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In practice, training data is often not fully representative of a target population due to sampling bias.The goal is then to ’transfer’ relevant information from the training (a.k.a. source) data to the target population. How much information is in the source data about the target population? Would some amount of target data improve transfer? These questions depend crucially on 'the distance' between source and target populations, viewed as probability measures.
We will argue that traditional notions of 'distance' between measures can yield an over-pessimistic picture of transferability. Instead, we show that some new notions of 'relative dimension' between source and target (which we simply term 'transfer-exponents') capture a tight continuum from easy to hard transfer, and help identify optimal transfer procedures.
Finally, in the case of transfer from multiple sources, we will discuss a strong dichotomy between minimax and adaptive rates: no adaptive procedure exists that can achieve the same rates as minimax (oracle) procedures.
The talk is based on earlier work with Guillaume Martinet, and ongoing work with Steve Hanneke.
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