inJournal
2024
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Algebraic optimization of sequential decision problems
In: Journal of symbolic computation, 121 (2024), p. 102241inJournal
2024
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Geometry and convergence of natural policy gradient methods
In: Information geometry, 7 (2024) 1 supplement, pp. 485-523inJournal
2023
Journal Open Access
Implicit bias of gradient descent for mean squared error regression with wide neural networks
In: Journal of machine learning research, 24 (2023), p. 137Preprint
2023
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Mildly overparameterized ReLU networks have a favorable loss landscape
Preprint
2023
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Function space and critical points of linear convolutional networks
(SIAM journal on discrete mathematics)inBook
2023
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Stochastic feedforward neural networks : universal approximation
In: Mathematical aspects of deep learning / Philipp Grohs... (eds.)Cambridge : Cambridge University Press, 2023. - pp. 267-313
inJournal
2023
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Continuity and additivity properties of information decompositions
In: International journal of approximate reasoning, 161 (2023), p. 108979Preprint
2023
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Supermodular rank : set function decomposition and optimization
Preprint
2023
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Expected gradients of maxout networks and consequences to parameter initialization
inBook
2022
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Oversquashing in GNNs through the lens of information contraction and graph expansion
In: 2022 58th Annual Allerton Conference on communication, control, and computing : 27-30 Sept. 2022Piscataway, N.J. : IEEE, 2022. - p. 9929363
Preprint
2022
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Implicit bias of MSE gradient optimization in underparameterized neural networks
inBook
2022
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Spectral bias outside the training set for deep networks in the kernel regime
In: Advances in neural information processing systems 35 : NeurIPS 2022 ; annual conference on neural information processing systems 2022[S. L.] : NeurIPS, 2022. - pp. 30362-30377
Preprint
2022
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Enumeration of max-pooling responses with generalized permutohedra
Preprint
2022
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FoSR : first-order spectral rewiring for addressing oversquashing in GNNs
inJournal
2022
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Geometry of linear convolutional networks
In: SIAM journal on applied algebra and geometry, 6 (2022) 3, pp. 368-406inBook
2022
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Decentralized multi-agents by imitations of a centralized controller
In: 2nd annual conference on mathematical and scientific machine learning : 16-19 August 2021, virtual conference[s. l.] : PMLR, 2022. - pp. 619-651
(Proceedings of machine learning research ; 145)
inJournal
2022
Journal Open Access
Distributed learning via filtered hyperinterpolation on manifolds
In: Foundations of computational mathematics, 22 (2022) 4, pp. 1219-1271inJournal
2022
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Sharp bounds for the number of regions of maxout networks and vertices of Minkowski sums
In: SIAM journal on applied algebra and geometry, 6 (2022) 4, pp. 618-649Preprint
2022
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Solving infinite-horizon POMDPs with memoryless stochastic policies in state-action space
inBook
2022
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The geometry of memoryless stochastic policy optimization in infinite-horizon POMDPs
In: ICLR 2022 : Tenth international conference on learning representations ; 25th April 2022[s. l.] : ICLR, 2022. - pp. 1-45
Preprint
2022
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Characterizing the spectrum of the NTK via a power series expansion
inBook
2022
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On the effectiveness of persistent homology
In: Advances in neural information processing systems 35 : NeurIPS 2022 ; annual conference on neural information processing systems 2022[S. L.] : NeurIPS, 2022. - pp. 35432-35448
inJournal
2022
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Cell graph neural networks enable the digital staging of tumor microenvironment and precise prediction of patient survival in gastric cancer
In: npj precision oncology, 6 (2022) 1, p. 45inBook
2021
Repository Open Access
Information complexity and generalization bounds
In: IEEE international symposium on information theory (ISIT) from 12 - 20 July 2021 ; Melbourne, Victoria, AustraliaPiscataway, NY : IEEE, 2021. - pp. 676-681
inBook
2021
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PAC-bayes and information complexity
In: ICLR 2021 workshop on neural compression : from information theory to applications[s. l.] : ICLR, 2021. - pp. 1-15
inBook
2021
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Weisfeiler and Lehman go cellular : CW networks
In: Advances in neural information processing systems 34 : NeurIPS 2021 ; annual conference on neural information processing systems 2021, December 6-14, 2021, virtual / Marc'Aurelio Ranzato (ed.)[S. L.] : NeurIPS, 2021. - pp. 2625-2640
inBook
2021
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Weisfeiler and Lehman go topological : message passing simplicial networks
In: ICML 2021 : Proceedings of the 38th international conference on machine learning ; 18-24 July 2021[s. l.] : PMLR, 2021. - pp. 1026-1037
(Proceedings of machine learning research ; 139)
inJournal
2021
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Wasserstein distance to independence models
In: Journal of symbolic computation, 104 (2021), pp. 855-873Preprint
2021
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Learning curves for Gaussian process regression with power-law priors and targets
Preprint
2021
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Training Wasserstein GANs without gradient penalties
inBook
2021
A top-down approach to attain decentralized multi-agents
In: Handbook of reinforcement learning and control / Kyriakos G. Vamvoudakis... (eds.)Cham : Springer, 2021. - pp. 419-431
(Studies in systems, decision and control ; 325)
inBook
2021
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Wasserstein proximal of GANs
In: Geometric science of information : 5th international conference, GSI 2021, Paris, France, July 21-23, 2021, proceedings / Frank Nielsen... (eds.)Cham : Springer, 2021. - pp. 524-533
(Lecture notes in computer science ; 12829)
inBook
2021
Journal Open Access
Tight bounds on the smallest eigenvalue of the neural tangent kernel for deep ReLU networks
In: ICML 2021 : Proceedings of the 38th international conference on machine learning ; 18-24 July 2021[s. l.] : PMLR, 2021. - pp. 8119-8129
(Proceedings of machine learning research ; 139)
inBook
2021
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On the expected complexity of maxout networks
In: Advances in neural information processing systems 34 : NeurIPS 2021 ; annual conference on neural information processing systems 2021, December 6-14, 2021, virtual / Marc'Aurelio Ranzato (ed.)[S. L.] : NeurIPS, 2021. - pp. 28995-29008
inBook
2021
Journal Open Access
How framelets enhance graph neural networks
In: ICML 2021 : Proceedings of the 38th international conference on machine learning ; 18-24 July 2021[s. l.] : PMLR, 2021. - pp. 12761-12771
(Proceedings of machine learning research ; 139)
Preprint
2020
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A Pytorch implementation of the KWNG estimator [Computer code]
inBook
2020
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Kernelized Wasserstein natural gradient
In: ICLR 2020 : Eighth international conference on learning representations ; Millennium Hall, Addis Ababa, Ethiopia ; 26th-30th April 2020[s. l.] : ICLR, 2020. - pp. 1-31
Preprint
2020
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computeUI [Computer code]
inBook
2020
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The variational deficiency bottleneck
In: Proceedings of the international joint conference on neural networks 2020 (IJCNN)Piscataway, NJ : IEEE Operations Center, 2020. - pp. 1-8
inBook
2020
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Optimal transport to a variety
In: Mathematical aspects of computer and information sciences : 8th international conference, MACIS 2019, Gebze-Istanbul, Turkey, November 13-15, 2019 ; revised selected papers / Daniel Slamanig... (eds.)Cham : Springer, 2020. - pp. 364-381
(Lecture notes in computer science ; 11989)
inBook
2020
Journal Open Access
Optimization theory for ReLU neural networks trained with normalization layers
In: ICML 2020 : Proceedings of the 37th international conference on machine learning ; 13-18 July 2020[s. l.] : PMLR, 2020. - pp. 2751-2760
(Proceedings of machine learning research ; 119)
Preprint
2020
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Wasserstein of Wasserstein loss for generative models - WWGAN [Computer code]
inJournal
2020
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Ricci curvature for parametric statistics via optimal transport
In: Information geometry, 3 (2020) 1, pp. 89-117inJournal
2020
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Factorized mutual information maximization
In: Kybernetika, 56 (2020) 5, pp. 948-978inBook
2020
Repository Open Access
Can neural networks learn persistent homology features?
In: NeurIPS 2020 : Workshop on topological data analysis and beyond ; 11 December 2020[S. L.] : NeurIPS, 2020.
inBook
2020
Journal Open Access
Haar graph pooling
In: ICML 2020 : Proceedings of the 37th international conference on machine learning ; 13-18 July 2020[s. l.] : PMLR, 2020. - pp. 9952-9962
(Proceedings of machine learning research ; 119)
inBook
2019
Repository Open Access
A continuity result for optimal memoryless planning in POMDPs
In: RLDM 2019 : 4th multidisciplinary conference on reinforcement learning and decision making ; July 7-10, 2019 ; Montréal, CanadaMontréal, Canada : University, 2019. - pp. 362-365
Preprint
2019
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Geometry and learning from data in 3D and beyond : IPAM long program, Spring 2019 [Report]
inBook
2019
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Wasserstein of Wasserstein loss for learning generative models
In: Proceedings of the 36th international conference on machine learning, 9-15 June 2019, Long Beach, California, USA / Kamalika Chaudhuri (ed.)Long Beach, California : PMLR, 2019. - pp. 1716-1725
(Proceedings of machine learning research ; 97)
inBook
2019
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Wasserstein diffusion Tikhonov regularization
In: NeurIPS 2019 : Workshop on optimal transport and machine learning ; Vancouver, December 13 2019[S. L.] : NeurIPS, 2019.
inBook
2019
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Affine natural proximal learning
In: Geometric science of information : 4th international conference, GSI 2019, Toulouse, France, August 27-29, 2019, proceedings / Frank Nielsen... (eds.)Cham : Springer, 2019. - pp. 705-714
(Lecture notes in computer science ; 11712)
Preprint
2019
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How well do WGANs estimate the Wasserstein metric?
Preprint
2019
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Computing the unique information - 1st workshop on semantic information - CVPR June 2019 - Long Beach [Slides]
Preprint
2019
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Contoursurf [Computer code]
inBook
2019
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Task-agnostic constraining in average reward POMDPs
In: Task-agnostic reinforcement learning : workshop at ICLR, 06 May 2019, New Orleans[S. L.] : ICLR, 2019.
Preprint
2019
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Wasserstein information geometry for learning from data : tutorial at geometry and learning from data, IPAM, March 2019 [Slides]
inBook
2018
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Computing the unique information
In: IEEE international symposium on information theory (ISIT) from June 17 to 22, 2018 at the Talisa Hotel in Vail, Colorado, USAPiscataway, NY : IEEE, 2018. - pp. 141-145
inJournal
2018
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Natural gradient via optimal transport
In: Information geometry, 1 (2018) 2, pp. 181-214Preprint
2018
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Illustration of maxout layer upper bound [Suppl. to: On the number of linear regions of deep neural networks]
inBook
2018
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Restricted Boltzmann machines : introduction and review
In: Information geometry and its applications : on the occasion of Shun-ichi Amari's 80th Birthday, IGAIA IV Liblice, Czech Republic, June 2016 / Nihat Ay... (eds.)Cham : Springer, 2018. - pp. 75-115
(Springer proceedings in mathematics and statistics ; 252)
inBook
2018
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Uncertainty and stochasticity of optimal policies
In: Proceedings of the 11th workshop on uncertainty processing WUPES '18, June 6-9, 2018 / Václav Kratochvíl (ed.)Praha : MatfyzPress, 2018. - pp. 133-140
inJournal
2018
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Mixtures and products in two graphical models
In: Journal of algebraic statistics, 9 (2018) 1, pp. 1-20inBook
2017
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Morphological computation : the good, the bad, and the ugly
In: 2017 IEEE/RSJ international conference on intelligent robots and systems (IROS) : Vancouver, BC, Canada ; September 24-28, 2017New York, NY : IEEE, 2017. - pp. 464-469
inJournal
2017
Journal Open Access
Dimension of marginals of Kronecker product models
In: SIAM journal on applied algebra and geometry, 1 (2017) 1, pp. 126-151inBook
2017
Repository Open Access
Geometry of policy improvement
In: Geometric science of information : Third International Conference, GSI 2017, Paris, France, November 7-9, 2017, proceedings / Frank Nielsen... (eds.)Cham : Springer, 2017. - pp. 282-290
(Lecture notes in computer science ; 10589)
inJournal
2017
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Hierarchical models as marginals of hierarchical models
In: International journal of approximate reasoning, 88 (2017), pp. 531-546inBook
2017
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Notes on the number of linear regions of deep neural networks
In: 2017 international conference on sampling theory and applications (SampTA) / Gholamreza Anbarjafari... (eds.)Piscataway, NJ : IEEE, 2017. - pp. 156-159
inJournal
2017
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Restricted Boltzmann machines [In: Algebraic statistics ; 16 April - 22 April 2017 ; report no. 20/2017]
In: Oberwolfach reports, 14 (2017) 2, pp. 1241-1242inBook
2017
Stochasticity of optimal policies for POMDPs
In: RLDM 2017 : 3rd multidisciplinary conference on reinforcement learning and decision making ; June 11-14, 2017 ; Ann Arbor, Michigan, USAMichigan : University, 2017. - T97
inJournal
2016
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Evaluating morphological computation in muscle and DC-motor driven models of hopping movements
In: Frontiers in robotics and AI, 3 (2016), p. 42inBook
2016
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Geometry of Boltzmann machines
In: International conference on information geometry and its applications IV : Liblice, June 12-17, 2016 ; in honor of Shun-ichi Amari / Nihat Ay... (eds.)Praha : Matfyzpress, 2016. - pp. 25-25
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2016
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Information theoretically aided reinforcement learning for embodied agents
inJournal
2016
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Mode poset probability polytopes
In: Journal of algebraic statistics, 7 (2016) 1, pp. 1-13inBook
2015
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A comparison of neural network architectures
In: Deep learning Workshop, ICML '15, Vauban Hall at Lille Grande Palais, France, July 10 and 11, 20152015.
inJournal
2015
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A theory of cheap control in embodied systems
In: PLoS computational biology, 11 (2015) 9, e1004427inBook
2015
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Deep narrow Boltzmann machines are universal approximators
In: Third international conference on learning representations - ICLR 2015 : May 7-9 2015, San Diego, CA. USASan Diego : ICLR, 2015.
inJournal
2015
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Discrete restricted Boltzmann machines
In: Journal of machine learning research, 16 (2015), pp. 653-672Preprint
2015
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Geometry and determinism of optimal stationary control in partially observable Markov decision processes
inJournal
2015
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Geometry and expressive power of conditional restricted Boltzmann machines
In: Journal of machine learning research, 16 (2015), pp. 2405-2436inBook
2015
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Hierarchical models as marginals of hierarchical models
In: Proceedings of the 10th workshop on uncertainty processing WUPES '15, Moninec, Czech Republic, September 16-19, 2015 / Václav Kratochvíl (ed.)Praha : Oeconomica, 2015. - pp. 131-145
inBook
2015
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Mode poset probability polytopes
In: Proceedings of the 10th workshop on uncertainty processing WUPES '15, Moninec, Czech Republic, September 16-19, 2015 / Václav Kratochvíl (ed.)Praha : Oeconomica, 2015. - pp. 147-154
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2015
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Universal approximation of Markov kernels by shallow stochastic feedforward networks
inJournal
2015
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When does a mixture of products contain a product of mixtures?
In: SIAM journal on discrete mathematics, 29 (2015) 1, pp. 321-347Preprint
2014
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Sequential recurrence-based multidimensional universal source coding of Lempel-Ziv type
inBook
2014
Geometry of hidden-visible products of statistical models
In: Algebraic Statistics 2014 : May 19-22Chicago, IL : Illinois Institute of Technology, 2014.
inJournal
2014
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On the Fisher metric of conditional probability polytopes
In: Entropy, 16 (2014) 6, pp. 3207-3233inBook
2014
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On the number of linear regions of deep neural networks
In: NIPS 2014 : Proceedings of the 27th international conference on neural information processing systems - volume 2 ; Montreal, Quebec, Canada, December 8th-13thCambridge, MA : MIT Press, 2014. - pp. 2924-2932
inJournal
2014
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Scaling of model approximation errors and expected entropy distances
In: Kybernetika, 50 (2014) 2, pp. 234-245inJournal
2014
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Universal approximation depth and errors of narrow belief networks with discrete units
In: Neural computation, 26 (2014) 7, pp. 1386-1407inBook
2014
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On the number of inference regions of deep feed forward networks with piece-wise linear activations
In: Second international conference on learning representations - ICLR 2014 : 14-16 April 2014, Banff, CanadaBanff : ICLR, 2014.
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2013
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Selection criteria for neuromanifolds of stochastic dynamics
In: Advances in cognitive neurodynamics III : proceedings of the 3rd International Conference on Cognitive Neurodynamics 2011 ; [June 9-13, 2011, Hilton Niseko Village, Hokkaido, Japan] / Yoko Yamaguchi (ed.)Dordrecht : Springer, 2013. - pp. 147-154
(Advances in cognitive neurodynamics)
inJournal
2013
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Universally typical sets for ergodic sources of multidimensional data
In: Kybernetika, 49 (2013) 6, pp. 868-882inBook
2013
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Maximal information divergence from statistical models defined by neural networks
In: Geometric science of information : first international conference, GSI 2013, Paris, France, August 28-30, 2013. Proceedings / Frank Nielsen... (eds.)Berlin [u. a.] : Springer, 2013. - pp. 759-766
(Lecture notes in computer science ; 8085)
inJournal
2013
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Mixture decompositions of exponential families using a decomposition of their sample spaces
In: Kybernetika, 49 (2013) 1, pp. 23-39inBook
2012
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Kernels and submodels of deep belief networks
In: NIPS 2012 : Deep learning and unsupervised feature learning workshop : [be held in conjunction with neural information processing systems on December 8, 2012 (TBD) at Lake Tahoe, USA]La Jolla, CA : Neural Information Processing Systems, 2012.
Academic
2012
On the expressive power of discrete mixture models, restricted Boltzmann machines, and deep belief networks - a unified mathematical treatment
Dissertation, Universität Leipzig, 2012inBook
2012
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Scaling of model approximation errors and expected entropy distances
In: Proceedings of the 9th workshop on uncertainty processing WUPES '12 : Marianske Lazne, Czech Republik ; 12-15th September 2012Praha : Academy of Sciences of the Czech Republik / Institute of Information Theory and Automation, 2012. - pp. 137-148
inBook
2012
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When does a mixture of products contain a product of mixtures?
In: NIPS 2012 : Deep learning and unsupervised feature learning workshop : [be held in conjunction with neural information processing systems on December 8, 2012 (TBD) at Lake Tahoe, USA]La Jolla, CA : Neural Information Processing Systems, 2012.
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2011
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Expressive power and approximation errors of restricted Boltzmann machines
In: Advances in neural information processing systems 24 : NIPS 2011 ; 25th annual conference on neural information processing systems 2011, Granada, Spain December 12th - 15th / John Shawe-Taylor (ed.)La Jolla, CA : Neural Information Processing Systems, 2011. - pp. 415-423
inJournal
2011
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Refinements of universal approximation results for deep belief networks and restricted Boltzmann machines
In: Neural computation, 23 (2011) 5, pp. 1306-1319inBook
2010
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Mixture models and representational power of RBM's, DBN's, and DBM's
In: NIPS 2010 : Deep learning and unsupervised feature learning workshop ; December 19, 2010, Hilton, Vancouver, Canada[s. l.] : NIPS, 2010. - pp. 1-9
inBook
2008
Theory of transport and photon-statistics in a biased nanostructure
In: 2008 International Nano-Optoelectronics workshop (iNOW 2008)Piscataway, NJ : IEEE, 2008. - pp. 243-244
Academic
2008
Theory of transport and photon-statistics in a biased nanostructure
Diploma thesis, Universität Berlin, 2008Academic
2007
Q-Sanov theorem for d \(\geq\) 2
Diploma thesis, Universität Berlin, 2007Open Access Types
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