# Minimax-optimal decoding of movement goals from local field potentials using complex spectral features

## TL;DR

This paper introduces a statistically optimal method for decoding eye movement goals from local field potentials by leveraging complex spectral features, significantly improving prediction accuracy over traditional power spectrum approaches.

## Contribution

It develops a minimax-optimal decoding framework using complex spectral features derived from Gaussian sequence modeling and Pinsker's theorem, incorporating phase information naturally.

## Key findings

- Achieves up to 94% prediction accuracy.
- Outperforms conventional power spectrum-based decoders.
- Provides a theoretical foundation for spectral feature extraction.

## Abstract

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.