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.

Multi-agent path-finding (MAPF) is important for applications such as the kind of warehousing done by Kiva systems. Solving the problem optimally is NP-hard, yet finding low-cost solutions is important. Bounded-suboptimal MAPF algorithms, such as enhanced conflict-based search (ECBS), often do not perform well in warehousing domains with many agents. We therefore develop bounded-suboptimal MAPF algorithms, called CBS+HWY and ECBS+HWY, that exploit the problem structure of a given MAPF instance by finding paths for the agents that include edges from user-provided highways, which encourages a global behavior of the agents that avoids collisions. On the theoretical side, we develop a simple approach that uses highways for MAPF and provides suboptimality guarantees. On the experimental side, we demonstrate that ECBS+HWY can decrease the runtimes and solution costs of ECBS in Kiva-like domains with many agents if the highways capture the problem structures well.

Recently, several researchers have brought forth the benefits of searching with multiple (and possibly inadmissible) heuristics, arguing how different heuristics could be independently useful in different parts of the state space. However, algorithms that use inadmissible heuristics in the traditional best-first sense, such as the recently developed Multi-Heuristic A* (MHA*), are subject to a crippling calibration problem: they prioritize nodes for expansion by additively combining the cost-to-come and the inadmissible heuristics even if those heuristics have no connection with the cost-to-go (e.g., the heuristics are uncalibrated) . For instance, if the inadmissible heuristic were an order of magnitude greater than the perfect heuristic, an algorithm like MHA* would simply reduce to a weighted A* search with one consistent heuristic. In this work, we introduce a general multi-heuristic search framework that solves the calibration problem and as a result a) facilitates the effective use of multiple uncalibrated inadmissible heuristics, and b) provides significantly better performance than MHA* whenever tighter sub-optimality bounds on solution quality are desired. Experimental evaluations on a complex full-body robotics motion planning problem and large sliding tile puzzles demonstrate the benefits of our framework.

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.

This paper provides a novel POMDP planning method, called Palm LEAf SEarch (PLEASE), which allows the selection of more than one outcome when their potential impacts are close to the highest one during its forward exploration. Compared with existing trial-based algorithms, PLEASE can save considerable time to propagate the bound improvements of beliefs in deep levels of the search tree to the root belief because of fewer backup operations. Experiments showed that PLEASE scales up SARSOP, one of the fastest algorithms, by orders of magnitude on some POMDP tasks with large observation spaces.

Solving cooperative path finding (CPF) by translating it to propositional satisfiability represents a viable option in highly constrained situations. The task in CPF is to relocate agents from their initial positions to given goals in a collision free manner. In this paper, we propose a reduced time expansion that is focused on makespan sub-optimal solving of the problem. The suggested reduced time expansion is especially beneficial in conjunction with a goal decomposition where agents are relocated one by one.

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.

Moving Target Search (MTS) is a dynamic path planning problem, where an agent is trying to reach a moving entity with a minimum path cost. Problems of this nature can be found in video games and dynamic robotics, which require fast processing time (real time). In this work, we introduce a new algorithm for this problem - the Moving Target Search with Subgoal Graphs (MTSub). MTSub is based on environment abstraction and uses Subgoal Graphs to speed up the searches for a minimal cost route to the target. The algorithm is optimal with respect to the knowledge that the agent has during the search. Experimental results show that MTSub can be used in real-time applications (e.g., applications requiring 5 microseconds response time per step). The experiments compared MTSub to G-FRA*, which is the best known dynamic algorithm so far, showing that MTSub is up to 29 times faster in average time per step, and up to 186 times faster in maximum time per step.

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.