讲座题目：Asymmetric AdaBoost for High Dimensional Maximum Score Regression
主 讲 人：Tae Hwy Lee 教授
加州大学河滨分校经济系教授，1990年6月毕业于加州大学圣地亚哥分校，获得经济学博士学位，导师为Halbert White Jr和诺贝尔经济学奖获得者Clive W.J. Granger先生。研究方向涵盖时间序列、金融风险分析、大数据、机器学习等方面。为American Economic Review，Econometric Theory，Journal of Econometrics，Economics Letters等顶级期刊杂志匿名审稿人。获得The Bank of Korea Research Award和Tjalling C. Koopmans Econometric Theory Prize等奖项。
Adaptive Boosting or AdaBoost, introduced by Freund and Schapire (1996) has been proved to be effective to solve the high-dimensional binary classification or binary prediction problems. Friedman, Hastie, and Tibshirani (2000) show that AdaBoost builds an additive logistic regression model via mini- mizing the ‘exponential loss’. We show that the exponential loss in AdaBoost is equivalent (up to scale) to the symmetric maximum score (Manski 1975, 1985) and also to the symmetric least square loss for binary prediction. Therefore, the standard AdaBoost using the exponential loss is a symmetric algo- rithm and solves the binary median regression. In this paper, we introduce Asymmetric AdaBoost that produces an additive logistic regression model from minimizing the new ‘asymmetric exponential loss’ which we introduce in this paper. The Asymmetric AdaBoost can handle the asymmetric maximum score problem (Granger and Pesaran 2000, Lee and Yang 2006, Lahiri and Yang 2012, and Elliot and Lieli 2013) and therefore solve the binary quantile regression. We also show that our asymmetric ex- ponential loss is equivalent (up to scale) to the asymmetric least square loss (Newey and Powell 1987) for binary classification / prediction. We extend the result of Bartlett and Traskin (2007) and show that the Asymmetric AdaBoost algorithm is consistent in the sense that the risk of the classifier it produces approaches the Bayes Risk. Monte Carlo experiments show that Asymmetric AdaBoost performs well relative to the lasso-regularized high-dimensional logistic regression under various situations especially when p>>n and in the tails. We apply the Asymmetric AdaBoost to predict the business cycle turning points and directions of stock price changes.