主题报告专场（三）| 首届机器学习与统计会议

摘要：This paper explores the group structure in large dimensional approximate factor models, which portrays homogeneous effects of the common factors on the individuals that fall into the same group. With the initial principal component estimates, we identify the unknown group structure by a combination of the agglomerative hierarchical clustering algorithm and an information criterion. The loadings and factors are then re-estimated conditional on the identified groups. Under some regularity conditions, we establish the consistency of the membership estimator as well as that of the group number estimator obtained from the information criterion. The new estimators under the group structure are shown to achieve efficiency gain compared to those obtained without this information. Numerical simulations and empirical applications demonstrate the nice finite sample performance of our proposed approach when group structure presents.

简介：涂云东，北京大学光华管理学院和北京大学统计科学中心联席教授。入选“日出东方”北大光华青年人才，北京大学优秀博士学位论文指导教师，教育部“长江学者奖励计划”青年长江学者。2004年和2006年先后获武汉大学理学学士学位和经济学硕士学位，2012年获美国加州大学河滨分校经济学博士学位。亚太青年计量经济学者会议发起人和组织者。30余篇学术论文发表在多个国际国内知名专业杂志。主持多个国家自然科学基金项目，并担任自然科学基金匿名评审。曾获世界计量经济学会、加州计量经济学会议等学术组织提供的青年学者研究资助。研究领域涵盖时间序列分析、非参数计量方法、大数据分析、金融计量和预测等。

摘要：Directed acyclic graph (DAG) models are widely used to represent casual relations among collected nodes. This paper proposes an efficient and consistent method to learn DAG with a general causal dependence structure, which is in sharp contrast to most existing methods assuming linear dependence of causal relations. To facilitate DAG learning, the proposed method leverages the concept of topological layer, and connects nonparametric DAG learning with kernel ridge regression in a smooth reproducing kernel Hilbert space (RKHS) and learning gradients by showing that the topological layers of a nonparametric DAG can be exactly reconstructed via kernel-based estimation, and the parent-child relations can be obtained directly by computing the estimated gradient function. The developed algorithm is computationally efficient in the sense that it attempts to solve a convex optimization problem with an analytic solution, and the gradient functions can be directly computed by using the derivative reproducing property in the smooth RKHS. The asymptotic properties of the proposed method are established in terms of exact DAG recovery without requiring any explicit model specification. Its superior performance is also supported by a variety of simulated and a real-life example.

简介：谌自奇，华东师范大学研究员、紫江青年学者、博士生导师。从事高维统计分析、函数型（纵向）数据分析、生存分析、机器学习、神经网络、因果推断等方面的研究。主持国家自然科学基金面上项目2项，国家自然科学基金青年项目1项，上海市自然科学基金项目1项，湖南省自然科学基金项目1项，获得中国博士后面上和特别资助等。曾于2016-2019在美国安德森癌症研究中心生物统计系从事博士后研究工作。在JASA, Biometrics, Statistica Sinica, Scandinavian Journal of Statistics等国际权威统计期刊和AAAI，IJCNN等国际著名机器学习和人工智能会议上发表论文20余篇。

摘要：Deep learning has enjoyed tremendous success in a variety of applications but its application to quantile regression remains scarce. A major advantage of the deep learning approach is its flexibility to model complex data in a more parsimonious way than nonparametric smoothing methods. However, while deep learning brought breakthroughs in prediction, it is not well suited for statistical inference due to its black box nature. In this paper, we leverage the advantages of deep learning and apply it to quantile regression where the goal is to produce interpretable results and perform statistical inference. We achieve this by adopting a semiparametric approach based on the partially linear quantile regression model, where covariates of primary interest for statistical inference are modelled linearly and all other covariates are modelled nonparametrically by means of a deep neural network. In addition to the new methodology, we provide theoretical justification for the proposed model by establishing the root-n consistency and asymptotically normality of the parametric coefficient estimator and the minimax optimal convergence rate of the neural nonparametric function estimator. Across numerical studies, the proposed model empirically produces superior estimates and more accurate predictions than various alternative approaches.