Transfer learning for piecewise-constant mean estimation: optimality, ℓ1 and ℓ0 penalization

SummaryWe study transfer learning for estimating piecewise-constant signals when source data, which may be relevant but disparate, are available in addition to target data. We first investigate transfer learning estimators that respectively employandpenalties for unisource data scenarios and then generalize these estimators to accommodate multisources. To further reduce estimation errors, especially when some sources significantly differ from the target, we introduce an informative source selection algorithm. We then examine these estimators with multisource selection and establish their minimax optimality. Unlike the common narrative in the transfer learning literature that the performance is enhanced through large source sample sizes, our approaches leverage higher observational frequencies and accommodate diverse frequencies across multiple sources. Our extensive numerical experiments show that the proposed transfer learning estimators significantly improve estimation performance compared to estimators that only use the target data.