1. 1
Relative Importance Weight for
Covariate Shift Adaptation
Makoto Yamada
Tokyo Institute of Technology
April/21/2012 (Ver.0)

2. Covariate Shift Adaptation (JSPI 2000) 2
Shimodaira
Training data:
Test data :
Assumption :
Importance weighted empirical error
minimization:
We can obtain unbiased model in theory.
But, it usually gives unsatisfactory results…
Why?

3. A Problem in Covariate Shift Adaptation 3
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

4. 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 

5. Relative importance-weighted (RIW) 5
empirical error minimizational. (NIPS 2011)
Yamada et
Use 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.html
RIW-empirical error minimization:
works well in practice.

6. Toy Example 6
Comparison EIW and RIW
LS: least-squares regression
RIW method gives smaller error and variance

7. 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

8. Summary 8
Covariate shift adaptation tends to be
unstable.
Relative importance weight (RIW) is useful to
stabilize the covariate shift adaptation.
( works well in practice)

9. Useful Softwares 9
RuLSIF
http://sugiyama-www.cs.titech.ac.jp/~yamada/RuLSIF.html
IWLS (Regression)
http://sugiyama-www.cs.titech.ac.jp/~sugi/software/IWLS/index.html
IWKLR (Classification)
http://sugiyama-www.cs.titech.ac.jp/~yamada/iwklr.html
IWLSPC (Classification)
http://sugiyama-www.cs.titech.ac.jp/~hachiya/software/IWLSPC/index.html