This research focuses on a variety of information acquisition and sensing applications in which a decision maker, by carefully controlling a sequence of actions with uncertain outcomes, dynamically refines his belief about a phenomenon of interest in a speedy, accurate, and efficient manner. The model includes a class of applications in communications, design of experiments, cognitive science, and sensor management. In particular, the following three problems are tackled. ? Active Sequential Hypothesis Testing: There are a set of hypotheses, one of which is true. A decision maker is asked to identify the correct hypothesis by sequentially employing either one of available sensing actions. Actions costs differently and produce statistically distinct observations. Given a penalty for error in declaration, the work investigates the optimal selection of sensing actions. ? Feedback Schemes for Joint Source-Channel Coding with Bandwidth Expansion: A message is to be conveyed to a receiver over a noisy memoryless channel with feedback. The expected distortion between the message and the receiver?s construction is sought to be minimized over the choice of causal encoding functions as well as the decoding function. ? Joint Source-Channel Coding over a Multiple Access Channel with Feedback: Multiple transmitters convey messages to a common receiver over a noisy memoryless multiple access channel with perfect output feedback. These problems boil down to the sequential control of a dynamical system whose system is the conditional distribution of the unknown (true hypothesis, message, etc) and whose dynamics is dictated by the Bayes? rule. In particular, the optimal choice of actions, i.e. refinement in the conditional distribution and reduction of uncertainty, is investigated.
Intellectual Merit: This research project focused on information acquisition and sensing applications in which a decision maker, by carefully controlling a sequence of actions with uncertain outcomes, dynamically refines his belief about a phenomenon of interest in a speedy, accurate, and efficient manner. The model includes a class of applications in communications, design of experiments, cognitive science, and sensor management. Consider the following simple example: a patient has symptoms which are consistent with more than one illness each of which requires a different prognosis. How does a physician go about ordering further more costly (and more advanced) diagnostic tests efficiently and in a timely manner? Even though some diagnostic tests produce more reliable results, they might not be the right ones to order at a given time and given the physician’s prior belief. In other words, a physician’s sequential diagnostic decisions critically impact the information dynamics, hence the timeliness of the diagnosis, its accuracy, and its cost. Mathematically, this class of problems boils down to a sequential control of a dynamical system in which the state of the system is the distribution of a certain random variable and the dynamics is dictated by the Bayes’ rule. In particular, the choice of actions and the noise in the observation refines the conditional distribution in form of a reduction in uncertainty. Specifically, we studied closely related issues of dynamic control of information state as they arise in the context of: Active and Sequential M -ary Hypothesis Testing:There are M hypotheses, one of which is true. A decision maker is asked to identify the correct hypothesis by sequentially employing either one of K sensing actions or a retire-declare action. A given sensing action has a certian cost and provides a noisy sample whose conditional distributions given true hypothesis is given. Given a penalty for error in declaration, what are the optimal selection of sensing actions, stopping time to retire, and declaration. The study involves ordering discrete random variables in a stochastic sense in order to optimally shape the appropriate conditional distribution of the true hypothesis. Here techniques from statistics, information theory and stochastic control were brought together to characterize the solution. The findings appeared in the following publications: M. Naghshvar and T. Javidi. Sequentiality and Adaptivity Gains in Active Hypothesis Testing. IEEE Journal of Selected Topics in Signal Processing, Vol. 7, No. 5, October 2013 M. Naghshvar and T. Javidi. Active Sequential Hypothesis Testing. Annals of Statistics. Vol 41. No 6. December 2013 Feedback Schemes for Joint Source-Channel Coding with Bandwidth Expansion: Consider a message with a given prior distribution to be conveyed to a receiver in T time slots over a noisy memoryless channel with feedback. After T channel uses, the expected distortion of the constructed message depends on the distribution of the message as well as the channel noise. The expected distortion after T channel uses is sought to be minimized over the choice of T causal encoding functions as well as the decoding function at the deadline T. Despite the existence of two agents with distributed information and decentralized control structure, this problem generalizes the active sequential hypothesis testing problem for continuous random variables and uncountable action space. Our proposed solutions are catalogued in the following accepted publications to appear. M. Naghshvar, T. Javidi, M. Wigger. Extrinsic Jensen–Shannon Divergence: Applications to Variable-Length Coding. To appear in IEEE Transactions on Information Theory Broader Impact: In addition to the broader impact of this research grant in a wide variety of applications, from computer vision to cyber physical systems to enhanced spectrum access, it also included various educational components, mentoring and outreach, as well as organization of workshops. In particular, the project included a strong element of partnership with the UCSD Information Theory and Application Center (ITA) for training two postdoctoral scholars who have since joined the academic and R&D workforce. Furthermore, the project enhanced the PI's activities in the area of outreach to and mentoring URM and women engineering students.
