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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
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Combining resampling and reweighting for faithful stochastic optimization
In: Communications in mathematical sciences, 21 (2023) 6, pp. 1569-1588inJournal
2023
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Quantitative steepness, semi-FKPP reactions, and pushmi-pullyu fronts
In: Archive for rational mechanics and analysis, 247 (2023) 5, p. 88inJournal
2023
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Competitive equilibrium always exists for combinatorial auctions with graphical pricing schemes
In: La matematica, 2 (2023) 1, pp. 1-30Preprint
2023
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Intersection bodies of polytopes : translations and convexity
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2023
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Multivariate volume, Ehrhart, and \(h*\)-polynomials of polytropes
In: Journal of symbolic computation, 114 (2023), pp. 209-230Preprint
2023
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The best ways to slice a polytope
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2023
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Tropical positivity and determinantal varieties
In: Algebraic combinatorics, 6 (2023) 4, pp. 999-1040Academic
2023
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Tropical positivity and semialgebraic sets from polytopes
Dissertation, Universität Leipzig, 2023inJournal
2023
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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
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2023
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Function space and critical points of linear convolutional networks
(SIAM journal on discrete mathematics)inJournal
2023
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Anomaly detection in dynamic graphs via transformer
In: IEEE transactions on knowledge and data engineering, 35 (2023) 12, pp. 12081-12094inBook
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
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2023
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Achieving high accuracy with PINNs via energy natural gradients
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2023
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Continuity and additivity properties of information decompositions
In: International journal of approximate reasoning, 161 (2023), p. 108979Academic
2023
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Expected complexity and gradients of deep maxout neural networks and implications to parameter initialization
Dissertation, Universität Leipzig, 2023Preprint
2023
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Expected gradients of maxout networks and consequences to parameter initialization
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2023
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Invariance properties of the natural gradient in overparametrised systems
In: Information geometry, 6 (2023) 1, pp. 51-67inJournal
2023
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MathNet : Haar-like wavelet multiresolution analysis for graph representation learning
In: Knowledge-based systems, 273 (2023), p. 110609inBook
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
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2022
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Implicit bias of MSE gradient optimization in underparameterized neural networks
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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
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2022
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Uniform convergence guarantees for the deep ritz method for nonlinear problems
In: Advances in continuous and discrete models : theory and modern applications, 2022 (2022), p. 49Preprint
2022
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Enumeration of max-pooling responses with generalized permutohedra
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2022
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FoSR : first-order spectral rewiring for addressing oversquashing in GNNs
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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)
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2022
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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. 618-649inBook
2022
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Error estimates for the Deep Ritz Method with boundary penalty
In: 3rd annual conference on mathematical and scientific machine learning : 15-17 August 2022, Peking University, Beijing, China[s. l.] : PMLR, 2022. - pp. 215-230
(Proceedings of machine learning research ; 190)
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2022
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Notes on exact boundary values in residual minimisation
In: 3rd annual conference on mathematical and scientific machine learning : 15-17 August 2022, Peking University, Beijing, China[s. l.] : PMLR, 2022. - pp. 231-240
(Proceedings of machine learning research ; 190)
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2022
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Solving infinite-horizon POMDPs with memoryless stochastic policies in state-action space
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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
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2022
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Characterizing the spectrum of the NTK via a power series expansion
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2022
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High dimensional change-point detection: a complete graph approach
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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
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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. 45inJournal
2022
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Decimated framelet system on graphs and fast \(G\)-framelet transforms
In: Journal of machine learning research, 23 (2022), p. 18inJournal
2021
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Fractional stochastic partial differential equation for random tangent fields on the sphere
In: Theory of probability and mathematical statistics, 104 (2021), pp. 3-22Preprint
2021
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Pushed, pulled and pushmi-pullyu fronts of the Burgers-FKPP equation
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2021
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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
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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
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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
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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)
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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
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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)
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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)
inJournal
2021
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Distributed filtered hyperinterpolation for noisy data on the sphere
In: SIAM journal on numerical analysis, 59 (2021) 2, pp. 634-659inJournal
2021
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Path integral based convolution and pooling for graph neural networks
In: Journal of statistical mechanics, 2021 (2021) 12, p. 124011Preprint
2021
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A note on connectivity of sublevel sets in deep learning
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2021
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On the proof of global convergence of gradient descent for deep ReLU networks with linear widths
In: ICML 2021 : Proceedings of the 38th international conference on machine learning ; 18-24 July 2021[s. l.] : PMLR, 2021. - pp. 8056-8062
(Proceedings of machine learning research ; 139)
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2021
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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)
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2021
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When are solutions connected in deep 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. 20956-20969
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
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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)
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2020
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Power-law scaling of brain wave activity associated with mental fatigue
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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
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2020
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computeUI [Computer code]
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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
Academic
2020
Unique information and the Blackwell order
Dissertation, Universität Leipzig, 2020inBook
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
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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)
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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. 89-117inBook
2020
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Path integral based convolution and pooling for graph neural networks
In: Advances in neural information processing systems 33 : NeurIPS 2020 ; annual conference on neural information processing systems 2020, December 6-12, 2020, virtual / Hugo Larochelle (ed.)[S. L.] : NeurIPS, 2020. - pp. 16421-16433
inJournal
2020
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Factorized mutual information maximization
In: Kybernetika, 56 (2020) 5, pp. 948-978inBook
2020
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Can neural networks learn persistent homology features?
In: NeurIPS 2020 : Workshop on topological data analysis and beyond ; 11 December 2020[S. L.] : NeurIPS, 2020.
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2020
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Deep Ritz revisited
In: ICLR 2020 workshop on integration of deep neural models and differential equations : Millennium Hall, Addis Ababa, Ethiopia ; 26th April 2020[S. L.] : ICLR, 2020.
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2020
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On the space-time expressivity of ResNets
In: ICLR 2020 workshop on integration of deep neural models and differential equations : Millennium Hall, Addis Ababa, Ethiopia ; 26th April 2020[S. L.] : ICLR, 2020.
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2020
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Global convergence of deep networks with one wide layer followed by pyramidal topology
In: Advances in neural information processing systems 33 : NeurIPS 2020 ; annual conference on neural information processing systems 2020, December 6-12, 2020, virtual / Hugo Larochelle (ed.)[S. L.] : NeurIPS, 2020. - pp. 11961-11972
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2020
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On the approximation lower bound for neural nets with random weights
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2020
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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)
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2019
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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
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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)
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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.
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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)
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2019
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How well do WGANs estimate the Wasserstein metric?
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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.
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2019
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Unique information and secret key decompositions
In: IEEE international symposium on information theory (ISIT) from July 7 to 12, 2019 ; Paris, FrancePiscataway, NY : IEEE, 2019. - pp. 3042-3046
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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
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2018
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Natural gradient via optimal transport
In: Information geometry, 1 (2018) 2, pp. 181-214inBook
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)
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2018
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Mixtures and products in two graphical models
In: Journal of algebraic statistics, 9 (2018) 1, pp. 1-20Open Access Types
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