Optimal Grouping for Group Minimax Hypothesis Testing

Bayesian hypothesis testing and minimax hypothesis testing represent extreme instances of detection in which the prior probabilities of the hypotheses are either completely and precisely known, or are completely unknown. Group minimax, also known as Gamma-minimax, is a robust intermediary between Bayesian and minimax hypothesis testing that allows for coarse or partial advance knowledge of the hypothesis priors by using information on sets in which the prior lies. Existing work on group minimax, however, does not consider the question of how to define the sets or groups of priors; it is assumed that the groups are given. In this work, we propose a novel intermediate detection scheme formulated through the quantization of the space of prior probabilities that optimally determines groups and also representative priors within the groups. We show that when viewed from a quantization perspective, group minimax amounts to determining centroids with a minimax Bayes risk error divergence distortion criterion: the appropriate Bregman divergence for this task. Moreover, the optimal partitioning of the space of prior probabilities is a Bregman Voronoi diagram. Together, the optimal grouping and representation points are an epsilon-net with respect to Bayes risk error divergence, and permit a rate-distortion type asymptotic analysis of detection performance with the number of groups. Examples of detecting signals corrupted by additive white Gaussian noise and of distinguishing exponentially-distributed signals are presented.Comment: 12 figure

Reliable Crowdsourcing for Multi-Class Labeling using Coding Theory

Crowdsourcing systems often have crowd workers that perform unreliable work on the task they are assigned. In this paper, we propose the use of error-control codes and decoding algorithms to design crowdsourcing systems for reliable classification despite unreliable crowd workers. Coding-theory based techniques also allow us to pose easy-to-answer binary questions to the crowd workers. We consider three different crowdsourcing models: systems with independent crowd workers, systems with peer-dependent reward schemes, and systems where workers have common sources of information. For each of these models, we analyze classification performance with the proposed coding-based scheme. We develop an ordering principle for the quality of crowds and describe how system performance changes with the quality of the crowd. We also show that pairing among workers and diversification of the questions help in improving system performance. We demonstrate the effectiveness of the proposed coding-based scheme using both simulated data and real datasets from Amazon Mechanical Turk, a crowdsourcing microtask platform. Results suggest that use of good codes may improve the performance of the crowdsourcing task over typical majority-voting approaches.Comment: 20 pages, 11 figures, under revision, IEEE Journal of Selected Topics in Signal Processin

A Coupon-Collector Model of Machine-Aided Discovery

Empirical studies of scientific discovery---so-called Eurekometrics---have indicated that the output of exploration proceeds as a logistic growth curve. Although logistic functions are prevalent in explaining population growth that is resource-limited to a given carrying capacity, their derivation do not apply to discovery processes. This paper develops a generative model for logistic \emph{knowledge discovery} using a novel extension of coupon collection, where an explorer interested in discovering all unknown elements of a set is supported by technology that can respond to queries. This discovery process is parameterized by the novelty and quality of the set of discovered elements at every time step, and randomness is demonstrated to improve performance. Simulation results provide further intuition on the discovery process.Comment: 5 pages, 9 figures, 2017 KDD Workshop on Data-Driven Discover

Diffusive Molecular Communication with Nanomachine Mobility

This work presents a performance analysis for diffusive molecular communication with mobile transmit and receive nanomachines. To begin with, the optimal test is obtained for symbol detection at the receiver nanomachine. Subsequently, closed-form expressions are derived for the probabilities of detection and false alarm, probability of error, and capacity considering also aberrations such as multi-source interference, inter-symbol interference, and counting errors. Simulation results are presented to corroborate the theoretical results derived and also, to yield various insights into the performance of the system. Interestingly, it is shown that the performance of the mobile diffusive molecular communication can be significantly enhanced by allocating large fraction of total available molecules for transmission as the slot interval increases.Comment: To be submitted in 52th Annual Conference on Information Sciences and Systems (CISS

Cognitive MIMO-RF/FSO Cooperative Relay Communication with Mobile Nodes and Imperfect Channel State Information

This work analyzes the performance of an underlay cognitive radio based decode-and-forward mixed multiple-input multiple-output (MIMO) radio frequency/free space optical (RF/FSO) cooperative relay system with multiple mobile secondary and primary user nodes. The effect of imperfect channel state information (CSI) arising due to channel estimation error is also considered at the secondary user transmitters (SU-TXs) and relay on the power control and symbol detection processes respectively. A unique aspect of this work is that both fixed and proportional interference power constraints are employed to limit the interference at the primary user receivers (PU-RXs). Analytical results are derived to characterize the exact and asymptotic outage and bit error probabilities of the above system under practical conditions of node mobility and imperfect CSI, together with impairments of the optical channel, such as path loss, atmospheric turbulence, and pointing errors, for orthogonal space-time block coded transmission between each SU-TX and relay. Finally, simulation results are presented to yield various interesting insights into the system performance such as the benefits of a midamble versus preamble for channel estimation.Comment: revision submitted to IEEE Transactions on Cognitive Communications and Networkin

Multi-object Classification via Crowdsourcing with a Reject Option

Consider designing an effective crowdsourcing system for an $M$-ary classification task. Crowd workers complete simple binary microtasks whose results are aggregated to give the final result. We consider the novel scenario where workers have a reject option so they may skip microtasks when they are unable or choose not to respond. For example, in mismatched speech transcription, workers who do not know the language may not be able to respond to microtasks focused on phonological dimensions outside their categorical perception. We present an aggregation approach using a weighted majority voting rule, where each worker's response is assigned an optimized weight to maximize the crowd's classification performance. We evaluate system performance in both exact and asymptotic forms. Further, we consider the setting where there may be a set of greedy workers that complete microtasks even when they are unable to perform it reliably. We consider an oblivious and an expurgation strategy to deal with greedy workers, developing an algorithm to adaptively switch between the two based on the estimated fraction of greedy workers in the anonymous crowd. Simulation results show improved performance compared with conventional majority voting.Comment: two column, 15 pages, 8 figures, submitted to IEEE Trans. Signal Proces

Design and Performance Analysis of Dual and Multi-hop Diffusive Molecular Communication Systems

This work presents a comprehensive performance analysis of diffusion based direct, dual-hop, and multi-hop molecular communication systems with Brownian motion and drift in the presence of various distortions such as inter-symbol interference (ISI), multi-source interference (MSI), and counting errors. Optimal decision rules are derived employing the likelihood ratio tests (LRTs) for symbol detection at each of the cooperative as well as the destination nanomachines. Further, closed-form expressions are also derived for the probabilities of detection, false alarm at the individual cooperative, destination nanomachines, as well as the overall end-to-end probability of error for source-destination communication. The results also characterize the impact of detection performance of the intermediate cooperative nanomachine(s) on the end-to-end performance of dual/multi hop diffusive molecular communication systems. In addition, capacity expressions are also derived for direct, dual-hop, and multi-hop molecular communication scenarios. Simulation results are presented to corroborate the theoretical results derived and also, to yield insights into system performance.Comment: in preparatio

Flavor Pairing in Medieval European Cuisine: A Study in Cooking with Dirty Data

An important part of cooking with computers is using statistical methods to create new, flavorful ingredient combinations. The flavor pairing hypothesis states that culinary ingredients with common chemical flavor components combine well to produce pleasant dishes. It has been recently shown that this design principle is a basis for modern Western cuisine and is reversed for Asian cuisine. Such data-driven analysis compares the chemistry of ingredients to ingredient sets found in recipes. However, analytics-based generation of novel flavor profiles can only be as good as the underlying chemical and recipe data. Incomplete, inaccurate, and irrelevant data may degrade flavor pairing inferences. Chemical data on flavor compounds is incomplete due to the nature of the experiments that must be conducted to obtain it. Recipe data may have issues due to text parsing errors, imprecision in textual descriptions of ingredients, and the fact that the same ingredient may be known by different names in different recipes. Moreover, the process of matching ingredients in chemical data and recipe data may be fraught with mistakes. Much of the `dirtiness' of the data cannot be cleansed even with manual curation. In this work, we collect a new data set of recipes from Medieval Europe before the Columbian Exchange and investigate the flavor pairing hypothesis historically. To investigate the role of data incompleteness and error as part of this hypothesis testing, we use two separate chemical compound data sets with different levels of cleanliness. Notably, the different data sets give conflicting conclusions about the flavor pairing hypothesis in Medieval Europe. As a contribution towards social science, we obtain inferences about the evolution of culinary arts when many new ingredients are suddenly made available.Comment: IJCA

How an Electrical Engineer Became an Artificial Intelligence Researcher, a Multiphase Active Contours Analysis

This essay examines how what is considered to be artificial intelligence (AI) has changed over time and come to intersect with the expertise of the author. Initially, AI developed on a separate trajectory, both topically and institutionally, from pattern recognition, neural information processing, decision and control systems, and allied topics by focusing on symbolic systems within computer science departments rather than on continuous systems in electrical engineering departments. The separate evolutions continued throughout the author's lifetime, with some crossover in reinforcement learning and graphical models, but were shocked into converging by the virality of deep learning, thus making an electrical engineer into an AI researcher. Now that this convergence has happened, opportunity exists to pursue an agenda that combines learning and reasoning bridged by interpretable machine learning models

Toward a Comparative Cognitive History: Archimedes and D. H. J. Polymath

Is collective intelligence just individual intelligence writ large, or are there fundamental differences? This position paper argues that a cognitive history methodology can shed light into the nature of collective intelligence and its differences from individual intelligence. To advance this proposed area of research, a small case study on the structure of argument and proof is presented. Quantitative metrics from network science are used to compare the artifacts of deduction from two sources. The first is the work of Archimedes of Syracuse, putatively an individual, and of other ancient Greek mathematicians. The second is work of the Polymath Project, a massively collaborative mathematics project that used blog posts and comments to prove new results in combinatorics.Comment: Presented at Collective Intelligence conference, 2012 (arXiv:1204.2991