TY - GEN
T1 - The Power and Limitation of Pretraining-Finetuning for Linear Regression under Covariate Shift
AU - Wu, Jingfeng
AU - Zou, Difan
AU - Braverman, Vladimir
AU - Gu, Quanquan
AU - Kakade, Sham M.
N1 - Publisher Copyright:
© 2022 Neural information processing systems foundation. All rights reserved.
PY - 2022/1/1
Y1 - 2022/1/1
N2 - We study linear regression under covariate shift, where the marginal distribution over the input covariates differs in the source and the target domains, while the conditional distribution of the output given the input covariates is similar across the two domains. We investigate a transfer learning approach with pretraining on the source data and finetuning based on the target data (both conducted by online SGD) for this problem. We establish sharp instance-dependent excess risk upper and lower bounds for this approach. Our bounds suggest that for a large class of linear regression instances, transfer learning with O(N2) source data (and scarce or no target data) is as effective as supervised learning with N target data. In addition, we show that finetuning, even with only a small amount of target data, could drastically reduce the amount of source data required by pretraining. Our theory sheds light on the effectiveness and limitation of pretraining as well as the benefits of finetuning for tackling covariate shift problems.
AB - We study linear regression under covariate shift, where the marginal distribution over the input covariates differs in the source and the target domains, while the conditional distribution of the output given the input covariates is similar across the two domains. We investigate a transfer learning approach with pretraining on the source data and finetuning based on the target data (both conducted by online SGD) for this problem. We establish sharp instance-dependent excess risk upper and lower bounds for this approach. Our bounds suggest that for a large class of linear regression instances, transfer learning with O(N2) source data (and scarce or no target data) is as effective as supervised learning with N target data. In addition, we show that finetuning, even with only a small amount of target data, could drastically reduce the amount of source data required by pretraining. Our theory sheds light on the effectiveness and limitation of pretraining as well as the benefits of finetuning for tackling covariate shift problems.
UR - https://www.scopus.com/pages/publications/85148274486
M3 - Conference contribution
AN - SCOPUS:85148274486
T3 - Advances in Neural Information Processing Systems
BT - Advances in Neural Information Processing Systems 35 - 36th Conference on Neural Information Processing Systems, NeurIPS 2022
A2 - Koyejo, S.
A2 - Mohamed, S.
A2 - Agarwal, A.
A2 - Belgrave, D.
A2 - Cho, K.
A2 - Oh, A.
PB - Neural information processing systems foundation
T2 - 36th Conference on Neural Information Processing Systems, NeurIPS 2022
Y2 - 28 November 2022 through 9 December 2022
ER -