| 主讲人 |
范剑青 |
简介 |
<p>Neural network-based methods for conditional density estimation have recently gained substantial attention, as various neural density estimators have outperformed classical approaches in real-data experiments. Despite these empirical successes, implementation can be challenging due to the need to ensure non-negativity and unit-mass constraints, and theoretical understanding remains limited. In particular, it is unclear whether such estimators can adaptively achieve faster convergence rates when the underlying density exhibits a low-dimensional structure. This paper addresses these gaps by proposing a structure-agnostic neural density estimator, called the classification-induced neural density estimator and simulator (CINDES) that is straightforward to implement and provably adaptive, attaining faster rates when the true density admits a low-dimensional composition structure. Another key contribution of our work is to show that the proposed estimator integrates naturally into generative sampling pipelines, most notably score-based diffusion models, where it achieves provably faster convergence when the underlying density is structured. We validate its performance through extensive simulations and a real-data application. We also prove the optimality of score-based diffusion models for density estimation when the target density admits a factorizable, low-dimensional, nonparametric structure in a separate work. The main challenge is that the low-dimensional, factorizable structure no longer holds for most diffused timesteps, and it is very difficult to show that these diffused score functions can be well approximated without a significant increase in the number of network parameters.</p> |
| 主讲人简介 |
<p>Jianqing Fan, Academician of Academia Sinica and Foreign member of the Royal Academies for Science and the Arts of Belgium, is Frederick L. Moore '18 Professor of Finance, Professor of Statistics, and former Chairman of the Department of Operations Research and Financial Engineering at Princeton University, where he directs both the financial econometrics lab and statistics lab. He previously held professorships at UNC-Chapel Hill and UCLA. He has authored or co-authored over 300 articles on finance, econometrics, statistical machine learning, analysis of Big Data, and various aspects of theoretical and methodological statistics and machine learning. His finance work focuses on the analysis of high-frequency data, empirical asset pricing, option pricing, portfolio theory, risk assessment, high-dimensional data, and time series. He is a joint editor of the <em>Journal of American Statistical Association</em>, and was the joint editor of<em> Journal of Business and Economics Statistics, Journal of Econometrics</em>, and<em> Annals of Statistics,</em> and has served as associate editor of <em>Econometrica, Management Science,</em> and<em> Journal of Financial Econometrics</em>. His published work has been recognized by the 2000 COPSS Presidents’ Award, the 2007 Morningside Gold Medal of Applied Mathematics, Guggenheim Fellowship in 2009, P.L. Hsu prize in 2013, Guy Medal in Silver in 2014, Noether Distinguished Scholar Award in 2018, and IMS Le Cam Award and Lecture in 2021, and IMS Wald Award and Lectures in 2025. He is an Elected Fellow of the American Association for Advancement of Science, the Society of Financial Econometrics, the Institute of Mathematical Statistics, and the American Statistical Association, and a past President of the Institute of Mathematical Statistics.</p> |
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