報告題目：Deep regression learning with optimal loss function
報 告 人：林華珍 教授 西南财經大學
報告時間：2024年8月4日上午 10:00-11:00
報告地點：數學樓第二報告廳
校内聯系人：朱複康 fzhu@jlu.edu.cn
報告摘要：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.
*Joint work with Xuancheng Wang and Ling Zhou
報告人簡介：林華珍，西南财經大學首席教授，統計研究中心主任， 首屆新基石研究員，國際數理統計學會IMS-fellow，國家傑出青年科學基金獲得者，國家級人才項目入選者。主要研究方向為深度學習理論、非參數方法、生存數據分析、函數型數據分析、因子模型、轉換模型等。研究成果發表在包括國際統計學四大頂級期刊JASA、AoS、JRSSB及Biometrika上。目前是國際統計學頂刊JASA的Associate Editor，還先後擔任生物統計頂刊《Biometrics》、計量經濟頂刊《Journal of Business & Economic Statistics》、及國際統計重要綜合類期刊《Scandinavian Journal of Statistics》、《Canadian Journal of Statistics》、《Statistics and Its Interface》、《Statistical Theory and Related Fields》的Associate Editor，國内權威或核心學術期刊《數學學報》（英文）、《應用概率統計》、《系統科學與數學》、《數理統計與管理》編委會編委。林華珍教授現任國際泛華統計學會ICSA董事會成員，中國現場統計研究會副理事長，中國現場統計研究會數據科學與人工智能分會理事長，全國工業統計學教學研究會副會長。
