{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,28]],"date-time":"2025-10-28T14:53:48Z","timestamp":1761663228984,"version":"build-2065373602"},"reference-count":51,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2014,4,22]],"date-time":"2014-04-22T00:00:00Z","timestamp":1398124800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>We propose a numerical method to learn maximum entropy (MaxEnt) distributions with spatio-temporal constraints from experimental spike trains. This is an extension of two papers, [10] and [4], which proposed the estimation of parameters where only spatial constraints were taken into account. The extension we propose allows one to properly handle memory effects in spike statistics, for large-sized neural networks.<\/jats:p>","DOI":"10.3390\/e16042244","type":"journal-article","created":{"date-parts":[[2014,4,22]],"date-time":"2014-04-22T12:18:37Z","timestamp":1398169117000},"page":"2244-2277","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":18,"title":["Parameter Estimation for Spatio-Temporal Maximum Entropy Distributions: Application to Neural Spike Trains"],"prefix":"10.3390","volume":"16","author":[{"given":"Hassan","family":"Nasser","sequence":"first","affiliation":[{"name":"INRIA, 2004 route de lucioles, 06560, Sophia-Antipolis, France"}]},{"given":"Bruno","family":"Cessac","sequence":"additional","affiliation":[{"name":"INRIA, 2004 route de lucioles, 06560, Sophia-Antipolis, France"}]}],"member":"1968","published-online":{"date-parts":[[2014,4,22]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Ferrea, E., Maccione, A., Medrihan, L., Nieus, T., Ghezzi, D., Baldelli, P., Benfenati, F., and Berdondini, L. (2012). Large-scale, high-resolution electrophysiological imaging of field potentials in brain slices with microelectronic multielectrode arrays. Front. Neural. Circ, 6.","DOI":"10.3389\/fncir.2012.00080"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"139","DOI":"10.1038\/nn.2731","article-title":"How advances in neural recording affect data analysis","volume":"14","author":"Stevenson","year":"2011","journal-title":"Nat. Neurosci"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"14859","DOI":"10.1523\/JNEUROSCI.0723-12.2012","article-title":"Mapping a Complete Neural Population in the Retina","volume":"43","author":"Marre","year":"2012","journal-title":"J. Neurosci"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"8699","DOI":"10.1523\/JNEUROSCI.0971-11.2011","article-title":"Quality Metrics to Accompany Spike Sorting of Extracellular Signals","volume":"31","author":"Hill","year":"2011","journal-title":"J. Neurosci"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"1434","DOI":"10.1109\/TNS.2004.832706","article-title":"What does the eye tell the brain?: Development of a system for the large scale recording of retinal output activity","volume":"51","author":"Litke","year":"2004","journal-title":"IEEE Trans. Nucl. Sci"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"1661","DOI":"10.1162\/089976604774201631","article-title":"Unsupervised spike detection and sorting with wavelets and superparamagnetic clustering","volume":"16","author":"Quiroga","year":"2004","journal-title":"Neural Comput"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"122","DOI":"10.1109\/TIT.1974.1055146","article-title":"On the computation of rate-distortion functions (Corresp.)","volume":"20","year":"1974","journal-title":"Inform. Theory, IEEE T on"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"620","DOI":"10.1103\/PhysRev.106.620","article-title":"Information theory and statistical mechanics","volume":"106","author":"Jaynes","year":"1957","journal-title":"Phys. Rev"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"1007","DOI":"10.1038\/nature04701","article-title":"Weak pairwise correlations imply strongly correlated network states in a neural population","volume":"440","author":"Schneidman","year":"2006","journal-title":"Nature"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"995","DOI":"10.1038\/nature07140","article-title":"Spatio-temporal correlations and visual signaling in a complete neuronal population","volume":"454","author":"Pillow","year":"2008","journal-title":"Nature"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"9679","DOI":"10.1073\/pnas.1019641108","article-title":"Sparse low-order interaction network underlies a highly correlated and learnable neural population code","volume":"108","author":"Ganmor","year":"2011","journal-title":"Proc. Natl. Acad. Sci. USA"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"3044","DOI":"10.1523\/JNEUROSCI.3682-10.2011","article-title":"The architecture of functional interaction networks in the retina","volume":"31","author":"Ganmor","year":"2011","journal-title":"J. Neurosci"},{"key":"ref_13","unstructured":"Tka\u010dik, G., Schneidman, E., Berry, M.J., and Bialek, W. (2009). Spin glass models for a network of real neurons. arXiv preprint arXiv:0912.5409."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"505","DOI":"10.1523\/JNEUROSCI.3359-07.2008","article-title":"A Maximum Entropy Model Applied to Spatial and Temporal Correlations from Cortical Networks","volume":"28","author":"Tang","year":"2008","journal-title":"In Vitro. J. Neurosci"},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Marre, O., El Boustani, S., Fr\u00e9gnac, Y., and Destexhe, A. (2009). Prediction of spatiotemporal patterns of neural activity from pairwise correlations. Phys. Rev. Lett, 102.","DOI":"10.1103\/PhysRevLett.102.138101"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"120","DOI":"10.1016\/j.jphysparis.2011.11.001","article-title":"Gibbs distribution analysis of temporal correlation structure on multicell spike trains from retina ganglion cells","volume":"106","author":"Vasquez","year":"2012","journal-title":"J. Physiol. Paris"},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Dud\u00edk, M., Phillips, S., and Schapire, R. (,  2004). Performance Guarantees for Regularized Maximum Entropy Density Estimation.","DOI":"10.1007\/978-3-540-27819-1_33"},{"key":"ref_18","unstructured":"Broderick, T., Dudik, M., Tkacik, G., Schapire, R.E., and Bialek, W. (2007). Faster solutions of the inverse pairwise Ising problem. arXiv:0712.2437."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"P03006","DOI":"10.1088\/1742-5468\/2013\/03\/P03006","article-title":"Spatio-temporal spike train analysis for large scale networks using the maximum entropy principle and Montecarlo method","volume":"2013","author":"Nasser","year":"2013","journal-title":"J. Stat. Mech"},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Schaub, M.T., and Schultz, S.R. (2010). The Ising decoder: reading out the activity of large neural ensembles. arXiv:1009.1828.","DOI":"10.1007\/s10827-011-0342-z"},{"key":"ref_21","unstructured":"Garibaldi, U., and Penco, M.A. (,  1985). Probability Theory and Physics Between Bernoulli and Laplace: The Contribution of J H. Lambert (1728\u20131777). Rome."},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Tkacik, G., Marre, O., Mora, T., Amodei, D.M.B., and Bialek,, W. (2013). The simplest maximum entropy model for collective behavior in a neural network. J. Stat. Mech, P03011.","DOI":"10.1088\/1742-5468\/2013\/03\/P03011"},{"key":"ref_23","unstructured":"Levine, D., and Tribus, M. (1978). The Maximum Entropy Formalism, MIT Press."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"579","DOI":"10.1146\/annurev.pc.31.100180.003051","article-title":"The minimum entropy production principle","volume":"31","author":"Jaynes","year":"1980","journal-title":"Ann. Rev. Phys. Chem"},{"key":"ref_25","unstructured":"Jaynes, E. (1985). Complex Systems - Operational Approaches in Neurobiology, Physics, and Computers, Springer."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"034119","DOI":"10.1063\/1.3455333","article-title":"Maximum caliber inference of nonequilibrium processes","volume":"133","author":"Otten","year":"2010","journal-title":"J. Chem. Phys"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"555","DOI":"10.1007\/s10955-004-8821-5","article-title":"Chains with complete connections : General theory, uniqueness, loss of memory and mixing properties","volume":"118","author":"Fernandez","year":"2005","journal-title":"J. Stat. Phys"},{"key":"ref_28","unstructured":"Gikhman, I., and Skorokhod, A. (1979). The Theory of Stochastic Processes, Springer."},{"key":"ref_29","doi-asserted-by":"crossref","unstructured":"Chazottes, J., and Keller, G. (2008). Pressure and Equilibrium States in Ergodic Theory. Isr. J. Math, 131.","DOI":"10.1007\/978-0-387-30440-3_414"},{"key":"ref_30","unstructured":"Ruelle, D. (1969). Statistical Mechanics: Rigorous Results, Benjamin."},{"key":"ref_31","doi-asserted-by":"crossref","unstructured":"Keller, G. (1998). Equilibrium States in Ergodic Theory, Cambridge University Press.","DOI":"10.1017\/CBO9781107359987"},{"key":"ref_32","unstructured":"Ruelle, D. (1978). Thermodynamic Formalism, Addison-Wesley."},{"key":"ref_33","unstructured":"Bowen, R. (1975). Lecture Notes in Mathatics, Springer-Verlag."},{"key":"ref_34","doi-asserted-by":"crossref","unstructured":"Georgii, H.O. (1988). Gibbs Measures and Phase Transitions (De Gruyter Studies in Mathematics), Springer.","DOI":"10.1515\/9783110850147"},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"120","DOI":"10.1016\/j.jphysparis.2011.11.001","article-title":"Gibbs distribution analysis of temporal correlation structure on multicell spike trains from retina ganglion cells","volume":"106","author":"Vasquez","year":"2012","journal-title":"J. Physiol. Paris"},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"253","DOI":"10.1023\/A:1013912006537","article-title":"Logistic Regression, AdaBoost and Bregman Distances","volume":"48","author":"Collins","year":"2002","journal-title":"Mach. Lear"},{"key":"ref_37","doi-asserted-by":"crossref","unstructured":"Mayer, V., and Urba\u0144ski, M. (2010). Thermodynamical formalism and multifractal analysis for meromorphic functions of finite order. Memoir. Am. Math. Soc, 203.","DOI":"10.1090\/S0065-9266-09-00577-8"},{"key":"ref_38","first-page":"280","article-title":"Boltzmann Machine learning using mean field theory and linear response correction","volume":"12","author":"Kearns","year":"1998","journal-title":"NIPS"},{"key":"ref_39","unstructured":"Available online: http:\/\/enas.gforge.inria.fr\/v3\/download.html."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"197","DOI":"10.1103\/PhysRevLett.80.197","article-title":"Entropy and information in neural spike trains","volume":"80","author":"Strong","year":"1998","journal-title":"Phys. Rev. Let"},{"key":"ref_41","unstructured":"Rosenfeld, R., Carbonell, J., and Rudnicky, A. (1994). Technical report, School of Computer Science, Carnegie Mellon University."},{"key":"ref_42","first-page":"139","article-title":"Chunking with maximum entropy models","volume":"7","author":"Koeling","year":"2000","journal-title":"Proceeding ConLL \u201900 Proceedings of the 2nd Workshop on Learning Language in Logic and the 4th conference on Computational Natural Language Learning"},{"key":"ref_43","doi-asserted-by":"crossref","unstructured":"Chen, S.F., and Rosenfeld, R. (1999). Efficient Sampling and Feature Selection in Whole Sentence Maximum. Ent. Lang Mod.","DOI":"10.1109\/ICASSP.1999.758184"},{"key":"ref_44","first-page":"39","article-title":"A Maximum Entropy approach to Natural Language Processing","volume":"22","author":"Berger","year":"1996","journal-title":"Comp. Lang"},{"key":"ref_45","unstructured":"Zhou, Y., and Wu, L. (, January July). A fast algorithm for feature selection in conditional maximum entropy modeling. Sapporo, Japan."},{"key":"ref_46","unstructured":"Cessac, B., and Cofre, R. (2013). Estimating maximum entropy distributions from periodic orbits in spike trains. research report RR-8329, INRIA."},{"key":"ref_47","doi-asserted-by":"crossref","unstructured":"Nakahara, H., and Amari, S. (2001). Information-Geometric Decomposition in Spike Analysis. Adv. Neural Inform. Process. Syst, 253\u2013260.","DOI":"10.7551\/mitpress\/1120.003.0037"},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"1701","DOI":"10.1109\/18.930911","article-title":"Information geometry on hierarchy of probability distributions","volume":"47","author":"Amari","year":"2001","journal-title":"IEEE T. Inf. Theory"},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"199","DOI":"10.1080\/713663221","article-title":"A simple white noise analysis of neuronal light responses","volume":"12","author":"Chichilnisky","year":"2001","journal-title":"Network Comput. Neural Syst"},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"e70894","DOI":"10.1371\/journal.pone.0070894","article-title":"Estimating Temporal Causal Interaction between Spike Trains with Permutation and Transfer Entropy","volume":"8","author":"Li","year":"2013","journal-title":"PloS One"},{"key":"ref_51","doi-asserted-by":"crossref","first-page":"105","DOI":"10.1038\/nn.2455","article-title":"Collective dynamics in human and monkey sensorimotor cortex: predicting single neuron spikes","volume":"13","author":"Truccolo","year":"2009","journal-title":"Nature Neurosci"}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/16\/4\/2244\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T21:10:35Z","timestamp":1760217035000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/16\/4\/2244"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,4,22]]},"references-count":51,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2014,4]]}},"alternative-id":["e16042244"],"URL":"https:\/\/doi.org\/10.3390\/e16042244","relation":{},"ISSN":["1099-4300"],"issn-type":[{"type":"electronic","value":"1099-4300"}],"subject":[],"published":{"date-parts":[[2014,4,22]]}}}