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

“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

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

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

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 nFiring rates at time n Error term at time n

Filter weights

Model:

Performance Results

Prediction ResultsSimulation Parameters• Trained decoders for 100 seconds on training data• Measured Mean-Squared Error (MSE) and Correlation Coefficient (CC) on 40

seconds of new dataPrediction Method

Position MSE Velocity MSE Position CC Velocity CC

LMS Filter 0.2018 0.0182 0.844 0.874

Wiener Filter 0.1714 0.0439 0.789 0.718

Echo-State Network

0.1043 0.0291 0.841 0.745

Adaptive Kalman

0.0895 0.0254 0.907 0.770

Standard Kalman Filter

0.0526 0.0180 0.930 0.836

Combined Kalman-ESN

0.0464 0.0173 0.932 0.842

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

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