Marginal Singularity, and the Benefits of Labels in Covariate-Shift

Understand

We present new minimax results that concisely capture the relative benefits of source and target labeled data, under covariate-shift.

• Namely, we show that the benefits of target labels are controlled by a transfer-exponent $\gamma$ that encodes how singular Q is locally w.r.t.
• P, and interestingly allows situations where transfer did not seem possible under previous insights.
• In fact, our new minimax analysis - in terms of $\gamma$ - reveals a continuum of regimes ranging from situations where target labels have little benefit, to regimes where target labels dramatically improve classification.