neural decision boundaries for maximal information transmission神经决定边界最大信息传输.pdfVIP

Neural Decision Boundaries for Maximal Information Transmission 1 2 Tatyana Sharpee *, William Bialek 1 Crick-Jacobs Center for Theoretical Biology and Laboratory of Computational Neurobiology, The Salk Institute for Biological Studies, La Jolla, California, United States of America, 2 Joseph Henry Laboratories of Physics, Lewis–Sigler Institute for Integrative Genomics, The Princeton Center for Theoretical Physics, Princeton University, Princeton, New Jersey, United States of America We consider here how to separate multidimensional signals into two categories, such that the binary decision transmits the maximum possible information about those signals. Our motivation comes from the nervous system, where neurons process multidimensional signals into a binary sequence of responses (spikes). In a small noise limit, we derive a general equation for the decision boundary that locally relates its curvature to the probability distribution of inputs. We show that for Gaussian inputs the optimal boundaries are planar, but for non–Gaussian inputs the curvature is nonzero. As an example, we consider exponentially distributed inputs, which are known to approximate a variety of signals from natural environment. Citation: Sharpee T, Bialek W (2007) Neural Decision Boundaries for Maximal Information Transmission. PLoS ONE 2(7): e646. doi:10.1371/ journal.pone.0000646 INTRODUCTION single neurons, and ask simply how much information the binary What we know about the world around us is represented in the spike/no spike decision conveys about the input signal. Let this nervous system by sequences of discrete electrical pulses termed input signal be a vector r in a space of d dimensions and let the action potentials or ‘‘spikes’’ [1]. One attractive