We treat the problem of estimation of orientation parameters whose values are invariant to transformations from a spherical symmetry group. Previous work has shown that any such group-invariant distribution must satisfy a restricted finite mixture representation, which allows the orientation parameter to be estimated using an Expectation Maximization (EM) maximum likelihood (ML) estimation algorithm. In this paper, we introduce two parametric models for this spherical symmetry group estimation problem: 1) the hyperbolic Von Mises Fisher (VMF) mixture distribution and 2) the Watson mixture distribution. We also introduce a new EM-ML algorithm for clustering samples that come from mixtures of group-invariant distributions with different parameters. We apply the models to the problem of mean crystal orientation estimation under the spherically symmetric group associated with the crystal form, e.g., cubic or octahedral or hexahedral. Simulations and experiments establish the advantages of the extended EM-VMF and EM-Watson estimators for data acquired by Electron Backscatter Diffraction (EBSD) microscopy of a polycrystalline Nickel alloy sample.

To scale Gaussian processes (GPs) to large data sets we introduce the robust Bayesian Committee Machine (rBCM), a practical and scalable product-of-experts model for large-scale distributed GP regression. Unlike state-of-the-art sparse GP approximations, the rBCM is conceptually simple and does not rely on inducing or variational parameters. The key idea is to recursively distribute computations to independent computational units and, subsequently, recombine them to form an overall result. Efficient closed-form inference allows for straightforward parallelisation and distributed computations with a small memory footprint. The rBCM is independent of the computational graph and can be used on heterogeneous computing infrastructures, ranging from laptops to clusters. With sufficient computing resources our distributed GP model can handle arbitrarily large data sets.

Model-based clustering imposes a finite mixture modelling structure on data for clustering. Finite mixture models assume that the population is a convex combination of a finite number of densities, the distribution within each population is a basic assumption of each particular model. Among all distributions that have been tried, the generalized hyperbolic distribution has the advantage that is a generalization of several other methods, such as the Gaussian distribution, the skew t-distribution, etc. With specific parameters, it can represent either a symmetric or a skewed distribution. While its inherent flexibility is an advantage in many ways, it means the estimation of more parameters than its special and limiting cases. The aim of this work is to propose a mixture of generalized hyperbolic factor analyzers to introduce parsimony and extend the method to high dimensional data. This work can be seen as an extension of the mixture of factor analyzers model to generalized hyperbolic mixtures. The performance of our generalized hyperbolic factor analyzers is illustrated on real data, where it performs favourably compared to its Gaussian analogue.

We introduce a new, efficient, principled and backpropagation-compatible algorithm for learning a probability distribution on the weights of a neural network, called Bayes by Backprop. It regularises the weights by minimising a compression cost, known as the variational free energy or the expected lower bound on the marginal likelihood. We show that this principled kind of regularisation yields comparable performance to dropout on MNIST classification. We then demonstrate how the learnt uncertainty in the weights can be used to improve generalisation in non-linear regression problems, and how this weight uncertainty can be used to drive the exploration-exploitation trade-off in reinforcement learning.

The Grid-Based Path Planning Competition has just completed its third iteration. The entriesused in the competition have improved significantly during this time, changing the view ofthe state of the art of grid-based pathfinding. Furthermore, the entries from the competition have beenmade publicly available, improving the ability of researchers to compare their work. Thispaper summarizes the entries to the 2014 competition, presents the 2014 competition results,and talks about what has been learned and where there is room for improvement.

Spacecraft missions to small celestial bodies face sensitive, strongly non-Keplerian dynamics that motivate the employment of automated sampling-based trajectory planning. However, the scarcity of onboard computing resources necessitates careful formulation of heuristics for efficiently searching the reachable sets, which exhibit complex and finely-detailed structure. We examine a global search heuristic that combines aspects of simulated annealing and hill-climbing to locate sparse regions of the planning domain that simultaneously satisfy numerous geometric and timing constraints associated with remote sensing objectives for points of interest on the central body surface. Subsequently, we demonstrate the use of a receding-horizon implementation of this maneuver-planning strategy to produce mission profiles that fulfill sets of such goals.

Vehicle sharing (ex: bike sharing, car sharing) systems, an attractive alternative of private transportation, are widely adopted in major cities around the world. In vehicle-sharing systems, base stations (ex: docking stations for bikes) are strategically placed throughout a city and each of the base stations contain a pre-determined number of vehicles at the beginning of each day. Due to the stochastic and individualistic movement of customers, there is typically either congestion (more than required) or starvation (fewer than required) of vehicles at certain base stations, which causes a significant loss in demand. We propose to dynamically redeploy idle vehicles using carriers so as to minimize lost demand or alternatively maximize revenue for the vehicle sharing company. To that end, we contribute an optimization formulation to jointly address the redeployment (of vehicles) and routing (of carriers) problems and provide two approaches that rely on decomposability and abstraction of problem domains to reduce the computation time significantly.

Hierarchical Task Network (HTN) planning with task insertion (TIHTN planning) is a variant of HTN planning. In HTN planning, the only means to alter task networks is to decompose compound tasks. In TIHTN planning, tasks may also be inserted directly. In this paper we provide tight complexity bounds for TIHTN planning along two axis: whether variables are allowed and whether methods must be totally ordered.

We compare five any-angle path-planning algorithms, Theta*, Block A*, Field D*, ANYA, and Any-Angle Subgoal Graphs in terms of solution quality and runtime. Any-angle path-planning is a fairly new research area, and no direct comparison exists between these algorithms. We implement each algorithm from scratch and use similar implementations to provide a fair comparison.

In this paper we treat the problem of feature selection in unsupervised learning as a state-space search problem. We introduce three different heuristic functions and perform extensive experiments on datasets with tens, hundreds, and thousands of features. Namely, we test different search algorithms using the heuristic functions we introduce. Our results show that the heuristic search approach for feature selection in unsupervised learning problems can be far superior than traditional baselines such as PCA and random projections.