1 Relative Importance Weight for Covariate Shift Adaptation Makoto Yamada Tokyo Institute of Technology April/21/2012 (Ver.0)
Covariate Shift Adaptation 2 Shimodaira (JSPI 2000) Training data: Test data : Assumption : Importance weighted empirical error minimizatio n: We can obtain unbiased model in theory. But, it usual y gives unsatisfactory results… Why?
3 A Problem in Covariate Shift Adaptation Importance 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) empir 4 ical er ror 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 giv e an unbiased model under covariate shift. It still needs importance weight estimation
Relative importance-weighted (RIW) e 5 mpiric al error minimization Yamada et al. (NIPS 2011) Use relative importance weight (RIW): If , RIW is bounded. Thus, estimating RIW is ea sier than estimating IW. RIW can be efficiently estimated by RuLSIF. http://sugiyama-www.cs.titech.ac.jp/~yamada/RuLSIF.html RIW-empirical error minimization: works well in practice.
Toy Example 6 Comparison 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 touch Activities: Walking, running, and bicycle riding Training data: 20 existing users Test data: New users Classifier: Kernel Logistic Regression (KLR) RIW method is also useful for practical data
Summary 8 Covariate shift adaptation tends to be unstabl e. Relative importance weight (RIW) is useful to s tabilize the covariate shift adaptation. ( works well in practice)