title: Searching for collective behavior in a large network of sensory neurons.
abstract: Maximum entropy models are the least structured probability distributions that exactly reproduce a chosen set of statistics measured in an interacting network. Here we use this principle to construct probabilistic models which describe the correlated spiking activity of populations of up to 120 neurons in the salamander retina as it responds to natural movies. Already in groups as small as 10 neurons, interactions between spikes can no longer be regarded as small perturbations in an otherwise independent system; for 40 or more neurons pairwise interactions need to be supplemented by a global interaction that controls the distribution of synchrony in the population. Here we show that such "K-pairwise" models--being systematic extensions of the previously used pairwise Ising models--provide an excellent account of the data. We explore the properties of the neural vocabulary by: 1) estimating its entropy, which constrains the population's capacity to represent visual information; 2) classifying activity patterns into a small set of metastable collective modes; 3) showing that the neural codeword ensembles are extremely inhomogenous; 4) demonstrating that the state of individual neurons is highly predictable from the rest of the population, allowing the capacity for error correction.
authors.affiliation: Institute of Science and Technology Austria, Klosterneuburg, Austria.
authors.forename: Gašper
authors.initials: G
authors.lastname: Tkačik
authors.affiliation: Institut de la Vision, INSERM U968, UPMC, CNRS U7210, CHNO Quinze-Vingts, Paris, France ; Department of Molecular Biology, Princeton Neuroscience Institute, Princeton University, Princeton, New Jersey, United States of America.
authors.forename: Olivier
authors.initials: O
authors.lastname: Marre
authors.affiliation: Department of Molecular Biology, Princeton Neuroscience Institute, Princeton University, Princeton, New Jersey, United States of America ; Joseph Henry Laboratories of Physics, Princeton University, Princeton, New Jersey, United States of America.
authors.forename: Dario
authors.initials: D
authors.lastname: Amodei
authors.affiliation: Department of Neurobiology, Weizmann Institute of Science, Rehovot, Israel.
authors.forename: Elad
authors.initials: E
authors.lastname: Schneidman
authors.affiliation: Joseph Henry Laboratories of Physics, Princeton University, Princeton, New Jersey, United States of America ; Lewis-Sigler Institute for Integrative Genomics, Princeton University, Princeton, New Jersey, United States of America.
authors.forename: William
authors.initials: W
authors.lastname: Bialek
authors.affiliation: Department of Molecular Biology, Princeton Neuroscience Institute, Princeton University, Princeton, New Jersey, United States of America.
authors.forename: Michael J
authors.initials: MJ
authors.lastname: Berry
mesh_terms: D000200:Action Potentials / Q000502:physiology; D000818:Animals; D019295:Computational Biology; D019277:Entropy; D005399:Fishes; D008959:Models, Neurological; D009068:Movement; D009415:Nerve Net / Q000502:physiology; D011336:Probability; D012160:Retina / Q000473:pathology*; D011984:Sensory Receptor Cells / Q000166:cytology*; D014562:Caudata / Q000502:physiology*