  One of the most effective approaches to improving the performance of a
machine learning model is to procure additional training data. A model owner
seeking relevant training data from a data owner needs to appraise the data
before acquiring it. However, without a formal agreement, the data owner does
not want to share data. The resulting Catch-22 prevents efficient data markets
from forming. This paper proposes adding a data appraisal stage that requires
no data sharing between data owners and model owners. Specifically, we use
multi-party computation to implement an appraisal function computed on private
data. The appraised value serves as a guide to facilitate data selection and
transaction. We propose an efficient data appraisal method based on forward
influence functions that approximates data value through its first-order loss
reduction on the current model. The method requires no additional
hyper-parameters or re-training. We show that in private, forward influence
functions provide an appealing trade-off between high quality appraisal and
required computation, in spite of label noise, class imbalance, and missing
data. Our work seeks to inspire an open market that incentivizes efficient,
equitable exchange of domain-specific training data.
