  There has been tremendous interest in designing stimuli (e.g. electrical
currents) that produce desired neural responses, e.g., for inducing therapeutic
effects for treatments. Traditionally, the design of such stimuli has been
model-driven. Due to challenges inherent in modeling neural responses
accurately, data-driven approaches offer an attractive alternative. The problem
of data-driven stimulus design can be thought of as estimating an inverse of a
non-linear ``forward" mapping, which takes in as inputs the stimulus parameters
and outputs the corresponding neural responses. In most cases of interest, the
forward mapping is many-to-one, and hence difficult to invert using traditional
methods. Existing methods estimate the inverse by using conditional density
estimation methods or numerically inverting an estimated forward mapping, but
both approaches tend to perform poorly at small sample sizes. In this work, we
develop a new optimization framework called PATHFINDER, which allows us to use
regression methods for estimating an inverse mapping. We use toy examples to
illustrate key aspects of PATHFINDER, and show, on computational models of
biological neurons, that PATHFINDER can outperform existing methods at small
sample sizes. The data-efficiency of PATHFINDER is especially valuable in
stimulus design as collecting data is expensive in this domain.
