Imperfect Information Learning Team Seminar (Talk by Haiyun He,National University of Singapore ).

Speaker: Haiyun He (National University of Singapore)

Title: FUNDAMENTAL PERFORMANCE LIMITS OF STATISTICAL PROBLEMS: FROM DETECTION THEORY TO SEMI-SUPERVISED LEARNING

Abstract:
Studying and designing close-to-optimal mechanisms to infer or learn useful information from raw data is of tremendous significance in this digital era. My PhD research explores the fundamental performance limits of three classes of statistical problems—distributed detection, change-point detection and the generalization capabilities of semi-supervised learning (SSL). The distributed detection problem concerns the scenario in which the fusion center needs to make a decision based on data sent from a number of sensors via different channels. The change-point detection problem concerns the scenario in which the data samples are collected under different conditions and one needs to estimate the change-points of the condition. In contrast to classical works where the underlying data distributions are assumed to be known, we consider the practical scenario where training data samples are available instead. We derived the asymptotically optimal test and error exponent for both the detection problems. Furthermore, we consider a more complicated scenario in which we are motivated to mitigate the high cost of labelling data. To do so, we analyse the fundamental limits of SSL which makes use of both labelled and unlabelled data. Using information-theoretic principles, we investigate the generalization performance of SSL, which quantifies the extent to which the algorithms overfits to the training data. We show that under iterative SSL with pseudo-labelling, for easier-to-distinguish classes, the generalization error decreases rapidly in the first few iterations and saturates afterwards while for difficult- to-distinguish classes, the generalization error increases instead. Regularization can help to mitigate this undesirable effect. Our experiments on benchmark datasets such as the MNIST and CIFAR-10 datasets corroborate our theoretical results.”