  When pre-processing observational data via matching, we seek to approximate
each unit with maximally similar peers that had an alternative treatment
status--essentially replicating a randomized block design. However, as one
considers a growing number of continuous features, a curse of dimensionality
applies making asymptotically valid inference impossible (Abadie and Imbens,
2006). The alternative of ignoring plausibly relevant features is certainly no
better, and the resulting trade-off substantially limits the application of
matching methods to "wide" datasets. Instead, Li and Fu (2017) recasts the
problem of matching in a metric learning framework that maps features to a
low-dimensional space that facilitates "closer matches" while still capturing
important aspects of unit-level heterogeneity. However, that method lacks key
theoretical guarantees and can produce inconsistent estimates in cases of
heterogeneous treatment effects. Motivated by straightforward extension of
existing results in the matching literature, we present alternative techniques
that learn latent matching features through either MLPs or through siamese
neural networks trained on a carefully selected loss function. We benchmark the
resulting alternative methods in simulations as well as against two
experimental data sets--including the canonical NSW worker training program
data set--and find superior performance of the neural-net-based methods.
