CNS*2006 Workshop on
Methods of Information Theory in Computational Neuroscience
Thursday, June 20, 2006
Methods originally developed in Information Theory have found wide applicability in
computational neuroscience. Beyond these original methods there is a need to
develop novel tools and approaches that are driven by problems arising in neuroscience.
A number of researchers in computational/systems neuroscience and in information/communication theory are investigating problems of information representation and processing. While the goals are often the same, these researchers bring different perspectives and points of view to a common set of neuroscience problems. Often they participate in different fora and their interaction is limited.
The goal of the workshop is to bring some of these researchers together to discuss challenges posed by neuroscience and to exchange ideas and present their latest work.
The workshop is targeted towards computational and systems neuroscientists with interest in methods of information theory as well as information/communication theorists with interest in neuroscience.
Aurel A. Lazar, Department of Electrical Engineering, Columbia University
Alex Dimitrov, Center for Computational Biology, Montana State University.
Thursday, June 20, 2006 (8:45 AM - 5:00 PM)
Morning Session (8:45 AM - 12:00 noon)
Entropy Models, Rate Distortion Measures & Design of Experiments
Chair: A.A. Lazar
8:45 AM - 9:30 AM
Information Theory and Neuroscience
Don H. Johnson and Christopher J. Rozell, Department of Electrical Engineering, Rice University.
When Shannon developed information theory, he envisioned a systematic way to determine how much "information" could be transmitted over an arbitrary communications channel. While this classic work embraces many of the key aspects of neural communication (e.g., stochastic stimuli and communication signals, multiple-neuron populations, etc.), there are difficulties in applying his concepts meaningfully to neuroscience applications. We describe the classic information theoretic quantities---entropy, mutual information, and capacity---and how they can be used to assess the ultimate fidelity of the neural stimulus representation. We also discuss some of the problems that accompany using and interpreting these quantities in a neuroscience context. We also present an overview of post-Shannon research areas that leverage his work in rate-distortion theory that are extremely relevant to neuroscientists looking to understand the neural code. The presentation is meant to be mostly tutorial in nature, setting the stage for other workshop presentations.
9:30 AM - 10:00 AM
Lossy Compression in Neural Sensory Systems: At what Cost (Function)?
Alex Dimitrov, Center for Computational Biology, Montana State University.
Biological sensory systems, and more so individual neurons, do not represent external stimuli exactly. This obvious statement is a consequence of the almost infinite richness of the sensory world compared to the relative paucity of neural resources that are used to represent it. Even if the intrinsic uncertainty present in all biological systems is disregarded, there will always be a many-to-one representation of whole regions of sensory space by indistinguishable neural responses. When noise is included, the representation is many-to-many. One direction of research in sensory neuroscience, espoused by us and others, is to identify and model such regions, with the goal of eventually completely describing neural sensory function as the partitioning of sensory space into distinguishable regions, associated to different response states of a sensory system. In essence, our goal is to quantify the distortion function of a particular biological system. In pursuing this agenda, the vastness of sensory space imposes a certain style of analysis that explicitly addresses the problem ensuing from the availability of relatively small datasets with which to provide description of relatively large sensory regions. We report our progress in this direction.
10:00 AM - 10:30 AM
I'll present an exact Bayesian treatment of a simple, yet sufficiently general probability distribution model, constructed by considering piecewise constant distributions P(X) with uniform (2nd order) prior over location of discontinuity points and assigned chances. The predictive distribution and the model complexity can be determined completely from the data in a computational time that is linear in the number of degrees of freedom and quadratic in the number of possible values of X. Furthermore, exact values of the expectations of entropies and their variances can be computed with polynomial effort. The expectation of the mutual information becomes thus available, too, and a strict upper bound on its variance. The resulting algorithm is particularly useful in experimental research areas where the number of available samples is severely limited (e.g. neurophysiology).
10:30 AM - 11:00 AM
11:00 AM - 11:30 AM
One of our main goals in life is to dream up distributions that do a good job approximating neural data. One natural class of distributions are maximum entropy ones, a class with a great deal of aesthetic appeal. Before applying these to real data, however, it would be nice to develop an understanding of their properties. This, however, is hard, mainly because for most correlated distributions even sampling is intractable, let alone doing anything analytic (the obvious exception, Gaussians, rarely occur in real life, something that is especially true for neural data). Fortunately, there's at least one correlated distribution for which we can calculate many things analytically; that model is what we investigate here. Our goal is twofold. First, we simply want to develop intuition for maximum entropy models. Second, we want to understand something about estimating these models from data, in particular whether results we get from a reasonably small number of neurons, say around 10, provide us with any information about what's happening when the number of neurons is large, on the order of 1000s or more.
11:30 AM - 12:00 PM
Real-time Adaptive Information-theoretic Optimization of Neurophysiological Experiments
Jeremy Lewi, Robert Butera, and Liam Paninski, Department of Statistics, Columbia University.
Adaptive optimal experimental design is a promising idea for minimizing the number of trials needed to characterize a neuron's response properties in the form of a parametric statistical encoding model. However, this potential has been limited to date by severe computational challenges: to find the stimulus which will provide the most information about the (typically high-dimensional) model parameters, we must perform a high-dimensional integration and optimization in near-real time. Here we develop a fast algorithm, based on a Fisher approximation of the Shannon information and specialized numerical linear algebra techniques, to compute this optimal (most informative) stimulus. This algorithm requires only a one-dimensional linesearch, and is therefore efficient even for high-dimensional stimulus and parameter spaces; for example, we require just 10 milliseconds on a desktop computer to optimize a 100-dimensional stimulus, making real-time adaptive experimental design feasible. Simulation results show that model parameters can be estimated much more efficiently using these adaptive techniques than by using random (nonadaptive) stimuli. Finally, we generalize the algorithm to efficiently handle both fast adaptation due to spike-history effects and slow, non-systematic drifts in the model parameters.
12:00 PM - 2:00 PM
Afternoon Session (2:00 PM - 5:00 PM)
Information Representation, Processing and Decoding
Chair: A. Dimitrov
2:00 PM - 2:30 PM
Some Interrelationship between Information,
Information Processing, and Energy
William B. Levy, Laboratory for Systems Neurodynamics, University of Virginia.
The talk will consider the development of quantitative predictions that arise when communication and information processing are constrained by efficient use of metabolic energy. Computation in brain is adiabatic. Information processing and communication use currents powered by ion gradients. Then, the Na-K ATPase pump expends metabolic energy to maintain these ion gradients via an unmixing process. Both ends of the process (computation and pumping) are essentially frictionless. The heat generated by brain comes from the inefficient conversion of glucose into ATP. Several ways that energy is used in brain can be surprising, particularly when compared to energy use in manufactured computers and communication equipment. Some examples will be discussed.
Attwell, D. & Gibb, A. Neurosci. 6, 2005, 841-849; Attwell, D. & Laughlin, S. B. J. Cerebral Blood Flow and Metabolism 21, 2001, 1133-1145;
Crotty. P., Sangrey, T., & Levy, W. B J Neurophysiol, in press, 2006; Levy, W. B & Baxter, R. A. Neural Comp. 8, 1996, 531-543;
Levy, W. B & Baxter, R. A. J. Neurosci. 22, 2002, 4746-4755; Levy, W. B, Crotty, P., Sangrey, T., & Friesen, O. J. Neurophysiol. 2006, in press; Sangrey, T. and Levy, W. B Neurocomputing 65-66, 2005, 907-913.
2:30 PM - 3:00 PM
Information Representation with an Ensemble of Hodgkin-Huxley Neurons
Aurel A. Lazar, Department of Electrical Engineering, Columbia University.
Information repesentation in Communications and Information Theory is based on the classical sampling theorem. A continuous-time bandlimited signal is represented by a sequence of equidistant signal samples. The signal can be perfectly recovered if the samples are taken at a rate higher than or equal to the Nyquist rate. A clock is needed for sampling, however. How can stimuli be represented in neural systems given the absence of an ubiquitous clock? Motivated by the natural representation of stimuli in sensory systems, we review the representation of bandlimited stimuli with integrate-and-fire neurons. As in the case of classical sampling, perfect recovery of a bandlimited stimulus from the spike sequence generated by an IAF neuron can be achieved provided that the average spike rate is greater than the Nyquist rate. We extend these results to stimuli encoded with a Hodgkin-Huxley neuron and describe a general algorithm for recovering the stimulus at the input of a neuronal ensemble.
3:00 PM - 3:30 PM
Decoding Spike Times without Knowing the Stimulus Time
Stefano Panzeri, Faculty of Life Sciences, University of Manchester.
In most studies of neural coding one considers whether regsitering the spike times with a fine temporal precision increases the information available about the external stimulus. However, most studies do not consider whether the information contained in precise spike times can be decoded by another neural system which, unlike the experimenter, does not have a precise knowledge of the stimulus time. In this talk we introduce in detail a class of information-theoretic metrics that can at the same time quantify how much information is encoded by precise spike times, and how much of this information can be decoded by a downstream system that has only a limited knowledge of the stimulus time. We discuss potential applications to experimental studies of neural coding, as well as directions for our future mathematical research on the issue. This is joint work with my long term collaborators Mathew Diamond (SISSA) and Ehsan Arabzadeh (Sidney University).
3:30 PM - 4:00 PM
4:00 PM - 4:30 PM
Correlations, Synergy and Coding in the Cortex: an Old Dogma
Learns New Tricks
Simon R. Schultz, Department of Bioengineering, Imperial College.
Recent results from a number of groups have revealed the "correlation = 0.2 in the cortex" dogma to be an over-simplification: with carefully constructed stimuli, inter-neuronal synchronization can depend upon stimulus properties in interesting ways. We have been using Information Theory to study the effect of this stimulus- dependent synchronization on the neural coding of orientation and contrast in V1. We analysed pairs of simultaneously recorded neurons in the macaque primary visual cortex, whose receptive fields were carefully mapped and co-stimulated. Direction coding showed weak synergistic effects at short timescales, trailing off to informational independence at long timescales. An information component analysis revealed that this was due to a balance of a synergistic contribution due to the stimulus-dependence of synchronization, with redundancy due to the overlap of tuning. In comparison, contrast coding was dominated by redundancy due to the similarity in contrast tuning curves and showed a weak synergy at only very short time scales (< 5 ms). Stimulus dependence of synchronization does therefore have an effect on coding - and its effect is to pull the coding regime back towards informational independence, when redundancy would otherwise rule due to (the possibly inevitable) effects of correlations and tuning overlap. Work performed in collaboration with Fernando Montani, Adam Kohn and Matthew Smith.
4:30 PM - 5:00 PM