Clinical Effects and Safety of Radiofrequency Microneedling for the Management of Melasma: A Retrospective Study.

High-dimensional parameter estimation methods have gained increasing attention due to their wide application in areas including bioinformatics, astronomy, and information technology (). With the dimension of unknown parameters being much larger than the sample size, the parameter estimation becomes much more challenging due to issues of error accumulation (). Nonetheless, existing methods primarily rely on independent and identically distributed (i.i.d.) data. In many scenarios, obtaining such high-dimensional i.i.d. data is costly or infeasible, posing challenges to accurate parameter estimation and reliable decision-making. Transfer learning is a promising framework that can improve the parameter estimation accuracy for the above low-data setting by incorporating side information from auxiliary source samples (). Specifically, this paper considers a parameter transfer setting, where we are given a target sample drawn from a target distribution parameterized by a high-dimensional target parameter , along with some auxiliary samples drawn from different source distributions parameterized by . The goal is to improve the estimation accuracy of the target parameter by incorporating from other source samples (). We consider a challenging scenario where the similarity between the source and target is completely captured through the closeness of and , with minimal additional structural similarity assumptions among the data distributions. Such a flexible setup encapsulates various types of distribution shifts of practical interests. For example, in a regression setting, it includes shifts in the marginal covariate distributions (). In high-dimensional scenarios, such a covariate shift can be more severe due to a more complex covariate correlation structure (; ). Besides covariate shifts, the distribution shifts may also come from the shift in the conditional distribution of the responses. For example, in genomic studies, some source data may suffer from overdispersion due to a higher-than-expected variance (). In the presence of distribution shifts, naively incorporating source samples can lead to estimation accuracy that is worse than using the target sample alone–a phenomenon known as “negative transfer” (). The challenge calls for the design of a high-dimensional parameter transfer procedure that can effectively exploit parameter similarity under these distribution shifts and can always prevent negative transfer. Beyond challenges brought by distribution shifts, another challenge that often arises in transfer learning is the distributed nature of source samples. For example, for electronic health record data analysis in multicenter research studies, source samples are collected from different institutes or organizations, where direct data sharing is often impractical due to privacy and regulation constraints or the prohibitive communication cost (). This necessitates the development of privacy-preserving and communication-efficient solutions that can achieve comparable estimation accuracy as their centralized counterparts.