  We consider the problem of predicting eye movement goals from local field
potentials (LFP) recorded through a multielectrode array in the macaque
prefrontal cortex. The monkey is tasked with performing memory-guided saccades
to one of eight targets during which LFP activity is recorded and used to train
a decoder. Previous reports have mainly relied on the spectral amplitude of the
LFPs as a feature in the decoding step to limited success, while neglecting the
phase without proper theoretical justification. This paper formulates the
problem of decoding eye movement intentions in a statistically optimal
framework and uses Gaussian sequence modeling and Pinsker's theorem to generate
minimax-optimal estimates of the LFP signals which are later used as features
in the decoding step. The approach is shown to act as a low-pass filter and
each LFP in the feature space is represented via its complex Fourier
coefficients after appropriate shrinking such that higher frequency components
are attenuated; this way, the phase information inherently present in the LFP
signal is naturally embedded into the feature space. The proposed complex
spectrum-based decoder achieves prediction accuracy of up to $94\%$ at
superficial electrode depths near the surface of the prefrontal cortex, which
marks a significant performance improvement over conventional power
spectrum-based decoders.
