We consider a general framework for a human-computer interface whereby the human's knowledge is represented as a point in Euclidean space, the intention of the human is signaled to the computer over a noisy channel, and the computer queries the human in a manner that is amenable to human operation. With these constraints at hand, we demonstrate a class of systems that are nonetheless information-theoretically optimal in that the computer very rapidly hones in on the intent of the human. Much recent work on feedback information theory has been dedicated to the exploration of methods by which optimal feedback may be derived for the purpose of expediting the communication of a message point between an inanimate encoder and decoder. Our framework not only takes advantage of previous work to demonstrate its communication optimality from this perspective as well as from an information-theoretic perspective but also contributes two distinct advantages. First, our framework provides a simplified method based on optimal transport theory to generate optimal feedback signals between the computer and human in high dimension, while still preserving communication optimality. Second, our framework specifically lends itself to the integration of a human user by attempting to moderate the difficulty of the task presented to the user, while still preserving optimality. We demonstrate applications of our framework within the context of multi-agent brain-computer interfaces.

The posterior matching (PM) scheme is a mutual information maximizing scheme for efficiently communicating a message point in a continuum over a noisy channel with feedback. It was recently developed when the message point was on a subset of the real line, and we more recently have generalized the framework to arbitrary dimensions with the theory of optimal transport. Although the PM scheme is guaranteed to maximize mutual information, in some situations it is not reliable (e.g. the posterior distribution does not converge to a point mass). Here, we show that the PM scheme is reliable if and only if the nonlinear filter of a certain hidden Markov model achieves maximal accuracy. We show that ergodicity of a random process pertaining to the channel input process is necessary for PM reliability. Lastly, we show that joint ergodicity of random processes pertaining to inputs and outputs of the channel is a sufficient condition for reliability. The latter results leverages optimal transport properties (invertibility) of the encoder map.

In this paper, we consider many problems in Bayesian inference - from drawing samples to posteriors, to calculating confidence intervals, to implementing posterior matching algorithms, by finding maps that push one distribution to another. We show that for a large class of problems (with log-concave likelihoods and log-concave priors), these problems can be efficiently solved using convex optimization. We provide example applications within the context of dynamic statistical signal processing.

This article presents a new approach to designing brain–computer interfaces (BCIs) that explicitly accounts for both the uncertainty of neural signals and the important role of sensory feedback. This approach views a BCI as the means by which users communicate intent to an external device and models intent as a string in an ordered symbolic language. This abstraction allows the problem of designing a BCI to be reformulated as the problem of designing a reliable communication protocol using tools from feedback information theory. Here, this protocol is given by a posterior matching scheme. This scheme is not only provably optimal but also easily understood and implemented by a human user. Experimental validation is provided by an interface for text entry and an interface for tracing smooth planar curves, where input is taken in each case from an electroencephalograph during left- and right-hand motor imagery.

We propose a new classification method, termed the Common Spatial Analytic Pattern, for brain-computer interfaces based on a simple EEG signal source and channel model. This blind source separation procedure recovers underlying source signals near the motor cortex which are indicative of motor imagery. A hidden Markov source model is applied to the evolution of the source signals and is used to estimate the type (left or right) of motor imagery performed by a subject. As a whole, the resulting asynchronous classifier offers significant improvement upon the current prevailing techniques in classification. Experiments show information transfer rates between subject and computer as high as 60.9 bits/minute.