A quantitative comparison of linear and non-linear models of motor cortical activity for the encoding and decoding of arm motions

Many models have been proposed for the motor cortical encoding of arm motion. In particular, recent work has shown that simple linear models can be used to approximate the firing rates of a population of cells in primary motor cortex as a function of the position, velocity, and acceleration of the hand. Here we perform a systematic study of these linear models and of various non-linear generalizations. Specifically we consider linear Gaussian models, Generalized Linear Models (GLM), and Generalized Additive Models (GAM) of neural encoding. We evaluate their ability to represent the relationship between hand motion and neural activity, by looking at the likelihood of observed patterns of neural firing in a test data set and by evaluating the decoding performance of the different models (i.e. in terms of the error in reconstructing hand position from firing rates). To provide a level playing field for evaluating the decoding performance, we test all the models using a general recursive Bayesian estimator known as the particle filter, thus isolating the effect of the encoding model on reconstruction accuracy.