Table of Contents Author Guidelines Submit a Manuscript
Mathematical Problems in Engineering
Volume 2010, Article ID 621670, 34 pages
http://dx.doi.org/10.1155/2010/621670
Research Article

Generalised Filtering

1Wellcome Trust Centre for Neuroimaging, University College London, Queen Square, London WC1N 3BG, UK
2Laboratory for Social and Neural Systems Research, Institute of Empirical Research in Economics, University of Zurich, 8006 Zurich, Switzerland
3College of Mechatronic Engineering and Automation, National University of Defense Technology, Changsha, Hunan 410073, China

Received 29 January 2010; Accepted 17 March 2010

Academic Editor: Massimo Scalia

Copyright © 2010 Karl Friston et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Citations to this Article [96 citations]

The following is the list of published articles that have cited the current article.

  • G. Prando, M. Zorzi, A. Bertoldo, and A. Chiuso, “Estimating effective connectivity in linear brain network models,” 2017 IEEE 56th Annual Conference on Decision and Control (CDC), pp. 5931–5936, . View at Publisher · View at Google Scholar
  • Ensor Rafael Palacios, Adeel Razi, Thomas Parr, Michael Kirchhoff, and Karl Friston. View at Publisher · View at Google Scholar
  • Sevada Hovsepyan, Itsaso Olasagasti, and Anne-Lise Giraud. View at Publisher · View at Google Scholar
  • Harriet Feldman, and Karl J. Friston, “Attention, uncertainty, and free-energy,” Frontiers in Human Neuroscience, vol. 4, 2010. View at Publisher · View at Google Scholar
  • Ming Li, Massimo Scalia, and Cristian Toma, “Nonlinear Time Series: Computations and Applications,” Mathematical Problems in Engineering, vol. 2010, pp. 1–5, 2010. View at Publisher · View at Google Scholar
  • Baojuan Li, Jean Daunizeau, Klaas E. Stephan, Will Penny, Dewen Hu, and Karl Friston, “Generalised filtering and stochastic DCM for fMRI,” NeuroImage, vol. 58, no. 2, pp. 442–457, 2011. View at Publisher · View at Google Scholar
  • Martin Havlicek, Karl J. Friston, Jiri Jan, Milan Brazdil, and Vince D. Calhoun, “Dynamic modeling of neuronal responses in fMRI using cubature Kalman filtering,” NeuroImage, vol. 56, no. 4, pp. 2109–2128, 2011. View at Publisher · View at Google Scholar
  • Karl Friston, and Will Penny, “Post hoc Bayesian model selection,” Neuroimage, vol. 56, no. 4, pp. 2089–2099, 2011. View at Publisher · View at Google Scholar
  • Karl J. Friston, Baojuan Li, Jean Daunizeau, and Klaas E. Stephan, “Network discovery with DCM,” NeuroImage, vol. 56, no. 3, pp. 1202–1221, 2011. View at Publisher · View at Google Scholar
  • Karl Friston, Jeremie Mattout, and James Kilner, “Action understanding and active inference,” Biological Cybernetics, vol. 104, no. 1-2, pp. 137–160, 2011. View at Publisher · View at Google Scholar
  • Stefan J. Kiebel, and Karl J. Friston, “Free energy and dendritic self-organization,” Frontiers in Systems Neuroscience, no. 2011, 2011. View at Publisher · View at Google Scholar
  • Ming Li, “A Class of Negatively Fractal Dimensional Gaussian Random Functions,” Mathematical Problems in Engineering, vol. 2011, pp. 1–18, 2011. View at Publisher · View at Google Scholar
  • Cesar Caballero Gaudes, Dimitri Van de Ville, Natalia Petridou, Francois Lazeyras, and Penny Gowland, “Paradigm-Free Mapping with Morphological Component Analysis: Getting Most O ut of fMRI Data,” Wavelets and Sparsity Xiv, vol. 8138, 2011. View at Publisher · View at Google Scholar
  • S. Dubeau, M. Havlicek, E. Beaumont, G. Ferland, F. Lesage, and P. Pouliot, “Neurovascular deconvolution of optical signals as a proxy for the true neuronal inputs,” Journal of Neuroscience Methods, vol. 210, no. 2, pp. 247–258, 2012. View at Publisher · View at Google Scholar
  • Klaas Enno Stephan, and Alard Roebroeck, “A short history of causal modeling of fMRI data,” NeuroImage, vol. 62, no. 2, pp. 856–863, 2012. View at Publisher · View at Google Scholar
  • J. Daunizeau, K. E. Stephan, and K. J. Friston, “Stochastic dynamic causal modelling of fMRI data: Should we care about neural noise?,” Neuroimage, vol. 62, no. 1, pp. 464–481, 2012. View at Publisher · View at Google Scholar
  • Karl Friston, “Embodied inference and spatial cognition,” Cognitive Processing, vol. 13, no. S1, pp. 171–177, 2012. View at Publisher · View at Google Scholar
  • Karl Friston, Michael Breakspear, and Gustavo Deco, “Perception and self-organized instability,” Frontiers in Computational Neuroscience, vol. 6, 2012. View at Publisher · View at Google Scholar
  • M. J. Rosa, K. Friston, and W. Penny, “Post-hoc selection of dynamic causal models,” Journal Of Neuroscience Methods, vol. 208, no. 1, pp. 66–78, 2012. View at Publisher · View at Google Scholar
  • Sebastian Bitzer, and Stefan J. Kiebel, “Recognizing recurrent neural networks (rRNN): Bayesian inference for recurrent neural networks,” Biological Cybernetics, vol. 106, no. 4-5, pp. 201–217, 2012. View at Publisher · View at Google Scholar
  • Friston Karl, “A Free Energy Principle for Biological Systems,” Entropy, vol. 14, no. 11, pp. 2100–2121, 2012. View at Publisher · View at Google Scholar
  • Rick A. Adams, Laurent U. Perrinet, and Karl Friston, “Smooth Pursuit and Visual Occlusion: Active Inference and Oculomotor Control in Schizophrenia,” PLoS ONE, vol. 7, no. 10, 2012. View at Publisher · View at Google Scholar
  • Karl J. Friston, Tamara Shiner, Thomas FitzGerald, Joseph M. Galea, Rick Adams, Harriet Brown, Raymond J. Dolan, Rosalyn Moran, Klaas Enno Stephan, and Sven Bestmann, “Dopamine, Affordance and Active Inference,” Plos Computational Biology, vol. 8, no. 1, 2012. View at Publisher · View at Google Scholar
  • Karl Friston, and Ping Ao, “Free Energy, Value, and Attractors,” Computational and Mathematical Methods in Medicine, vol. 2012, pp. 1–27, 2012. View at Publisher · View at Google Scholar
  • Karl Friston, Rick A. Adams, Laurent Perrinet, and Michael Breakspear, “Perceptions as hypotheses: Saccades as experiments,” Frontiers in Psychology, vol. 3, no. MAY, 2012. View at Publisher · View at Google Scholar
  • Karl Friston, Baojuan Li, Xiang Wang, Shuqiao Yao, and Dewen Hu, “Task-dependent modulation of effective connectivity within the default mode network,” Frontiers in Psychology, vol. 3, 2012. View at Publisher · View at Google Scholar
  • Karl Friston, Rick Adams, and Read Montague, “What is value-accumulated reward or evidence?,” Frontiers in Neurorobotics, 2012. View at Publisher · View at Google Scholar
  • Christophe Phillips, Andrea Soddu, Melanie Boly, Pierre Boveroux, Audrey Vanhaudenhuyse, Marie-Aurelie Bruno, Olivia Gosseries, Vincent Bonhomme, Steven Laureys, and Quentin Noirhomme, “Changes in Effective Connectivity by Propofol Sedation,” Plos One, vol. 8, no. 8, 2013. View at Publisher · View at Google Scholar
  • Fikret Işık Karahanoğlu, César Caballero-Gaudes, François Lazeyras, and Dimitri Van De Ville, “Total activation: fMRI deconvolution through spatio-temporal regularization,” NeuroImage, vol. 73, pp. 121–134, 2013. View at Publisher · View at Google Scholar
  • D. Bernal-Casas, E. Balaguer-Ballester, M.F. Gerchen, S. Iglesias, H. Walter, A. Heinz, A. Meyer-Lindenberg, K.E. Stephan, and P. Kirsch, “Multi-site reproducibility of prefrontal–hippocampal connectivity estimates by stochastic DCM,” NeuroImage, 2013. View at Publisher · View at Google Scholar
  • Cesar Caballero Gaudes, Natalia Petridou, Susan T. Francis, Ian L. Dryden, and Penny A. Gowland, “Paradigm free mapping with sparse regression automatically detects single-trial functional magnetic resonance imaging blood oxygenation level dependent responses,” Human Brain Mapping, vol. 34, no. 3, pp. 501–518, 2013. View at Publisher · View at Google Scholar
  • Rick A. Adams, Isabel Parees, Mark Edwards, and Karl Friston, “Active inference, sensory attenuation and illusions,” Cognitive Processing, vol. 14, no. 4, pp. 411–427, 2013. View at Publisher · View at Google Scholar
  • Klaas E. Stephan, Jean Daunizeau, Marta I. Garrido, and Karl J. Friston, “A Neurocomputational Model of the Mismatch Negativity,” Plos Computational Biology, vol. 9, no. 11, 2013. View at Publisher · View at Google Scholar
  • Sophie Deneve, “Circular inferences in schizophrenia,” Brain, vol. 136, pp. 3227–3241, 2013. View at Publisher · View at Google Scholar
  • J. Daunizeau, L. Lemieux, A.E. Vaudano, K.J. Friston, and K.E. Stephan, “An electrophysiological validation of stochastic DCM for fMRI,” Frontiers in Computational Neuroscience, 2013. View at Publisher · View at Google Scholar
  • Jason F. Smith, Kewei Chen, Ajay S. Pillai, and Barry Horwitz, “Identifying effective connectivity parameters in simulated fMRI: A direct comparison of switching linear dynamic system, stochastic dynamic causal, and multivariate autoregressive models,” Frontiers in Neuroscience, no. 7, 2013. View at Publisher · View at Google Scholar
  • Laurent U. Perrinet, Rick A. Adams, and Karl J. Friston, “Active inference, eye movements and oculomotor delays,” Biological Cybernetics, 2014. View at Publisher · View at Google Scholar
  • Dirk Ostwald, Evgeniya Kirilina, Ludger Starke, and Felix Blankenburg, “A tutorial on variational Bayes for latent linear stochastic time-series models,” Journal of Mathematical Psychology, vol. 60, pp. 1–19, 2014. View at Publisher · View at Google Scholar
  • Baojuan Li, Karl J. Friston, Jian Liu, Yang Liu, Guopeng Zhang, Fenglin Cao, Linyan Su, Shuqiao Yao, Hongbing Lu, and Dewen Hu, “Impaired Frontal-Basal Ganglia Connectivity in Adolescents with Internet Addiction,” Scientific Reports, vol. 4, 2014. View at Publisher · View at Google Scholar
  • Joshua Kahan, Maren Urner, Rosalyn Moran, Guillaume Flandin, Andre Marreiros, Laura Mancini, Mark White, John Thornton, Tarek Yousry, Ludvic Zrinzo, Marwan Hariz, Patricia Limousin, Karl Friston, and Tom Foltynie, “Resting state functional MRI in Parkinson's disease: the impact of deep brain stimulation on 'effective' connectivity,” Brain, vol. 137, pp. 1130–1144, 2014. View at Publisher · View at Google Scholar
  • Biswa Sengupta, and Gennaro Auletta, “Cognitive Dynamics: From Attractors to Active Inference,” Proceedings of The Ieee, vol. 102, no. 4, pp. 427–445, 2014. View at Publisher · View at Google Scholar
  • Karl Friston, Michael Breakspear, and Gustavo Deco, “Critical Slowing and Perception,” Criticality in Neural Systems, pp. 191–226, 2014. View at Publisher · View at Google Scholar
  • Adeel Razi, Joshua Kahan, Geraint Rees, and Karl J. Friston, “Construct Validation of a DCM for resting state fMRI,” NeuroImage, 2014. View at Publisher · View at Google Scholar
  • Natasha Khovanova, Yan Zhang, and Tim A. Holt, “Generalised stochastic model for characterisation of subcutaneous glucose time series,” 2014 IEEE-EMBS International Conference on Biomedical and Health Informatics, BHI 2014, pp. 484–487, 2014. View at Publisher · View at Google Scholar
  • Gerald K. Cooray, Biswa Sengupta, Pamela Douglas, Marita Englund, Ronny Wickstrom, and Karl Friston, “Characterising seizures in anti-NMDA-receptor encephalitis with dynamic causal modelling,” NeuroImage, vol. 118, pp. 508–519, 2015. View at Publisher · View at Google Scholar
  • Klaas E. Stephan, Baojuan Li, Sandra Iglesias, and Karl J. Fristonpp. 365–386, 2015. View at Publisher · View at Google Scholar
  • Jakob Hohwy, Bryan Paton, and Colin Palmer, “Distrusting the present,” Phenomenology and the Cognitive Sciences, 2015. View at Publisher · View at Google Scholar
  • Martin Havlicek, Alard Roebroeck, Karl Friston, Anna Gardumi, Dimo Ivanov, and Kamil Uludag, “Physiologically informed dynamic causal modeling of fMRI data,” NeuroImage, 2015. View at Publisher · View at Google Scholar
  • Ryota Kanai, Yutaka Komura, Stewart Shipp, and Karl Friston, “Cerebral hierarchies: predictive processing, precision and the pulvinar,” Philosophical Transactions Of The Royal Society B-Biological Sciences, vol. 370, no. 1668, pp. 69–81, 2015. View at Publisher · View at Google Scholar
  • Stefan Frässle, Klaas Enno Stephan, Karl John Friston, Marlena Steup, Sören Krach, Frieder Michel Paulus, and Andreas Jansen, “Test-retest reliability of dynamic causal modeling for fMRI,” NeuroImage, 2015. View at Publisher · View at Google Scholar
  • Karl J. Friston, and Christopher D. Frith, “Active inference, communication and hermeneutics,” Cortex, 2015. View at Publisher · View at Google Scholar
  • P. Osório, P. Rosa, C. Silvestre, and P. Figueiredo, “Stochastic Dynamic Causal Modelling of fMRI Data with Multiple-Model Kalman Filters,” Methods of Information in Medicine, vol. 54, no. 20150424, pp. 232–239, 2015. View at Publisher · View at Google Scholar
  • K. Friston, M. Levin, B. Sengupta, and G. Pezzulo, “Knowing one's place: a free-energy approach to pattern regulation,” Journal of The Royal Society Interface, vol. 12, no. 105, pp. 20141383–20141383, 2015. View at Publisher · View at Google Scholar
  • Stephanvol. 1, pp. 617–624, 2015. View at Publisher · View at Google Scholar
  • Jibiao Zhang, Baojuan Li, Junling Gao, Huqing Shi, Xiang Wang, Yali Jiang, Qingsen Ming, Yidian Gao, Ren Ma, and Shuqiao Yao, “Impaired Frontal-Basal Ganglia Connectivity in Male Adolescents with Conduct Disorder,” Plos One, vol. 10, no. 12, 2015. View at Publisher · View at Google Scholar
  • Long-Biao Cui, Jian Liu, Liu-Xian Wang, Chen Li, Yi-Bin Xi, Fan Guo, Hua-Ning Wang, Lin-Chuan Zhang, Wen-Ming Liu, Hong He, Ping Tian, Hong Yin, and Hongbing Lu, “Anterior cingulate cortex-related connectivity in first-episode schizophrenia: a spectral dynamic causal modeling study with functional magnetic resonance imaging,” Frontiers in Human Neuroscience, vol. 9, 2015. View at Publisher · View at Google Scholar
  • Yan Zhang, Tim A. Holt, and Natalia Khovanova, “A data driven nonlinear stochastic model for blood glucose dynamics,” Computer Methods and Programs in Biomedicine, 2015. View at Publisher · View at Google Scholar
  • Payam Piray, Hanneke E.M. den Ouden, Marieke E. van der Schaaf, Ivan Toni, and Roshan Cools, “Dopaminergic Modulation of the Functional Ventrodorsal Architecture of the Human Striatum,” Cerebral Cortex, pp. bhv243, 2015. View at Publisher · View at Google Scholar
  • Dario Cuevas Rivera, Sebastian Bitzer, and Stefan J. Kiebel, “Modelling Odor Decoding in the Antennal Lobe by Combining Sequential Firing Rate Models with Bayesian Inference,” PLoS Computational Biology, vol. 11, no. 10, 2015. View at Publisher · View at Google Scholar
  • Karl Friston, and Christopher Frith, “A Duet for one,” Consciousness and Cognition, 2015. View at Publisher · View at Google Scholar
  • Rick A. Adams, Eduardo Aponte, Louise Marshall, and Karl J. Friston, “Active inference and oculomotor pursuit: The dynamic causal modelling of eye movements,” Journal of Neuroscience Methods, 2015. View at Publisher · View at Google Scholar
  • Yan Zhang, David Lowe, David Briggs, Robert Higgins, and Natasha Khovanova, “Novel data-driven stochastic model for antibody dynamics in kidney transplantation∗∗This work has been supported by EPSRC UK (EP/K02504X/1).,” IFAC-PapersOnLine, vol. 48, no. 20, pp. 249–254, 2015. View at Publisher · View at Google Scholar
  • Rick A. Adams, Harriet R. Brown, and Karl J. Friston, “Bayesian inference, predictive coding and delusions,” Avant, vol. 5, no. 3, pp. 51–88, 2015. View at Publisher · View at Google Scholar
  • Léo Pio-Lopez, Ange Nizard, Karl Friston, and Giovanni Pezzulo, “Active inference and robot control: a case study,” Journal of The Royal Society Interface, vol. 13, no. 122, pp. 20160616, 2016. View at Publisher · View at Google Scholar
  • Sahil Bajaj, Bhim M. Adhikari, Karl J. Friston, and Mukesh Dhamala, “Bridging the Gap: Dynamic Causal Modeling and Granger Causality Analysis of Resting State Functional Magnetic Resonance Imaging,” Brain Connectivity, 2016. View at Publisher · View at Google Scholar
  • Yi-Bin Xi, Chen Li, Long-Biao Cui, Jian Liu, Fan Guo, Liang Li, Ting-Ting Liu, Kang Liu, Gang Chen, Min Xi, Hua-Ning Wang, and Hong Yin, “Anterior Cingulate Cortico-Hippocampal Dysconnectivity in Unaffected Relatives of Schizophrenia Patients: A Stochastic Dynamic Causal Modeling Study,” Frontiers in Human Neuroscience, vol. 10, 2016. View at Publisher · View at Google Scholar
  • Serdar Aslan, Ali Taylan Cemgil, and Ata Akın, “Joint state and parameter estimation of the hemodynamic model by particle smoother expectation maximization method,” Journal of Neural Engineering, vol. 13, no. 4, pp. 046010, 2016. View at Publisher · View at Google Scholar
  • Adeel Razi, and Karl J. Friston, “The Connected Brain Causality, models, and intrinsic dynamics,” Ieee Signal Processing Magazine, vol. 33, no. 3, pp. 14–35, 2016. View at Publisher · View at Google Scholar
  • Hanneke den Ouden, Monique Timmer, Bastiaan R. Bloem, Rick C. Helmich, Michiel F. Dirkx, Esther Aarts, and Ivan Toni, “The cerebral network of parkinson’s tremor: An effective connectivity fMRI study,” Journal of Neuroscience, vol. 36, no. 19, pp. 5362–5372, 2016. View at Publisher · View at Google Scholar
  • Dirk Ostwald, and Ludger Starke, “Probabilistic delay differential equation modeling of event-related potentials,” NeuroImage, 2016. View at Publisher · View at Google Scholar
  • Serdar Aslan, “Comparison of the hemodynamic filtering methods and particle filter with extended Kalman filter approximated proposal function as an efficient hemodynamic state estimation method,” Biomedical Signal Processing and Control, vol. 25, pp. 99–107, 2016. View at Publisher · View at Google Scholar
  • Serdar Aslan, Ali Taylan Cemgil, Murat Şamil Aslan, Behçet Uğur Töreyin, and Ata Akın, “Joint parameter and state estimation of the hemodynamic model by iterative extended Kalman smoother,” Biomedical Signal Processing and Control, vol. 24, pp. 47–62, 2016. View at Publisher · View at Google Scholar
  • Junhai Xu, Xuntao Yin, Haitao Ge, Yan Han, Zengchang Pang, Baolin Liu, Shuwei Liu, and Karl Friston, “Heritability of the Effective Connectivity in the Resting-State Default Mode Network,” Cerebral Cortex, vol. 27, no. 12, pp. 5626–5634, 2016. View at Publisher · View at Google Scholar
  • Klaas E. Stephan, Zina M. Manjaly, Christoph D. Mathys, Lilian A. E. Weber, Saee Paliwal, Tim Gard, Marc Tittgemeyer, Stephen M. Fleming, Helene Haker, Anil K. Seth, and Frederike H. Petzschner, “Allostatic Self-efficacy: A Metacognitive Theory of Dyshomeostasis-Induced Fatigue and Depression,” Frontiers in Human Neuroscience, vol. 10, 2016. View at Publisher · View at Google Scholar
  • Karl J Friston, Thomas Parr, and Bert de Vries, “The graphical brain: Belief propagation and active inference,” Network Neuroscience, pp. 1–78, 2017. View at Publisher · View at Google Scholar
  • Paco Calvo, and Karl Friston, “Predicting green: really radical (plant) predictive processing,” Journal of The Royal Society Interface, vol. 14, no. 131, pp. 20170096, 2017. View at Publisher · View at Google Scholar
  • Karl J. Friston, A. David Redish, and Joshua A. Gordon, “Computational Nosology and Precision Psychiatry,” Computational Psychiatry, pp. 1–22, 2017. View at Publisher · View at Google Scholar
  • Karl Friston, “The Variational Principles of Action,” Geometric and Numerical Foundations of Movements, vol. 117, pp. 207–235, 2017. View at Publisher · View at Google Scholar
  • Linchuan Zhang, Baojuan Li, Huaning Wang, Liang Li, Qimei Liao, Yang Liu, Xianghong Bao, Wenlei Liu, Hong Yin, Hongbing Lu, and Qingrong Tan, “Decreased middle temporal gyrus connectivity in the language network in schizophrenia patients with auditory verbal hallucinations,” Neuroscience Letters, 2017. View at Publisher · View at Google Scholar
  • Baojuan Li, Long-Biao Cui, Yi-Bin Xi, Karl J. Friston, Fan Guo, Hua-Ning Wang, Lin-Chuan Zhang, Yuan-Han Bai, Qing-Rong Tan, Hong Yin, and Hongbing Lu, “Abnormal Effective Connectivity in the Brain is Involved in Auditory Verbal Hallucinations in Schizophrenia,” Neuroscience Bulletin, vol. 33, no. 3, pp. 281–291, 2017. View at Publisher · View at Google Scholar
  • Christopher L. Buckley, Chang Sub Kim, Simon McGregor, and Anil K. Seth, “The free energy principle for action and perception: A mathematical review,” Journal of Mathematical Psychology, 2017. View at Publisher · View at Google Scholar
  • Adeel Razi, Mohamed L. Seghier, Yuan Zhou, Peter McColgan, Peter Zeidman, Hae-Jeong Park, Olaf Sporns, Geraint Rees, and Karl J. Friston, “Large-scale DCMs for resting-state fMRI,” Network Neuroscience, vol. 1, no. 3, pp. 222–241, 2017. View at Publisher · View at Google Scholar
  • Mina A. Khoei, Guillaume S. Masson, and Laurent U. Perrinet, “The Flash-Lag Effect as a Motion-Based Predictive Shift,” PLOS Computational Biology, vol. 13, no. 1, pp. e1005068, 2017. View at Publisher · View at Google Scholar
  • Serdar Aslan, “Hemodynamic Model Inversion by Iterative Extended Kalman Smoother,” Handbook of Neural Computation, pp. 181–199, 2017. View at Publisher · View at Google Scholar
  • Thomas Parr, and Karl J. Friston, “The Discrete and Continuous Brain: From Decisions to Movement—And Back Again,” Neural Computation, vol. 30, no. 9, pp. 2319–2347, 2018. View at Publisher · View at Google Scholar
  • Jbabdi, Abeysuriya, Hadida, Sotiropoulos, and Woolrich, “Bayesian Optimisation of Large-Scale Biophysical Networks,” NeuroImage, vol. 174, pp. 219–236, 2018. View at Publisher · View at Google Scholar
  • Yuan Wang, Yao Wang, and Yvonne W. Lui, “Generalized Recurrent Neural Network accommodating Dynamic Causal Modeling for functional MRI analysis,” NeuroImage, 2018. View at Publisher · View at Google Scholar
  • Feng Chen, Zhaofei Yu, and Fei Deng, “Unification of MAP Estimation and Marginal Inference in Recurrent Neural Networks,” IEEE Transactions on Neural Networks and Learning Systems, vol. 29, no. 11, pp. 5761–5766, 2018. View at Publisher · View at Google Scholar
  • Fadi Salo, Ali Bou Nassif, and Aleksander Essex, “Dimensionality Reduction with IG-PCA and Ensemble Classifier for Network Intrusion Detection,” Computer Networks, 2018. View at Publisher · View at Google Scholar
  • Thomas Parr, and Karl J. Friston, “The Anatomy of Inference: Generative Models and Brain Structure,” Frontiers in Computational Neuroscience, vol. 12, 2018. View at Publisher · View at Google Scholar
  • Thomas Parr, and Karl J Friston, “Active inference and the anatomy of oculomotion,” Neuropsychologia, 2018. View at Publisher · View at Google Scholar
  • César Caballero-Gaudes, Stefano Moia, Puja Panwar, Peter A. Bandettini, and Javier Gonzalez-Castillo, “A deconvolution algorithm for multi-echo functional MRI: Multi-echo Sparse Paradigm Free Mapping,” NeuroImage, pp. 116081, 2019. View at Publisher · View at Google Scholar
  • Franz Kuchling, Karl Friston, Georgi Georgiev, and Michael Levin, “Morphogenesis as bayesian inference: A variational approach to pattern formation and control in complex biological systems,” Physics of Life Reviews, 2019. View at Publisher · View at Google Scholar
  • Joshua Kahan, Laura Mancini, Guillaume Flandin, Mark White, Anastasia Papadaki, John Thornton, Tarek Yousry, Ludvic Zrinzo, Marwan Hariz, Patricia Limousin, Karl Friston, and Tom Foltynie, “Deep brain stimulation has state-dependent effects on motor connectivity in Parkinson’s disease,” Brain, 2019. View at Publisher · View at Google Scholar
  • Manuel Baltieri, and Christopher Buckley, “PID Control as a Process of Active Inference with Linear Generative Models,” Entropy, vol. 21, no. 3, pp. 257, 2019. View at Publisher · View at Google Scholar
  • Thomas Parr, Dimitrije Markovic, Stefan J. Kiebel, and Karl J. Friston, “Neuronal message passing using Mean-field, Bethe, and Marginal approximations,” Scientific Reports, vol. 9, no. 1, 2019. View at Publisher · View at Google Scholar