Sequentiality and Adaptivity Gains in Active Hypothesis Testing

Consider a decision maker who is responsible to collect observations so as to enhance his information in a speedy manner about an underlying phenomena of interest. The policies under which the decision maker selects sensing actions can be categorized based on the following two factors: i) sequential vs. non-sequential; ii) adaptive vs. non-adaptive. Non-sequential policies collect a fixed number of observation samples and make the final decision afterwards; while under sequential policies, the sample size is not known initially and is determined by the observation outcomes. Under adaptive policies, the decision maker relies on the previous collected samples to select the next sensing action; while under non-adaptive policies, the actions are selected independent of the past observation outcomes. In this paper, performance bounds are provided for the policies in each category. Using these bounds, sequentiality gain and adaptivity gain, i.e., the gains of sequential and adaptive selection of actions are characterized.Comment: 12 double-column pages, 1 figur

Active sequential hypothesis testing

Consider a decision maker who is responsible to dynamically collect observations so as to enhance his information about an underlying phenomena of interest in a speedy manner while accounting for the penalty of wrong declaration. Due to the sequential nature of the problem, the decision maker relies on his current information state to adaptively select the most ``informative'' sensing action among the available ones. In this paper, using results in dynamic programming, lower bounds for the optimal total cost are established. The lower bounds characterize the fundamental limits on the maximum achievable information acquisition rate and the optimal reliability. Moreover, upper bounds are obtained via an analysis of two heuristic policies for dynamic selection of actions. It is shown that the first proposed heuristic achieves asymptotic optimality, where the notion of asymptotic optimality, due to Chernoff, implies that the relative difference between the total cost achieved by the proposed policy and the optimal total cost approaches zero as the penalty of wrong declaration (hence the number of collected samples) increases. The second heuristic is shown to achieve asymptotic optimality only in a limited setting such as the problem of a noisy dynamic search. However, by considering the dependency on the number of hypotheses, under a technical condition, this second heuristic is shown to achieve a nonzero information acquisition rate, establishing a lower bound for the maximum achievable rate and error exponent. In the case of a noisy dynamic search with size-independent noise, the obtained nonzero rate and error exponent are shown to be maximum.Comment: Published in at http://dx.doi.org/10.1214/13-AOS1144 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Adaptive Object Detection Using Adjacency and Zoom Prediction

State-of-the-art object detection systems rely on an accurate set of region proposals. Several recent methods use a neural network architecture to hypothesize promising object locations. While these approaches are computationally efficient, they rely on fixed image regions as anchors for predictions. In this paper we propose to use a search strategy that adaptively directs computational resources to sub-regions likely to contain objects. Compared to methods based on fixed anchor locations, our approach naturally adapts to cases where object instances are sparse and small. Our approach is comparable in terms of accuracy to the state-of-the-art Faster R-CNN approach while using two orders of magnitude fewer anchors on average. Code is publicly available.Comment: Accepted to CVPR 201