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.

Qualitative and quantitative approaches to reasoning about uncertainty can lead to different logical systems for formalizing such reasoning, even when the language for expressing uncertainty is the same. In the case of reasoning about relative likelihood, with statements of the form $\varphi\succsim\psi$ expressing that $\varphi$ is at least as likely as $\psi$, a standard qualitative approach using preordered preferential structures yields a dramatically different logical system than a quantitative approach using probability measures. In fact, the standard preferential approach validates principles of reasoning that are incorrect from a probabilistic point of view. However, in this paper we show that a natural modification of the preferential approach yields exactly the same logical system as a probabilistic approach--not using single probability measures, but rather sets of probability measures. Thus, the same preferential structures used in the study of non-monotonic logics and belief revision may be used in the study of comparative probabilistic reasoning based on imprecise probabilities.

How to measure the degree of uncertainty of a given frame of discernment has been a hot topic for years. A lot of meaningful works have provided some effective methods to measure the degree properly. However, a crucial factor, sequence of propositions, is missing in the definition of traditional frame of discernment. In this paper, a detailed definition of ordinal frame of discernment has been provided. Besides, an innovative method utilizing a concept of computer vision to combine the order of propositions and the mass of them is proposed to better manifest relationships between the two important element of the frame of discernment. More than that, a specially designed method covering some powerful tools in indicating the degree of uncertainty of a traditional frame of discernment is also offered to give an indicator of level of uncertainty of an ordinal frame of discernment on the level of vector.

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.

Humans possess a unique social cognition capability; nonverbal communication can convey rich social information among agents. In contrast, such crucial social characteristics are mostly missing in the existing scene understanding literature. In this paper, we incorporate different nonverbal communication cues (e.g., gaze, human poses, and gestures) to represent, model, learn, and infer agents' mental states from pure visual inputs. Crucially, such a mental representation takes the agent's belief into account so that it represents what the true world state is and infers the beliefs in each agent's mental state, which may differ from the true world states. By aggregating different beliefs and true world states, our model essentially forms "five minds" during the interactions between two agents. This "five minds" model differs from prior works that infer beliefs in an infinite recursion; instead, agents' beliefs are converged into a "common mind". Based on this representation, we further devise a hierarchical energy-based model that jointly tracks and predicts all five minds. From this new perspective, a social event is interpreted by a series of nonverbal communication and belief dynamics, which transcends the classic keyframe video summary. In the experiments, we demonstrate that using such a social account provides a better video summary on videos with rich social interactions compared with state-of-the-art keyframe video summary methods.

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.