CIF: EAGER: Statistical Inference and Decision-Making With Sequential Samples

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The modern world is rich with diverse sources of data that provide invaluable insights into underlying random phenomena. The data, however, generally provide only indirect or imprecise information about the latent phenomena due to measurement limitations or privacy protections. This project develops efficient algorithms to use sequential samples to infer a hidden random phenomenon and use this knowledge to make decisions. Outcomes of the project will improve the efficiency and accuracy of data-driven decision-making and inference in a wide range of applications such as marketing and recommendation systems, cloud computing, manufacturing, and health care. The investigators will publish the research outcomes to broad academic and professional audiences and incorporate them into teaching curricula via graduate and undergraduate courses.The framework studied in this project consists of a hidden random variable (or, a random vector) that can be indirectly sampled by choosing one of several measurement mechanisms (referred to as arms). Upon choosing one of the arms, an arbitrary function of a realization of the hidden random variable is observed, instead of a direct sample. Within this framework, the investigators pursue problems including i) maximizing the reward obtained by sampling different arms in a correlated multi-armed bandit setting; and ii) estimating the probability distribution of the hidden random variable using minimum number of samples. These research thrusts will be studied with three main goals: 1) understanding the fundamental limits of the problem via bounds on the cumulative regret, and the error in the estimated distribution; 2) designing efficient sampling algorithms that meet the fundamental limits; and 3) validating the proposed algorithms on real-world datasets. The project deviates from the classic multi-armed bandit framework due to the correlation between arms and from the classic statistical inference due to the sequential and multi-fidelity nature of the data generation.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.