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Presentation 1
Time: 11:00am – 11:30am
Speaker: Jiayang Yin, UBC Statistics MSc student
Title: On the Improvement of Density Ratio Estimation – Theoretical Study and Its Applications
Abstract: Density ratio estimation is an effective tool in the world of machine learning and data science, especially in transfer learning and contrastive learning. By contrastive learning, it is also linked to intractable likelihood and un-normalized model inference. Our work mainly focuses on a type of density ratio estimation based on a probabilistic classification from the perspective of statistical inference. We study how such a density ratio estimation relates to a probabilistic classifier such as Logistic regression. We analyze the potential cause for its inefficiency and inaccuracy when the two distributions are much different from each other. Opposite to the target of a probabilistic classification, a density ratio estimation task with a more efficient estimator indicates the corresponding classification task is harder, which means it is more difficult to separate the two samples by a probabilistic classifier. We provide a theoretical explanation for this phenomenon from a mathematical and statistical standpoint. For the basic density ratio estimation by a probabilistic classification, we give a necessary and sufficient condition for its existence under a sample level. We analyze the probability with such conditions held asymptotically. Besides, we explore the asymptotic properties of a recent proposed approach to improving density ratio estimation by a probabilistic classification – Telescoping Density Ratio Estimation TDRE by Rhodes, et al. Numerically, we compare the asymptotic variance of basic density ratio estimation and TDRE. We also explore some generalization on TDRE with unbalanced data and under some model misspecification by both theoretical discussion and empirical analysis. Based on our work, some suggestions for future work on un-normalized model inference are also provided.
Presentation 2
Time: 11:30am – 12:00pm
Speaker: Jintong Yan, UBC Statistics MSc student
Title: Biostatistical Analysis of Biomarker Discovery in Two Chronic Diseases
Abstract: Exploring biomarkers, such as DNA sequencing, RNA sequencing, and protein data, that may be correlated with a specific disease can help guide its treatment and diagnosis. During my co-op at PROOF Centre, I worked on multiple projects with a focus on two: using Somalogic protein profiling to explore early diagnosis of acute rheumatic fever from plasma, and developing biomarkers to guide immunosuppression strategies during cytomegalovirus (CMV) infection in heart transplant patients. The main objective of this presentation is to demonstrate how statistics can be used in these two projects to help identify biomarkers that can be used for diagnosing or treating diseases.