Brain machine interfaces (BMI) utilize linear or non-linear models to map the neural activity to the associated behavior which is typically the 2D or 3D hand position of a primate. Linear models are plagued by the massive disparity of the input and output dimensions thereby leading to poor generalization. A solution would be to use non-linear models like the recurrent multi-layer perceptron (RMLP) that provide parsimonious mapping functions with better generalization. However, this results in a drastic increase in the training complexity, which can be critical for practical use of a BMI. This paper bridges the gap between superior performance per trained weight and model learning complexity. Towards this end, we propose to use echo state networks (ESN) to transform the neuronal firing activity into a higher dimensional space and then derive an optimal sparse linear mapping in the transformed space to match the hand position. The sparse mapping is obtained using a weight constrained cost function whose optimal solution is determined using a stochastic gradient algorithm.