Transformation Function Based Methods for Model Shift

Transfer learning techniques are often used when one tries to adapt a model learned from a source domain with abundant labeled samples to the target domain with limited labeled samples. In this paper, we consider the regression problem under model shift condition, i.e., regression functions are different but related in the source and target domains. We approach this problem through the use of transformation functions which characterize the relation between the source and the target domain. These transformation functions are able to transform the original problem of learning the complicated regression function of target domain into a problem of learning a simple auxiliary function. This transformation function based technique includes some previous works as special cases, but the class we propose is significantly more general. In this work we consider two widely used non-parametric estimators, Kernel Smoothing (KS) and Kernel Ridge Regression (KRR) for this setting and show improved statistical rates for excess risk than non-transfer learning. Through an -cover technique, we show that we can find the best transformation function a function class. Lastly, experiments on synthesized, robotics and neural imaging data demonstrate the effectiveness of our framework.

[1]  Mehryar Mohri,et al.  New Analysis and Algorithm for Learning with Drifting Distributions , 2012, ALT.

[2]  C. Craig.  On the Tchebychef Inequality of Bernstein , 1933 .

[3]  Vladimir Vovk,et al.  Kernel Ridge Regression , 2013, Empirical Inference.

[4]  M. Botvinick,et al.  Conflict monitoring and cognitive control. , 2001, Psychological review.

[5]  Ilja Kuzborskij,et al.  Fast rates by transferring from auxiliary hypotheses , 2014, Machine Learning.

[6]  J. Ridley.  Studies of Interference in Serial Verbal Reactions , 2001 .

[7]  André Elisseeff,et al.  Stability and Generalization , 2002, J. Mach. Learn. Res..

[8]  Koby Crammer,et al.  Learning Bounds for Domain Adaptation , 2007, NIPS.

[9]  Jeff G. Schneider,et al.  Generalization Bounds for Transfer Learning under Model Shift , 2015, UAI.

[10]  Yishay Mansour,et al.  Domain Adaptation: Learning Bounds and Algorithms , 2009, COLT.

[11]  Don R. Hush,et al.  Optimal Rates for Regularized Least Squares Regression , 2009, COLT.

[12]  Mehryar Mohri,et al.  Adaptation Algorithm and Theory Based on Generalized Discrepancy , 2014, KDD.

[13]  Raymond J. Carroll,et al.  Measurement error in nonlinear models: a modern perspective , 2006 .

[14]  Qiang Yang,et al.  A Survey on Transfer Learning , 2010, IEEE Transactions on Knowledge and Data Engineering.

[15]  Lawrence Carin,et al.  Logistic regression with an auxiliary data source , 2005, ICML.

[16]  Stergios B. Fotopoulos,et al.  All of Nonparametric Statistics , 2007, Technometrics.

[17]  Mehryar Mohri,et al.  Domain Adaptation in Regression , 2011, ALT.

[18]  Sanjiv Singh,et al.  Modeling and Calibrating Visual Yield Estimates in Vineyards , 2012, FSR.

[19]  Bernhard Schölkopf,et al.  Domain Adaptation under Target and Conditional Shift , 2013, ICML.

[20]  Barnabás Póczos,et al.  Nonparametric Risk and Stability Analysis for Multi-Task Learning Problems , 2016, IJCAI.

[21]  Rich Caruana,et al.  Inductive Transfer for Bayesian Network Structure Learning , 2007, ICML Unsupervised and Transfer Learning.

[22]  Andrew Y. Ng,et al.  Transfer learning for text classification , 2005, NIPS.

[23]  Shai Ben-David,et al.  On the Hardness of Domain Adaptation and the Utility of Unlabeled Target Samples , 2012, ALT.

[24]  Vikas K. Garg,et al.  Adaptivity to Local Smoothness and Dimension in Kernel Regression , 2013, NIPS.

[25]  Yaoliang Yu,et al.  Analysis of Kernel Mean Matching under Covariate Shift , 2012, ICML.

[26]  P. Cochat,et al.  Et al , 2008, Archives de pediatrie : organe officiel de la Societe francaise de pediatrie.

[27]  Robert D. Nowak,et al.  Signal Reconstruction From Noisy Random Projections , 2006, IEEE Transactions on Information Theory.

[28]  Mehryar Mohri,et al.  Domain adaptation and sample bias correction theory and algorithm for regression , 2014, Theor. Comput. Sci..

[29]  Bernhard Schölkopf,et al.  Correcting Sample Selection Bias by Unlabeled Data , 2006, NIPS.

[30]  Koby Crammer,et al.  Analysis of Representations for Domain Adaptation , 2006, NIPS.

[31]  T. Verstynen.  The organization and dynamics of corticostriatal pathways link the medial orbitofrontal cortex to future behavioral responses. , 2014, Journal of neurophysiology.

[32]  Jeff G. Schneider,et al.  Flexible Transfer Learning under Support and Model Shift , 2014, NIPS.

[33]  Tyler Lu,et al.  Impossibility Theorems for Domain Adaptation , 2010, AISTATS.

[34]  Motoaki Kawanabe,et al.  Direct Importance Estimation with Model Selection and Its Application to Covariate Shift Adaptation , 2007, NIPS.

[35]  Ilja Kuzborskij,et al.  Stability and Hypothesis Transfer Learning , 2013, ICML.