Federated Bayesian learning offers a principled framework for the definition of collaborative training algorithms that are able to quantify epistemic uncertainty and to produce trustworthy decisions. Upon the completion of collaborative training, an agent may decide to exercise her legal "right to be forgotten", which calls for her contribution to the jointly trained model to be deleted and discarded. This paper studies federated learning and unlearning in a decentralized network within a Bayesian framework. It specifically develops federated variational inference (VI) solutions based on the decentralized solution of local free energy minimization problems within exponential-family models and on local gossip-driven communication. The proposed protocols are demonstrated to yield efficient unlearning mechanisms.

In this paper, we present a state-of-the-art reinforcement learning method for autonomous driving. Our approach employs temporal difference learning in a Bayesian framework to learn vehicle control signals from sensor data. The agent has access to images from a forward facing camera, which are preprocessed to generate semantic segmentation maps. We trained our system using both ground truth and estimated semantic segmentation input. Based on our observations from a large set of experiments, we conclude that training the system on ground truth input data leads to better performance than training the system on estimated input even if estimated input is used for evaluation. The system is trained and evaluated in a realistic simulated urban environment using the CARLA simulator. The simulator also contains a benchmark that allows for comparing to other systems and methods. The required training time of the system is shown to be lower and the performance on the benchmark superior to competing approaches.

This includes missions related to environment exploration and monitoring in which an UAV is tasked with producing a map for a quantity of interest (e.g., pollutant concentration, terrain elevation, or vegetation growth) by collecting measurements at various locations across a region of interest (e.g., a reservoir, a city, or a crop) [10, 13, 17, 23, 40]. The data collected by the UAV can be used to construct a statistical model for the quantity of interest, which in turn can be used for analysis and policy making. Of course, the statistical model is only as good as the measurements made by the UAV. Therefore, the question of data collection (i.e., how, when, and where to make measurements) is of paramount importance, especially from the standpoint of detecting anomalies in the environment. Path-planning algorithms for environment exploration come in two flavors. Approaches in which the UAV decides on its next move one step at a time are referred to as myopic [24, 42]. Myopic algorithms are suitable for most situations but lack a mechanism for anticipation, which may be problematic in cases where path-planning decisions may have negative longterm consequences (e.g., the UAV gets stuck because of maneuverability constraints).

The increasing availability of data presents an opportunity to calibrate unknown parameters which appear in complex models of phenomena in the biomedical, physical and social sciences. However, model complexity often leads to parameter-to-data maps which are expensive to evaluate and are only available through noisy approximations. This paper is concerned with the use of interacting particle systems for the solution of the resulting inverse problems for parameters. Of particular interest is the case where the available forward model evaluations are subject to rapid fluctuations, in parameter space, superimposed on the smoothly varying large scale parametric structure of interest. Multiscale analysis is used to study the behaviour of interacting particle system algorithms when such rapid fluctuations, which we refer to as noise, pollute the large scale parametric dependence of the parameter-to-data map. Ensemble Kalman methods (which are derivative-free) and Langevin-based methods (which use the derivative of the parameter-to-data map) are compared in this light. The ensemble Kalman methods are shown to behave favourably in the presence of noise in the parameter-to-data map, whereas Langevin methods are adversely affected. On the other hand, Langevin methods have the correct equilibrium distribution in the setting of noise-free forward models, whilst ensemble Kalman methods only provide an uncontrolled approximation, except in the linear case. Therefore a new class of algorithms, ensemble Gaussian process samplers, which combine the benefits of both ensemble Kalman and Langevin methods, are introduced and shown to perform favourably.

Gaussian processes (GPs) enable principled computation of model uncertainty, making them attractive for safety-critical applications. Such scenarios demand that GP decisions are not only accurate, but also robust to perturbations. In this paper we present a framework to analyse adversarial robustness of GPs, defined as invariance of the model's decision to bounded perturbations. Given a compact subset of the input space $T\subseteq \mathbb{R}^d$, a point $x^*$ and a GP, we provide provable guarantees of adversarial robustness of the GP by computing lower and upper bounds on its prediction range in $T$. We develop a branch-and-bound scheme to refine the bounds and show, for any $\epsilon > 0$, that our algorithm is guaranteed to converge to values $\epsilon$-close to the actual values in finitely many iterations. The algorithm is anytime and can handle both regression and classification tasks, with analytical formulation for most kernels used in practice. We evaluate our methods on a collection of synthetic and standard benchmark datasets, including SPAM, MNIST and FashionMNIST. We study the effect of approximate inference techniques on robustness and demonstrate how our method can be used for interpretability. Our empirical results suggest that the adversarial robustness of GPs increases with accurate posterior estimation.

During a geosteering operation the well path is intentionally adjusted in response to the new data acquired while drilling. To achieve consistent high-quality decisions, especially when drilling in complex environments, decision support systems can help cope with high volumes of data and interpretation complexities. They can assimilate the real-time measurements into a probabilistic earth model and use the updated model for decision recommendations. Recently, machine learning (ML) techniques have enabled a wide range of methods that redistribute computational cost from on-line to off-line calculations. In this paper, we introduce two ML techniques into the geosteering decision support framework. Firstly, a complex earth model representation is generated using a Generative Adversarial Network (GAN). Secondly, a commercial extra-deep electromagnetic simulator is represented using a Forward Deep Neural Network (FDNN). The numerical experiments demonstrate that the combination of the GAN and the FDNN in an ensemble randomized maximum likelihood data assimilation scheme provides real-time estimates of complex geological uncertainty. This yields reduction of geological uncertainty ahead of the drill-bit from the measurements gathered behind and around the well bore.

Manual labelling of training examples is common practice in supervised learning. When the labelling task is of non-trivial difficulty, the supplied labels may not be equal to the ground-truth labels, and label noise is introduced into the training dataset. If the manual annotation is carried out by multiple experts, the same training example can be given different class assignments by different experts, which is indicative of label noise. In the framework of model-based classification, a simple, but key observation is that when the manual labels are sampled using the posterior probabilities of class membership, the noisy labels are as valuable as the ground-truth labels in terms of statistical information. A relaxation of this process is a random effects model for imperfect labelling by a group that uses approximate posterior probabilities of class membership. The relative efficiency of logistic regression using the noisy labels compared to logistic regression using the ground-truth labels can then be derived. The main finding is that logistic regression can be robust to label noise when label noise and classification difficulty are positively correlated. In particular, when classification difficulty is the only source of label errors, multiple sets of noisy labels can supply more information for the estimation of a classification rule compared to the single set of ground-truth labels.

Topic models such as the Structural Topic Model (STM) estimate latent topical clusters within text. An important step in many topic modeling applications is to explore relationships between the discovered topical structure and metadata associated with the text documents. Methods used to estimate such relationships must take into account that the topical structure is not directly observed, but instead being estimated itself. The authors of the STM, for instance, perform repeated OLS regressions of sampled topic proportions on metadata covariates by using a Monte Carlo sampling technique known as the method of composition. In this paper, we propose two improvements: first, we replace OLS with more appropriate Beta regression. Second, we suggest a fully Bayesian approach instead of the current blending of frequentist and Bayesian methods. We demonstrate our improved methodology by exploring relationships between Twitter posts by German members of parliament (MPs) and different metadata covariates.

Mixture of experts (MoE) is a popular class of models in statistics and machine learning that has sustained attention over the years, due to its flexibility and effectiveness. We consider the Gaussian-gated localized MoE (GLoME) regression model for modeling heterogeneous data. This model poses challenging questions with respect to the statistical estimation and model selection problems, including feature selection, both from the computational and theoretical points of view. We study the problem of estimating the number of components of the GLoME model, in a penalized maximum likelihood estimation framework. We provide a lower bound on the penalty that ensures a weak oracle inequality is satisfied by our estimator. To support our theoretical result, we perform numerical experiments on simulated and real data, which illustrate the performance of our finite-sample oracle inequality.

Ensemble learning combines several individual models to obtain better generalization performance. Currently, deep learning models with multilayer processing architecture is showing better performance as compared to the shallow or traditional classification models. Deep ensemble learning models combine the advantages of both the deep learning models as well as the ensemble learning such that the final model has better generalization performance. This paper reviews the state-of-art deep ensemble models and hence serves as an extensive summary for the researchers. The ensemble models are broadly categorised into ensemble models like bagging, boosting and stacking, negative correlation based deep ensemble models, explicit/implicit ensembles, homogeneous /heterogeneous ensemble, decision fusion strategies, unsupervised, semi-supervised, reinforcement learning and online/incremental, multilabel based deep ensemble models. Application of deep ensemble models in different domains is also briefly discussed. Finally, we conclude this paper with some future recommendations and research directions.