A Stochastic Control Approach to Variable Length Menus in P300 Neural Communication Prostheses

Julian A. Jarzebowski, UIUC; Lakshminarayan Srinivasan, Corrosion Sensors, LLC; Todd P. Coleman, UIUC

The P300 neural communication prosthesis allows an individual to type words from an on-screen menu by recording visually evoked potentials related to the user’s intention. Typing rates are affected in part by two sources of uncertainty: (a) noise in the P300 signal, and (b) statistical language structure. Early system designs focused on classification to address P300 noise. More recently, word completion has been applied to exploit statistical language structure. In general, the time to specify a menu option is proportional to menu size. However, previous approaches employ fixed menu size, independent of P300 noise or statistical language structure. Here we propose developing statistical models of the two sources of uncertainty and applying dynamic programming and stochastic control theory for the principled design of variable-length menus based upon these models.

The basic idea behind our setup is perhaps best illustrated by an example. If the characters “t,h” have already been conveyed, then it is a whole lot more likely that a vowel will appear next as compared to a consonant. So rather than displaying a menu with 26 possibilities (which will require 26 time units before decoding), we could instead display a menu with 6 possibilities: the five vowels as well as an “other” character - with the treatment of “other” being selected leads to another menu appearing. On average, by showing the more likely characters in menus of shorter length, a better resulting time to convey a desired character ensues. Finding the optimal policy to display menus, given previously conveyed characters, can be cast in terms of “dynamic programming” or “stochastic control”.

We illustrate how the optimal policy of this dynamic programming problem satisfies a menu depth to character probability relation analogous to that of the Huffman code in data compression and information theory. By exploiting this optimality property, we illustrate how the state space of the stochastic control problem can be greatly diminished (from exponential growth to linear growth), and we exhibit optimal policies for a probabilistic models pertaining to the statistical structure of the English language.

Through this methodology, we plan to explore a completely new, principled, mathematical formulation of the P300 communication prosthesis problem that couples a quantitative characterization of the brain with a novel application of stochastic control theory that ultimately demonstrates faster, more accurate communication prostheses for individuals with related deficits in neural or muscular function.