Non-Adaptive Policies for 20 Questions Target Localization

The problem of target localization with noise is addressed. The target is a sample from a continuous random variable with known distribution and the goal is to locate it with minimum mean squared error distortion. The localization scheme or policy proceeds by queries, or questions, weather or not the target belongs to some subset as it is addressed in the 20-question framework. These subsets are not constrained to be intervals and the answers to the queries are noisy. While this situation is well studied for adaptive querying, this paper is focused on the non adaptive querying policies based on dyadic questions. The asymptotic minimum achievable distortion under such policies is derived. Furthermore, a policy named the Aurelian1 is exhibited which achieves asymptotically this distortion

Unequal Error Protection Querying Policies for the Noisy 20 Questions Problem

In this paper, we propose an open-loop unequal-error-protection querying policy based on superposition coding for the noisy 20 questions problem. In this problem, a player wishes to successively refine an estimate of the value of a continuous random variable by posing binary queries and receiving noisy responses. When the queries are designed non-adaptively as a single block and the noisy responses are modeled as the output of a binary symmetric channel the 20 questions problem can be mapped to an equivalent problem of channel coding with unequal error protection (UEP). A new non-adaptive querying strategy based on UEP superposition coding is introduced whose estimation error decreases with an exponential rate of convergence that is significantly better than that of the UEP repetition coding introduced by Variani et al. (2015). With the proposed querying strategy, the rate of exponential decrease in the number of queries matches the rate of a closed-loop adaptive scheme where queries are sequentially designed with the benefit of feedback. Furthermore, the achievable error exponent is significantly better than that of random block codes employing equal error protection.Comment: To appear in IEEE Transactions on Information Theor

COARSE-TO-FINE MULTIPLE TESTING STRATEGIES.

We consider a multiple testing scenario encountered in the biological sciences and elsewhere: there are a great many null hypotheses about the distribution of a high-dimensional random variable but only a very small fraction are false (or “active”); moreover, controlling the false positives rate through FWER or FDR is imperative. Not surprisingly, the usual methods applied to control the two former criteria are often too conservative and lead to a small number of true detections. Clearly, some additional assumptions or domain-specific knowledge are then necessary to improve power. Motivated by applications in genomics, particularly genome-wide association studies, we suppose the set indexing the hypotheses has a natural hierarchical structure, the simplest case being a partition into “cells.” In principle, it should then be possible to gain power if the active hypotheses tend to cluster within cells. We explore different coarse-to-fine, two-level multiple testing strategies, which control the FWER or the FDR and are designed to gain power relative to usual single level methods, in so far as clustering allows it. Simulations confirm a sharp improvement for in data models we consider