Bayesian Optimal Active Search and Surveying

We consider two active binary-classification problems with atypical objectives. In the first, active search, our goal is to actively uncover as many members of a given class as possible. In the second, active surveying, our goal is to actively query points to ultimately predict the proportion of a given class. Numerous real-world problems can be framed in these terms, and in either case typical model-based concerns such as generalization error are only of secondary importance. We approach these problems via Bayesian decision theory; after choosing natural utility functions, we derive the optimal policies. We provide three contributions. In addition to introducing the active surveying problem, we extend previous work on active search in two ways. First, we prove a novel theoretical result, that less-myopic approximations to the optimal policy can outperform more-myopic approximations by any arbitrary degree. We then derive bounds that for certain models allow us to reduce (in practice dramatically) the exponential search space required by a naive implementation of the optimal policy, enabling further lookahead while still ensuring that optimal decisions are always made.Comment: Appears in Proceedings of the 29th International Conference on Machine Learning (ICML 2012

Adaptive Path Planning for Depth Constrained Bathymetric Mapping with an Autonomous Surface Vessel

This paper describes the design, implementation and testing of a suite of algorithms to enable depth constrained autonomous bathymetric (underwater topography) mapping by an Autonomous Surface Vessel (ASV). Given a target depth and a bounding polygon, the ASV will find and follow the intersection of the bounding polygon and the depth contour as modeled online with a Gaussian Process (GP). This intersection, once mapped, will then be used as a boundary within which a path will be planned for coverage to build a map of the Bathymetry. Methods for sequential updates to GP's are described allowing online fitting, prediction and hyper-parameter optimisation on a small embedded PC. New algorithms are introduced for the partitioning of convex polygons to allow efficient path planning for coverage. These algorithms are tested both in simulation and in the field with a small twin hull differential thrust vessel built for the task.Comment: 21 pages, 9 Figures, 1 Table. Submitted to The Journal of Field Robotic

Active Classification: Theory and Application to Underwater Inspection

We discuss the problem in which an autonomous vehicle must classify an object based on multiple views. We focus on the active classification setting, where the vehicle controls which views to select to best perform the classification. The problem is formulated as an extension to Bayesian active learning, and we show connections to recent theoretical guarantees in this area. We formally analyze the benefit of acting adaptively as new information becomes available. The analysis leads to a probabilistic algorithm for determining the best views to observe based on information theoretic costs. We validate our approach in two ways, both related to underwater inspection: 3D polyhedra recognition in synthetic depth maps and ship hull inspection with imaging sonar. These tasks encompass both the planning and recognition aspects of the active classification problem. The results demonstrate that actively planning for informative views can reduce the number of necessary views by up to 80% when compared to passive methods.Comment: 16 page

A Probabilistic Interpretation of Sampling Theory of Graph Signals

We give a probabilistic interpretation of sampling theory of graph signals. To do this, we first define a generative model for the data using a pairwise Gaussian random field (GRF) which depends on the graph. We show that, under certain conditions, reconstructing a graph signal from a subset of its samples by least squares is equivalent to performing MAP inference on an approximation of this GRF which has a low rank covariance matrix. We then show that a sampling set of given size with the largest associated cut-off frequency, which is optimal from a sampling theoretic point of view, minimizes the worst case predictive covariance of the MAP estimate on the GRF. This interpretation also gives an intuitive explanation for the superior performance of the sampling theoretic approach to active semi-supervised classification.Comment: 5 pages, 2 figures, To appear in International Conference on Acoustics, Speech, and Signal Processing (ICASSP) 201