  A central goal of neuroscience is to understand how activity in the nervous
system is related to features of the external world, or to features of the
nervous system itself. A common approach is to model neural responses as a
weighted combination of external features, or vice versa. The structure of the
model weights can provide insight into neural representations. Often, neural
input-output relationships are sparse, with only a few inputs contributing to
the output. In part to account for such sparsity, structured regularizers are
incorporated into model fitting optimization. However, by imposing priors,
structured regularizers can make it difficult to interpret learned model
parameters. Here, we investigate a simple, minimally structured model
estimation method for accurate, unbiased estimation of sparse models based on
Bootstrapped Adaptive Threshold Selection followed by ordinary least-squares
refitting (BoATS). Through extensive numerical investigations, we show that
this method often performs favorably compared to L1 and L2 regularizers. In
particular, for a variety of model distributions and noise levels, BoATS more
accurately recovers the parameters of sparse models, leading to more
parsimonious explanations of outputs. Finally, we apply this method to the task
of decoding human speech production from ECoG recordings.
