Relative Importance Weight for Covariate Shift Adaptation
1Relative Importance Weight for Covariate Shift Adaptation Makoto Yamada Tokyo Institute of Technology April/21/2012 (Ver.0)
Covariate Shift Adaptation (JSPI 2000) 2 ShimodairaTraining data:Test data :Assumption :Importance weighted empirical error minimization: We can obtain unbiased model in theory. But, it usually gives unsatisfactory results… Why?
A Problem in Covariate Shift Adaptation 3Importance weight can diverge to infinity under a rather simple setting. Cortes et al. (NIPS 2010) In this situation, the covariate shift adaptation is unstable since estimated importance weight is unstable
Exponentially-flattened IW (EIW) 4 empirical error minimization Shimodaira (JSPI 2000)Flatten the importance weight by empirical error minimization. Intermediate IW empirical error minimization Setting to is practically useful for stabilizing the covariate shift adaptation, even though it cannot give an unbiased model under covariate shift. It still needs importance weight estimation
Relative importance-weighted (RIW) 5 empirical error minimizational. (NIPS 2011) Yamada etUse relative importance weight (RIW): If , RIW is bounded. Thus, estimating RIW is easier than estimating IW. RIW can be efficiently estimated by RuLSIF. http://sugiyama-www.cs.titech.ac.jp/~yamada/RuLSIF.htmlRIW-empirical error minimization: works well in practice.
Toy Example 6Comparison EIW and RIW LS: least-squares regression RIW method gives smaller error and variance
Real Experiments 7 (Human Activity Recognition)Data: Accelerometer data collected by iPod touchActivities: Walking, running, and bicycle ridingTraining data: 20 existing usersTest data: New usersClassifier: Kernel Logistic Regression (KLR) RIW method is also useful for practical data
Summary 8Covariate shift adaptation tends to be unstable.Relative importance weight (RIW) is useful to stabilize the covariate shift adaptation. ( works well in practice)