Journal of Data Science

The assignment problem, crucial in various real-world applications, involves optimizing the allocation of agents to tasks for maximum utility. While it has been well-studied in the optimization literature when the underlying utilities between all agent-task pairs are known, research is sparse when the utilities are unknown and need to be learned from data on the fly. This paper addresses this gap, as motivated by mentor-mentee matching programs at many U.S. universities. We develop an efficient sequential assignment algorithm, with the aim of nearly maximizing the overall utility simultaneously over different time periods. Our proposed algorithm is to use stochastic bandit feedback to adaptively estimate the unknown utilities through linear regression models, integrating the Upper Confidence Bound (UCB) algorithm in the multi-armed bandit problem with the Hungarian algorithm in the assignment problem. We provide theoretical bounds of our algorithm for both the estimation error and the total regret. Additionally, numerical studies are also conducted to demonstrate the practical effectiveness of our algorithm.

Pupillary response behavior (PRB) refers to changes in pupil diameter in response to simple or complex stimuli. There are underlying, unique patterns hidden within complex, high-frequency PRB data that can be utilized to classify visual impairment, but those patterns cannot be described by traditional summary statistics. For those complex high-frequency data, Hurst exponent, as a measure of long-term memory of time series, becomes a powerful tool to detect the muted or irregular change patterns. In this paper, we proposed robust estimators of Hurst exponent based on non-decimated wavelet transforms. The properties of the proposed estimators were studied both theoretically and numerically. We applied our methods to PRB data to extract the Hurst exponent and then used it as a predictor to classify individuals with different degrees of visual impairment. Compared with other standard wavelet-based methods, our methods reduce the variance of the estimators and increase the classification accuracy.