bounds for fluid quantities such as velocity and pressure. The uncertainties capture include both model form uncertainty as well as epistemic uncertainty induced by the limited training data. An invariant Bayesian deep neural network is used to predict the anisotropic tensor component of the Reynolds stress. This model is trained using Stein's variational gradient decent algorithm. The computed uncertainty on the Reynolds stress is propagated to the quantities of interest by vanilla Monte Carlo simulation. Results are presented for two test cases that differ geometrically from the training flows at several different Reynolds numbers. The prediction enhancement of the data-driven model is discussed as well as the associated probabilistic bounds for flow properties of interest. Ultimately this framework allows for a quantitative measurement of model confidence and uncertainty quantification for flows in which no high-fidelity observations or prior knowledge is available.

The main objectives of particle physics in the post-Higgs boson discovery era is to exploit the full physics potential of both the Large Hadron Collider (LHC) and its upgrade, the high luminosity LHC (HL-LHC), in addition to present and future neutrino experiments. The HL-LHC will deliver data from 100 times the luminosity compared to the LHC, bringing quantitatively and qualitatively new challenges due to event size, data volume, and complexity. The physics reach of the experiments will be limited by the physics performance of algorithms and computational resources. Machine learning (ML) applied to particle physics promises to provide improvements in both of these areas. Incorporating machine learning in particle physics workflows will require significant research and development over the next five years. Areas where significant improvements are needed include: - Physics performance of reconstruction and analysis algorithms; - Execution time of computationally expensive parts of event simulation, pattern recognition, and calibration; - Realtime implementation of machine learning algorithms; - Reduction of the data footprint with data compression, placement and access.

The mean-median-mode trio involves the three most frequently used measures of central tendency of a dataset. They are taught within the very first classes of any course on basic Statistics. However, they do not share the same degree of importance: the sample mean (or average) is normally well understood and employed in everyday situations, the sample median is also useful and easy to visualize, but the mode, usually defined as the value of the dataset having the highest frequency of appearance, looks like a more bizarre measure of location. This uneven treatment was already noted by Dalenius (1965), but it keeps being present as of today, to some extent. Indeed, when the dataset consists of realizations from a continuous random variable then all the observed values are different with probability one and, therefore, the mode does not even make much sense.

Bayesian optimization is an approach to optimizing objective functions that take a long time (minutes or hours) to evaluate. It is best-suited for optimization over continuous domains of less than 20 dimensions, and tolerates stochastic noise in function evaluations. It builds a surrogate for the objective and quantifies the uncertainty in that surrogate using a Bayesian machine learning technique, Gaussian process regression, and then uses an acquisition function defined from this surrogate to decide where to sample. In this tutorial, we describe how Bayesian optimization works, including Gaussian process regression and three common acquisition functions: expected improvement, entropy search, and knowledge gradient. We then discuss more advanced techniques, including running multiple function evaluations in parallel, multi-fidelity and multi-information source optimization, expensive-to-evaluate constraints, random environmental conditions, multi-task Bayesian optimization, and the inclusion of derivative information. We conclude with a discussion of Bayesian optimization software and future research directions in the field. Within our tutorial material we provide a generalization of expected improvement to noisy evaluations, beyond the noise-free setting where it is more commonly applied. This generalization is justified by a formal decision-theoretic argument, standing in contrast to previous ad hoc modifications.

A Bayesian approach termed BAyesian Least Squares Optimization with Nonnegative L1-norm constraint (BALSON) is proposed. The error distribution of data fitting is described by Gaussian likelihood. The parameter distribution is assumed to be a Dirichlet distribution. With the Bayes rule, searching for the optimal parameters is equivalent to finding the mode of the posterior distribution. In order to explicitly characterize the nonnegative L1-norm constraint of the parameters, we further approximate the true posterior distribution by a Dirichlet distribution. We estimate the statistics of the approximating Dirichlet posterior distribution by sampling methods. Four sampling methods have been introduced. With the estimated posterior distributions, the original parameters can be effectively reconstructed in polynomial fitting problems, and the BALSON framework is found to perform better than conventional methods.

This paper is an attempt to bridge the conceptual gaps between researchers working on the two widely used approaches based on positive definite kernels: Bayesian learning or inference using Gaussian processes on the one side, and frequentist kernel methods based on reproducing kernel Hilbert spaces on the other. It is widely known in machine learning that these two formalisms are closely related; for instance, the estimator of kernel ridge regression is identical to the posterior mean of Gaussian process regression. However, they have been studied and developed almost independently by two essentially separate communities, and this makes it difficult to seamlessly transfer results between them. Our aim is to overcome this potential difficulty. To this end, we review several old and new results and concepts from either side, and juxtapose algorithmic quantities from each framework to highlight close similarities. We also provide discussions on subtle philosophical and theoretical differences between the two approaches.

Within the realm of service robotics, researchers have placed a great amount of effort into learning motions and manipulations for task execution by robots. The task of robot learning is very broad, as it involves many tasks such as object detection, action recognition, motion planning, localization, knowledge representation and retrieval, and the intertwining of computer vision and machine learning techniques. In this paper, we focus on how knowledge can be gathered, represented, and reproduced to solve problems as done by researchers in the past decades. We discuss the problems which have existed in robot learning and the solutions, technologies or developments (if any) which have contributed to solving them. Specifically, we look at three broad categories involved in task representation and retrieval for robotics: 1) activity recognition from demonstrations, 2) scene understanding and interpretation, and 3) task representation in robotics - datasets and networks. Within each section, we discuss major breakthroughs and how their methods address present issues in robot learning and manipulation.

Smart-home is an application domain which brings together home automation and ambient intelligence to ease life of dwellers and to provide support to people in loss of autonomy. The development of smarthomes is not only a cultural and technological evolution but is also recognized as one way to address the challenges created by an aging population in developed countries [42]. If home automation is concerned with sensing (sensors, actuators, middle-ware) and low-level automation (heating control, lighting control), Ambient Intelligence should provide perception and reasoning capabilities into the smart-home ecosystem. However, although the development of smart-homes is supported by a large amount of research and industrial projects, it has not reached a large public since many challenges are still to be addressed. One of the main challenges is due to the complexity of setting up the smart-home system in case of new situations (devices, house, dwellers, after an accident, etc.).

We introduce a kernel approximation strategy that enables computation of the Gaussian process log marginal likelihood and all hyperparameter derivatives in $\mathcal{O}(p)$ time. Our GRIEF kernel consists of $p$ eigenfunctions found using a Nystr\"om approximation from a dense Cartesian product grid of inducing points. By exploiting algebraic properties of Kronecker and Khatri-Rao tensor products, computational complexity of the training procedure can be practically independent of the number of inducing points. This allows us to use arbitrarily many inducing points to achieve a globally accurate kernel approximation, even in high-dimensional problems. The fast likelihood evaluation enables type-I or II Bayesian inference on large-scale datasets. We benchmark our algorithms on real-world problems with up to two-million training points and $10^{33}$ inducing points.

Dropout, a stochastic regularisation technique for training of neural networks, has recently been reinterpreted as a specific type of approximate inference algorithm for Bayesian neural networks. The main contribution of the reinterpretation is in providing a theoretical framework useful for analysing and extending the algorithm. We show that the proposed framework suffers from several issues; from undefined or pathological behaviour of the true posterior related to use of improper priors, to an ill-defined variational objective due to singularity of the approximating distribution relative to the true posterior. Our analysis of the improper log uniform prior used in variational Gaussian dropout suggests the pathologies are generally irredeemable, and that the algorithm still works only because the variational formulation annuls some of the pathologies. To address the singularity issue, we proffer Quasi-KL (QKL) divergence, a new approximate inference objective for approximation of high-dimensional distributions. We show that motivations for variational Bernoulli dropout based on discretisation and noise have QKL as a limit. Properties of QKL are studied both theoretically and on a simple practical example which shows that the QKL-optimal approximation of a full rank Gaussian with a degenerate one naturally leads to the Principal Component Analysis solution.