We present a novel analytical approach for studying neural encoding. As a first step we model a neural sensory system as a communication channel. Using the method of typical sequence in this context, we show that a coding scheme is an almost bijective relation between equivalence classes of stimulus/response pairs. The analysis allows a quantitative determination of the type of information encoded in neural activity patterns and, at the same time, identification of the code with which that information is represented. Due to the high dimensionality of the sets involved, such a relation is extremely difficult to quantify. To circumvent this problem, and to use whatever limited data set is available most efficiently, we use another technique from information theory— quantization. We quantize the neural responses to a reproduction set of small finite size. Amongmany possible quantizations, we choose one which preserves as much of the informativeness of the original stimulus/response relation as possible, through the use of an information-based distortion function. This method allows us to study coarse but highly informative approximations of a coding scheme model, and then to refine them automatically when more data become available.

A central goal of robotics and AI is to be able to deploy an agent to act autonomously in the real world over an extended period of time. It is commonly asserted that in order to do so, the agent must be able to learn to deal with unexpected environmental conditions. However an ability to learn is not sufficient. For true extended autonomy, an agent must also be able to recognize when to abandon its current model in favor of learning a new one; and how to learn in its current situation. This paper presents a fully implemented example of such autonomy in the context of color map learning on a vision-based mobile robot for the purpose of image segmentation. Past research established the ability of a robot to learn a color map in a single fixed lighting condition when manually given a “curriculum, ” an action sequence designed to facilitate learning. This paper introduces algorithms that enable a robot to i) devise its own curriculum; and ii) recognize when the lighting conditions have changed sufficiently to warrant learning a new color map. 1

We define a new distance measure the resistor-average distance between two probability distributions that is closely related to the Kullback-Leibler distance. While the KullbackLeibler distance is asymmetric in the two distributions, the resistor-average distance is not. It arises from geometric considerations similar to those used to derive the Chernoff distance. Determining its relation to well-known distance measures reveals a new way to depict how commonly used distance measures relate to each other. 1 Introduction The Kullback-Leibler distance [15, 16] is perhaps the most frequently used information-theoretic "distance" measure from a viewpoint of theory. If p 0 , p 1 are two probability densities, the KullbackLeibler distance is defined to be D(p 1 #p 0 )= # p 1 (x)log p 1 (x) p 0 (x) dx . (1) In this paper, log() has base two. The Kullback-Leibler distance is but one example of the AliSilvey class of information-theoretic distance measures [1], which are defined to ...

this article that the choice of a variability model has a major, nontrivial impact on the encoding properties of the neural population. The immense variability of individual response parameters, such as tuning widths or correlation coef#cients, has also been neglected in most previous work. Although these parameter variations are always found in empirical data, they were considered functionally insignificant, and hence theoretical studies have almost always assumed uniform parameters throughout the population. We will show here that this uniform case is unfavorable in the sense that the introduction of parameter variability improves the encoding performance

Neural spike train decoding algorithms and techniques to compute Shannon mutual information are important methods for analyzing how neural systems represent biological signals.Decoding algorithms are also one of several strategies being used to design controls for brain-machine interfaces. Developing optimal strategies to desig n decoding algorithms and compute mutual information are therefore important problems in computational neuroscience. We present a general recursive Žlter decoding algorithm based on a point process model of individual neuron spiking activity and a linear stochastic state-space model of the biological signal. We derive from the algorithm new instantaneous estimates of the entropy, entropy rate, and the mutual information between the signal and the ensemble spiking activity. We assess the accuracy of the algorithm by computing, along with the decoding error, the true coverage probability of the approximate 0.95 conŽdence regions for the individual signal estimates. We illustrate the new algorithm by reanalyzing the position and ensemble neural spiking activity of CA1 hippocampal neurons from two rats foraging in an open circular environment. We compare the performance of this algorithm with a linear Žlter constructed by the widely used reverse correlation method. The median decoding error for Animal 1 (2) during 10 minutes of open foraging was 5.9 (5.5) cm, the median entropy was 6.9 (7.0) bits, the median information was 9.4 (9.4) bits, and the true coverage probability for 0.95 conŽdence regions was 0.67 (0.75) using 34 (32) neurons. These Žndings improve signiŽcantly on our previous results and suggest an integrated approach to dynamically reading neural codes, measuring their properties, and quantifying the accuracy with which encoded information is extracted.

Abstract An important problem in processing large data streams is detecting changes in the underly-ing distribution that generates the data. The challenge in designing change detection schemes is making them general, scalable, and statistically sound. In this paper, we take a general,information-theoretic approach to the change detection problem, which works for multidimensional as well as categorical data. We use relative entropy, also called the Kullback-Leiblerdistance, to measure the difference between two given distributions. The KL-distance is known to be related to the optimal error in determining whether the two distributions are the sameand draws on fundamental results in hypothesis testing. The KL-distance also generalizes traditional distance measures in statistics, and has invariance properties that make it ideally suitedfor comparing distributions. Our scheme is general; it is nonparametric and requires no assumptions on the underlyingdistributions. It employs a statistical inference procedure based on the theory of bootstrapping, which allows us to determine whether our measurements are statistically significant. The schemeis also quite flexible from a practical perspective; it can be implemented using any spatial partitioning scheme that scales well with dimensionality. In addition to providing change detections,our method generalizes Kulldorff's spatial scan statistic, allowing us to quantitatively identify specific regions in space where large changes have occurred.We provide a detailed experimental study that demonstrates the generality and efficiency of our approach with different kinds of multidimensional datasets, both synthetic and real. 1 Introduction We are collecting and storing data in unprecedented quantities and varieties--streams, images, audio, text, metadata descriptions, and even simple numbers. Over time, these data streams change as the underlying processes that generate them change. Some changes are spurious and pertain to glitches in the data. Some are genuine, caused by changes in the underlying distributions. Some changes are gradual and some are more precipitous. We would like to detect changes in a variety of settings:

Information processing theory endeavors to quantify how well signals encode information and how well systems, by acting on signals, process information. We use information-theoretic distance measures, the Kullback-Leibler distance in particular, to quantify how well signals represent information. The ratio of distances between a system's output and input quantifies the system's information processing properties.

We present a simple but general model for feature-based information processing with selective attention. We model feature extraction as projections onto frames of subspaces, which accounts for redundancies in the representations of individual features as well as between features. To manage limited resources, we use feedback attentional signals to dynamically allocate system resources according to the observed events. In our model, attention maximizes the average information retained about all events weighted by their relative priorities. We illustrate the model with a simple system under a total bit constraint and discuss how the organization of the feature extraction affects the optimal bit allocation. 1.

A method for divergence estimation between multidimensional distributions based on nearest neighbor distances is proposed. Given i.i.d. samples, both the bias and the variance of this estimator are proven to vanish as sample sizes go to infinity. In experiments on high-dimensional data, the nearest neighbor approach generally exhibits faster convergence compared to previous algorithms based on partitioning.

Researchers studying neural coding have speculated that populations of neurons would more effectively represent the stimulus if the neurons "cooperated:" by interacting through lateral connections, the neurons would process and represent information better than if they functioned independently. We apply our