  System identification techniques -- projection pursuit regression models
(PPRs) and convolutional neural networks (CNNs) -- provide state-of-the-art
performance in predicting visual cortical neurons' responses to arbitrary input
stimuli. However, the constituent kernels recovered by these methods are often
noisy and lack coherent structure, making it difficult to understand the
underlying component features of a neuron's receptive field.
  In this paper, we show that using a dictionary of diverse kernels with
complex shapes learned from natural scenes based on efficient coding theory, as
the front-end for PPRs and CNNs can improve their performance in neuronal
response prediction as well as algorithmic data efficiency and convergence
speed. Extensive experimental results also indicate that these sparse-code
kernels provide important information on the component features of a neuron's
receptive field. In addition, we find that models with the complex-shaped
sparse code front-end are significantly better than models with a standard
orientation-selective Gabor filter front-end for modeling V1 neurons that have
been found to exhibit complex pattern selectivity. We show that the relative
performance difference due to these two front-ends can be used to produce a
sensitive metric for detecting complex selectivity in V1 neurons.
