摘要：The Population-based HIV Impact Assessment (PHIA) is an ongoing project that conducts nationally representative HIV-focused surveys for measuring national and regional progress toward UNAIDS’90-90-90 targets, the primary strategy to end the HIV epidemic. We believe the PHIA survey offers a unique opportunity to better understand the key factors that drive the HIV epidemics in the most affected countries in sub-Saharan Africa. In this article, we propose a novel causal structural learning algorithm to discover important covariates and potential causal pathways for 90-90-90 targets. Existing constrained-based causal structural learning algorithms are quite aggressive in edge removal. The proposed algorithm preserves more information about important features and potential causal pathways. It is applied to the Malawi PHIA (MPHIA) data set and leads to interesting results. We further compare and validate the proposed algorithm using BIC and using Monte Carlo simulations, and show that the proposed algorithm achieves improvement in true positive rates in important feature discovery over existing algorithms.

简介：李长城，大连理工大学数学科学学院教授。本科就读于北京大学数学科学学院，获得统计学学士学位；博士阶段师从美国宾夕法尼亚州州立大学统计系李润泽教授，进行高维统计领域的学习，获得统计学博士学位。研究兴趣主要包括高维统计推断及高维因果推断。在高维统计的理论、应用以及计算方面进行了一系列研究，文章发表于一流学术期刊Journal of American Statistical Association、Journal of Econometrics、Annals of Applied Statistics、Statistica Sinica等，入选国家级青年人才计划。

摘要：深度学习在诸如图像处理、自然语言处理、运筹、博弈等领域取得了巨大的成功。但其成功的原因依然缺乏严格的理论解释与验证。在这种未知性下，学术界与业界掀起了深度学习浪潮， 试图用深度神经网络去处理所有学习问题。很显然，在某些应用上，效果不如预期。该报告将从数学上（统计学习的角度）揭露深度神经网络的学习能力并在一定程度阐明深度学习的适用范围。特别地，该报告聚焦如下四个基本问题：

1.  深度网是否一定比单层网好?

2.  在什么情况下用深度学习会更有效？

3.  为什么深度网在大数据时代取得这么大成功？

4.  过参数化深度神经网络为何可规避过拟合现象?

简介：杨玥含，中央财经大学统计与数学学院副教授，北京大学数学科学学院应用数学博士。主主要从事多重结构数据建模、因果推断、迁移学习等研究。在Journal of the American Statistical Association、Biometrika、Pattern Recognition、Expert Systems with Applications、《中国科学：数学》等国内外期刊发表论文30余篇。

摘要：Multi-task learning has attracted much attention due to growing multi-purpose research with multiple related data sources. Moreover, transduction with matrix completion is a useful method in multi-label learning. In this paper, we propose a transductive matrix completion algorithm that incorporates a calibration constraint for the features under the multi-task learning framework. The proposed algorithm recovers the incomplete feature matrix and target matrix simultaneously. Fortunately, the calibration information improves the completion results. In particular, we provide a statistical guarantee for the proposed algorithm, and the theoretical improvement induced by calibration information is also studied. Moreover, the proposed algorithm enjoys a sub-linear convergence rate. Several synthetic data experiments are conducted, which show the proposed algorithm out-performs other methods, especially when the target matrix is associated with the feature matrix in a nonlinear way.