題目一：Coefficient-based lq- regularized direct learning for estimating individual treatment rule
内容簡介：The aim of precision medicine is to identify the best treatment approach for each individual patient by taking into account their unique characteristics. This involves developing a decision function, known as an individual treatment rule (ITR), which maximizes the expected clinical outcome. Direct learning (D-learning) is one of the main algorithms estimating the optimal ITR. In this talk, we mainly study the coefficient-based D-learning with lq -regularizer (where 1 < q ≤ 2) with unbounded clinical outcome. We establish the error bounds for the algorithm by constructing the stepping stone function and applying concentration inequality with empirical covering numbers. Fast learning rates are derived explicitly under a moment condition on the clinical outcome.
報告人：向道紅
報告人簡介：浙江師範大學數學科學學院教授，博士生導師，德國洪堡學者，浙江省高校中青年學科帶頭人，浙江省應用數學研究會副理事長。于2009年2月獲香港城市大學博士學位，2009-2010年在香港中文大學作博士後，2010年3月入職浙江師範大學至今。研究領域為統計學習理論、穩健統計等。在《Journal of Machine Learning Research》《Journal of Approximation Theory》《Advances in Computational Mathematics》《Journal of Multivariate Analysis》《Science China Mathematics》等國内外學術刊物上發表論文多篇。主持完成國家自然科學基金面上項目2項、青年基金1項、浙江省自然科學基金1項。
題目二：Graph Fourier Transform On Directed Graphs
内容簡介：Graph signal processing provides an innovative framework to process data on graphs. The widely used graph Fourier transform on the undirected graph is based on the eigen-decomposition of the Laplacian. In many engineering applications, the data is time-varying and pairwise interactions among agents of a network are not always mutual and equitable, such as the interaction data on a social network. Then the graph Fourier transform on directed graph is in demand and it should be designed to reflect the spectral characteristic for different directions, decompose graph signals into different frequency components, and to efficiently represent the graph signal by different modes of variation. In this talk, I will present our recent work on the graph Fourier transforms on directed graphs which are based on the singular value decompositions of the Laplacians.
報告人：成誠
報告人簡介：中山大學數學學院副教授，在此之前在美國杜克大學和美國統計和應用數學研究所做博士後研究，期間合作導師是美國三院院士Ingrid Daubechies 教授。成誠畢業于中佛羅裡達大學數學系，指導老師是孫颀彧教授和李欣教授，她的主要研究方向為應用調和分析，特别是采樣理論，相位恢複以及圖信号處理中的數學理論，目前已有多篇論文發表在 Applied and Computational Harmonic Analysis, Journal of Functional Analysis, Journal of Fourier Analysis and Applications, IEEE Transaction on Signal Processing, Signal Processing, and IEEE Signal Processing letters 等。現主持國家自然科學基金一項，廣東省自然科學基金一項。
時 間：2023年10月16日（周一）上午9：30 始
地 點：騰訊會議：388-854-158
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