报告题目：Deep regression learning with optimal loss function
时 间：2024年12月7日（星期六）14:00
地 点：科研楼18号楼1102
主 办：数学与统计学院、分析数学及应用教育部重点实验室、福建省分析数学及应用重点实验室、福建省应用数学中心（福建师范大学）
参加对象：感兴趣的老师和学生
报告摘要：In this paper, we develop a novel efficient and robust nonparametric regression estimator under a framework of a feedforward neural network (FNN). There are several interesting characteristics for the proposed estimator. First, the loss function is built upon an estimated maximum likelihood function, which integrates the information from observed data as well as the information from the data structure. Consequently, the resulting estimator has desirable optimal properties, such as efficiency. Second, different from the traditional maximum likelihood estimation (MLE), the proposed method avoids the specification of the distribution and thus is flexible to any kind of distribution, such as heavy tails and multimodal or heterogeneous distributions. Third, the proposed loss function relies on probabilities rather than direct observations as in least square loss, hence contributing to the robustness of the proposed estimator. Finally, the proposed loss function involves a nonparametric regression function only. This enables the direct application of the existing packages, simplifying the computational and programming requirements. We establish the large sample property of the proposed estimator in terms of its excess risk and minimax near-optimal rate. The theoretical results demonstrate that the proposed estimator is equivalent to the true MLE where the density function is known. Our simulation studies show that the proposed estimator outperforms the existing methods in terms of prediction accuracy, efficiency and robustness. Particularly, it is comparable to the true MLE and even gets better as the sample size increases. This implies that the adaptive and data-driven loss function from the estimated density may offer an additional avenue for capturing valuable information. We further apply the proposed method to four real data examples, resulting in significantly reduced out-of-sample prediction errors compared to existing methods.
报告人简介：林华珍，西南财经大学首席教授，统计研究中心主任， 首届新基石研究员，国际数理统计学会IMS-fellow，教育部长江学者特聘教授，国家杰出青年科学基金获得者。主要研究方向为深度学习理论、非参数方法、生存数据分析、函数型数据分析、因子模型、转换模型等。研究成果发表在包括国际统计学四大顶刊JASA、AoS、JRSSB及Biometrika上。先后担任国际7个统计学杂志的Associate Editor，包括JASA、《Biometrics》（生物统计顶刊）、 《Journal of Business & Economic Statistics》（计量经济学顶刊）、国际统计重要综合类期刊《Scandinavian Journal of Statistics》、《Canadian Journal of Statistics》等，国内权威或核心学术期刊《数学学报》（英文）、《应用概率统计》、《系统科学与数学》、《数理统计与管理》编委会编委。林华珍教授现任国际泛华统计学会ICSA董事会成员，中国现场统计研究会副理事长，中国现场统计研究会数据科学与人工智能分会理事长，全国工业统计学教学研究会副会长。