Learning Thought-Based Motor Control using Gaussian Processes

Transcript

1. Learning Thought-Based Motor Control using Gaussian Processes Safwan Choudhury - SYDE 422 Project
2. Background •Machine learning in brain-computer interface (BCI) applications •Controlling Wheelchair Motion with Electroencephalography (EEG) •Traditional approaches for wheelchair and mobile robot control via EEG
3. EEG Interface •Emotiv EPOC (Research Edition) headset from Sydney, Australia •Comes with training interface and a proprietary machine learning algorithm •Raw EEG data collection from 14 electrodes into Matlab via EEGLAB •The noise problem
4. Project Goals • Improve classification accuracy of thought-based motor commands - Forward, Backward, Turn Left, Turn Right & Neutral • Embed external sensory information in decision-making - Head orientation from gyroscope readings - Speed sensor readings from optical encoders • Supervised learning with a reasonably small training datasets - User should not have to provide 1000 examples of one action
5. Gaussian Processes • A Gaussian Process (GP) is a collection of random variables, any finite number of which have a joint Gaussian distribution. • Completely specified by its mean and covariance functions: • Mathematically, a Gaussian Process is expressed by the following notation: µ(x) = E[ f (x)] ∑(x,x') = E[( f (x) − µ(x))( f (x') − µ(x'))] f (x) ~ GP(µ(x),∑(x,x'))
6. Gaussian Processes • One of several machine learning approaches which use kernel methods - Others include Support Vector Machines (SVM), Linear Discriminant Analysis (LDA), Principle Component Analysis (PCA), etc. • Can be used for regression and classification applications. - In this project, GPs are used to learn classification of motor movements (i.e. forward/backward) from EEG signals • Novelty: Exploiting the probabilistic output of GP classification - We can use the uncertainty in the predictions from GP coupled with other sensory information to improve decision making.
7. Simple Example • Very simple supervised learning example where input-output mapping is learned from training data using GP. • 1-D example illustrating the use of GP in regression - Assumption: Mean function centered at zero initially • 2-D example illustrating the use of GP in binary classification - Assumption: Use of logistic function for “squashing”
8. Example: Samples from Prior
9. Example: Samples from Posterior
10. Example: Binary Classification Training Data
11. Example: Squashing with Response Function λ(z) = 1 1+ exp(−z)
12. Example: Binary Classification Decision Boundaries
13. Covariance Function • The properties of the sample functions are controlled by the choice of covariance function and its parameters. - Squared-Exponential Covariance Function: • The variables l, Мf and Мn are known as the hyperparameters ∑(x,x') = σ f 2 exp − 1 2l2 (x − x')2 ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ + σ2 n δ xx '
14. Progress & Implementation • 14 simultaneous input signals from electrodes on Emotiv EPOC headset - AF3, F7, F3, FC5, T7, P7, O1, O2, PB, TB, FC6, F4, F8, AF4 • Using Gaussian Processes for Machine Learning (GPML) toolbox - Available at http://www.gaussianprocess.org by Rasmussen et al. • Almost have binary classification working for neutral/forward with decision algorithm for incorporating gyroscopic data. - Key challenges: picking appropriate covariance function and hyperparameters to yield “decent” results.
15. Questions?