1. Brain-Machine Interface (BMI) System Identification Siddharth Dangi and Suraj Gowda BMIs decode neural activity into control signals for prosthetic limbs Aim to improve quality of life for severely disabled patients suffering from neurological injuries and disease Restore a human’s ability to move and communicate with the world

3. “Center-Out” Training Task Monkey uses joystick to move a cursor to targets Record neural firing rates and cursor kinematic data Train decoding algorithm using collected data to predict cursor kinematics Switch cursor control from joystick to decoder

5. Echo-State Network (ESN) Problem – relationship between neural signals and limb kinematics is highly nonlinear Idea – create a large, recurrent neural network with random weights Can be used to learn the input-output behavior of a nonlinear system Training connections inside the reservoir is difficult and computationally expensive Use supervised learning to train only the output layer weights

7. Kalman Filter-based methods Adaptive Kalman filter – Allow parameters to auto-adjust – Stochastic gradient descent Standard model State prediction Kinematic state at time t Firing rates at time t Gaussian noise variables Combined Kalman-ESN method – Weight estimates based on error variances

9. LMS and Wiener Filter Wiener Filter – Rewrite model equation by tiling collected data: – Closed-form solution for weight matrix: Least-Mean Squares (LMS) – Gradient descent solution for weight matrix: Kinematic state at time n Firing rates at time n Error term at time n Filter weights Model:

11. Performance Results

13. Prediction Results Simulation Parameters Trained decoders for 100 seconds on training data Measured Mean-Squared Error (MSE) and Correlation Coefficient (CC) on 40 seconds of new data Prediction Method Position MSEVelocity MSEPosition CCVelocity CC LMS Filter0.20180.01820.8440.874 Wiener Filter0.17140.04390.7890.718 Echo-State Network 0.10430.02910.8410.745 Adaptive Kalman 0.08950.02540.9070.770 Standard Kalman Filter 0.05260.01800.9300.836 Combined Kalman-ESN 0.04640.01730.9320.842

15. Classification of Neural State Neuron firing rates signals can be treated as (behavior- driven) state-space trajectories Experiment – use logistic regression to classify trajectories into higher-level states (e.g., planning vs. not planning) Classes: Logistic Regression Model: Online Estimation Algorithm 93.1% classification accuracy All errors were “false alarm” before/after planning periods

17. Conclusions Ranking methods based on MSE of position predictions shows that: – “Pure” linear regression models (LMS and Wiener) need more training time to perform well – Kalman-based models that maintain a state-space/dynamics model perform better than those that don’t – Combination of linear (Kalman) and nonlinear (ESN) methods performs the best, and better than any single method alone