Safe autonomous navigation is an essential and challenging problem for robots operating in highly unstructured or completely unknown environments. Under these conditions, not only robotic systems must deal with limited localisation information, but also their manoeuvrability is constrained by their dynamics and often suffer from uncertainty. In order to cope with these constraints, this manuscript proposes an uncertainty-based framework for mapping and planning feasible motions online with probabilistic safety-guarantees. The proposed approach deals with the motion, probabilistic safety, and online computation constraints by: (i) incrementally mapping the surroundings to build an uncertainty-aware representation of the environment, and (ii) iteratively (re)planning trajectories to goal that are kinodynamically feasible and probabilistically safe through a multi-layered sampling-based planner in the belief space. In-depth empirical analyses illustrate some important properties of this approach, namely, (a) the multi-layered planning strategy enables rapid exploration of the high-dimensional belief space while preserving asymptotic optimality and completeness guarantees, and (b) the proposed routine for probabilistic collision checking results in tighter probability bounds in comparison to other uncertainty-aware planners in the literature. Furthermore, real-world in-water experimental evaluation on a non-holonomic torpedo-shaped autonomous underwater vehicle and simulated trials in the Stairwell scenario of the DARPA Subterranean Challenge 2019 on a quadrotor unmanned aerial vehicle demonstrate the efficacy of the method as well as its suitability for systems with limited on-board computational power.

LWF chain graphs combine directed acyclic graphs and undirected graphs. We present a PC-like algorithm that finds the structure of chain graphs under the faithfulness assumption to resolve the problem of scalability of the proposed algorithm by Studeny (1997). We prove that our PC-like algorithm is order dependent, in the sense that the output can depend on the order in which the variables are given. This order dependence can be very pronounced in high-dimensional settings. We propose two modifications of the PC-like algorithm that remove part or all of this order dependence. Simulation results under a variety of settings demonstrate the competitive performance of the PC-like algorithms in comparison with the decomposition-based method, called LCD algorithm, proposed by Ma et al. (2008) in low-dimensional settings and improved performance in high-dimensional settings.

The DeepWalk algorithm is used to assign embedding vectors to nodes in the Atomspace weighted, labeled hypergraph that is used to represent knowledge in the OpenCog AGI system, in the context of an application to probabilistic inference regarding the causes of longevity based on data from biological ontologies and genomic analyses. It is shown that vector difference operations between embedding vectors are, in appropriate conditions, approximately alignable with "intensional difference" operations between the hypergraph nodes corresponding to the embedding vectors. This relationship hints at a broader functorial mapping between uncertain intensional logic and vector arithmetic, and opens the door for using embedding vector algebra to guide intensional inference control.

Multi-Armed Bandit (MAB) techniques have been successfully applied to many classes of sequential decision problems in the past decades. However, non-stationary settings -- very common in real-world applications -- received little attention so far, and theoretical guarantees on the regret are known only for some frequentist algorithms. In this paper, we propose an algorithm, namely Sliding-Window Thompson Sampling (SW-TS), for nonstationary stochastic MAB settings. Our algorithm is based on Thompson Sampling and exploits a sliding-window approach to tackle, in a unified fashion, two different forms of non-stationarity studied separately so far: abruptly changing and smoothly changing. In the former, the reward distributions are constant during sequences of rounds, and their change may be arbitrary and happen at unknown rounds, while, in the latter, the reward distributions smoothly evolve over rounds according to unknown dynamics. Under mild assumptions, we provide regret upper bounds on the dynamic pseudo-regret of SW-TS for the abruptly changing environment, for the smoothly changing one, and for the setting in which both the non-stationarity forms are present. Furthermore, we empirically show that SW-TS dramatically outperforms state-of-the-art algorithms even when the forms of non-stationarity are taken separately, as previously studied in the literature.

With both the introduction of new ways of storing, sharing and streaming data and the drastic development of the capacity of computers to handle large computations, the conception of models have changed. Mathematical models were first designed following prior ideas or conjectures from physical or biological models, then tested by designing experiments to test the validity of the ideas of their inventors. The model holds until new observations enable to reject its assumptions. The so-called Big Data's area introduced a new paradigm. The observed data convey enough information to understand the complexity of real life and the more the data, the better the description of the reality. Hence building models optimised to fit the data has become an efficient way to obtain generalizable models able to describe and forecast the real world. In this framework, the principle of supervised machine learning is to build a decision rule from a set of labeled examples called the learning sample, that fits the data.

This paper demonstrates the application of Bayesian Artificial Neural Networks to Ordinary Differential Equation (ODE) inverse problems. We consider the case of estimating an unknown chaotic dynamical system transition model from state observation data. Inverse problems for chaotic systems are numerically challenging as small perturbations in model parameters can cause very large changes in estimated forward trajectories. Bayesian Artificial Neural Networks can be used to simultaneously fit a model and estimate model parameter uncertainty. Knowledge of model parameter uncertainty can then be incorporated into the probabilistic estimates of the inferred system's forward time evolution. The method is demonstrated numerically by analysing the chaotic Sprott B system. Observations of the system are used to estimate a posterior predictive distribution over the weights of a parametric polynomial kernel Artificial Neural Network. It is shown that the proposed method is able to perform accurate time predictions. Further, the proposed method is able to correctly account for model uncertainties and provide useful prediction uncertainty bounds.

Gaussian processes (GPs) are distributions over functions, which provide a Bayesian nonparametric approach to regression and classification. In spite of their success, GPs have limited use in some applications, for example, in some cases a symmetric distribution with respect to its mean is an unreasonable model. This implies, for instance, that the mean and the median coincide, while the mean and median in an asymmetric (skewed) distribution can be different numbers. In this paper, we propose Skew-Gaussian processes (SkewGPs) as a non-parametric prior over functions. A SkewGP extends the multivariate Unified Skew-Normal distribution over finite dimensional vectors to a stochastic processes. The SkewGP class of distributions includes GPs and, therefore, SkewGPs inherit all good properties of GPs and increase their flexibility by allowing asymmetry in the probabilistic model. By exploiting the fact that SkewGP and probit likelihood are conjugate model, we derive closed form expressions for the marginal likelihood and predictive distribution of this new nonparametric classifier. We verify empirically that the proposed SkewGP classifier provides a better performance than a GP classifier based on either Laplace's method or Expectation Propagation.

Machine learning has seen in the last 5-10 years an explosion in its growth from a research centered area of computer science and mathematics to a driving force for innovation in every aspect of our lives [1, 2, 3]. This was driven mainly by the success of deep learning and the significant investment of big technology firms in open source machine learning research [4, 5, 6]. Real life machine learning based solutions often require a number of models to work together to achieve the business goal of the product(s) [7]. Such models can be trained independently or as part of an optimised training pipeline [8, 9]. Breaking down the product into multiple models has several advantages: I) It allows for parallel model development with model designers focused on solving relatively small and well-defined problems.

Bayesian Networks (BN) are probabilistic graphical models that are widely used for uncertainty modeling, stochastic prediction and probabilistic inference. A Quantum Bayesian Network (QBN) is a quantum version of the Bayesian network that utilizes the principles of quantum mechanical systems to improve the computational performance of various analyses. In this paper, we experimentally evaluate the performance of QBN on various IBM QX hardware against Qiskit simulator and classical analysis. We consider a 4-node BN for stock prediction for our experimental evaluation. We construct a quantum circuit to represent the 4-node BN using Qiskit, and run the circuit on nine IBM quantum devices: Yorktown, Vigo, Ourense, Essex, Burlington, London, Rome, Athens and Melbourne. We will also compare the performance of each device across the four levels of optimization performed by the IBM Transpiler when mapping a given quantum circuit to a given device. We use the root mean square percentage error as the metric for performance comparison of various hardware.

This paper presents a new approach to generate samples from conditional belief functions for a restricted but non trivial subset of conditional belief functions. It assumes the factorization (decomposition) of a belief function along a bayesian network structure. It applies general conditional belief functions. The most profoundly studied measure of uncertainty is the probability. There exist methods of so-called graphoidal representation of joint probability distribution - called Bayesian networks [7] - allowing for expression of qualitative independence, causality, efficient reasoning, explanation, learning from data and sample generation.