報 告 人：崔恒建 教授
報告題目：Model-free feature screening based on Hellinger distance for ultrahigh dimensional data
報告時間：2024年3月29日（周五）下午2：30
報告地點(diǎn)：騰訊會議 243-343-042
主辦單位：數(shù)學(xué)研究院、數(shù)學(xué)與統(tǒng)計學(xué)院、科學(xué)技術(shù)研究院
報告人簡介：
崔恒建，現(xiàn)為首都師范大學(xué)教授，博士生導(dǎo)師，中國科協(xié)第十屆全委會委員，曾任國務(wù)院學(xué)位委員會學(xué)科評議組專家。中國科學(xué)院系統(tǒng)科學(xué)研究所博士畢業(yè)。在大數(shù)據(jù)統(tǒng)計建模、高維統(tǒng)計及其穩(wěn)健統(tǒng)計理論和方法、統(tǒng)計機(jī)器學(xué)習(xí)、金融統(tǒng)計、以及質(zhì)量管理等領(lǐng)域取得過許多重要的研究成果，發(fā)表論文180余篇，其中包括發(fā)表在國際頂級的統(tǒng)計和計量經(jīng)濟(jì)學(xué)雜志JASA、AoS、JRSS(B)、Biometrika和JoE上。主持國家自然科學(xué)基金重點(diǎn)項(xiàng)目、杰青（B）項(xiàng)目以及多項(xiàng)面上項(xiàng)目、主要參加教育部重大科研基金項(xiàng)目、科技部863等項(xiàng)目?，F(xiàn)擔(dān)任《數(shù)學(xué)學(xué)報》和《應(yīng)用數(shù)學(xué)學(xué)報》中、英文版以及《Statistical Theory and Related Fields》編委，中國現(xiàn)場統(tǒng)計研究會副理事長，全國工業(yè)統(tǒng)計教育研究會副理事長，北京應(yīng)用統(tǒng)計學(xué)會會長，國際數(shù)理統(tǒng)計學(xué)會（中國分會）常務(wù)理事。曾獲得教育部高等學(xué)?？茖W(xué)技術(shù)獎-自然科學(xué)獎二等獎；全國統(tǒng)計科學(xué)研究優(yōu)秀成果獎一等獎等。
報告摘要：
With the explosive development of data acquisition and processing technology, the dimension of features increases exponentially with the sample size, which poses great challenges for data analysis. It is vital to accurately identify useful features from thousands of them. In this paper, we develop an omnibus model-free feature screening procedure based on the Hellinger distance with some appealing merits. First, we define the Hellinger distance index for discrete response variables in discriminant analysis. Second, this procedure works consistently for continuous response variables, in which the continuous responses are discretized by slice-and-fused technique. Third, it is robust to the potential outliers and model misspecification. Theoretically, the procedure for discrete and continuous response variables possess sure screening properties and ranking consistency properties under mild conditions. Numerical studies demonstrate that this procedure exhibits strong competitiveness in heavy-tailed and skewed data, while remaining comparable to existing approaches for light-tailed data, indicating its robustness performance across a range of data. Real data contains two examples, discrete and continuous response variables, to illustrate the effectiveness of the proposed method.