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Adversarial Networks and Autoencoders: The Primal-Dual Relationship and Generalization Bounds [article]

Hisham Husain, Richard Nock, Robert C. Williamson
2019 arXiv   pre-print
Our findings thus present the first primal-dual relationship between GANs and Autoencoder models, comment on generalization abilities and make a step towards unifying these models.  ...  First, we find that the f-GAN and WAE objectives partake in a primal-dual relationship and are equivalent under some assumptions, which then allows us to explicate the success of WAE.  ...  (20) can be reparametrized by setting ϕ(x) ← x 2 /2−ϕ(x) and ψ(y) ← y 2 /2 − ψ(y), and so the constraint changes: The optimization problem in Equation  ... 
arXiv:1902.00985v2 fatcat:monu5zgn6bc5lmfavwmgwgroam

From optimal transport to generative modeling: the VEGAN cookbook [article]

Olivier Bousquet, Sylvain Gelly, Ilya Tolstikhin, Carl-Johann Simon-Gabriel, Bernhard Schoelkopf
2017 arXiv   pre-print
Our theoretical results include (a) a better understanding of the commonly observed blurriness of images generated by VAEs, and (b) establishing duality between Wasserstein GAN (Arjovsky and Bottou, 2017  ...  We study unsupervised generative modeling in terms of the optimal transport (OT) problem between true (but unknown) data distribution P_X and the latent variable model distribution P_G.  ...  Acknowledgments The authors are thankful to Mateo Rojas-Carulla and Fei Sha for stimulating discussions. CJSG is supported by a Google European Doctoral Fellowship in Causal Inference.  ... 
arXiv:1705.07642v1 fatcat:bzjdm53wc5hvnfaj2q323bnhve

Regularising Inverse Problems with Generative Machine Learning Models [article]

Margaret Duff, Neill D. F. Campbell, Matthias J. Ehrhardt
2022 arXiv   pre-print
In our numerical experiments, we evaluate three common generative models, autoencoders, variational autoencoders and generative adversarial networks, against our desired criteria.  ...  The success of generative regularisers depends on the quality of the generative model and so we propose a set of desired criteria to assess models and guide future research.  ...  NDFC acknowledges support from the EPSRC CAMERA Research Centre (EP/M023281/1 and EP/T022523/1) and the Royal Society.  ... 
arXiv:2107.11191v2 fatcat:xno43ggolfbclk6chsq4aiivam

Sinkhorn AutoEncoders [article]

Giorgio Patrini, Rianne van den Berg, Patrick Forré, Marcello Carioni, Samarth Bhargav, Max Welling, Tim Genewein, Frank Nielsen
2019 arXiv   pre-print
We therefore advertise this framework, which holds for any metric space and prior, as a sweet-spot of current generative autoencoding objectives.  ...  encoder aggregated posterior and the prior in latent space, plus a reconstruction error.  ...  WAE and WGAN objectives are linked respectively to primal and dual formulations of OT. Figure 1 1 : a) Swiss Roll and its b) squared and c) spherical embeddings learned by Sinkhorn encoders.  ... 
arXiv:1810.01118v3 fatcat:ne5cibw7gnai3nbbho35nsp6ou

Wasserstein Auto-Encoders [article]

Ilya Tolstikhin and Olivier Bousquet and Sylvain Gelly and Bernhard Schoelkopf
2019 arXiv   pre-print
WAE minimizes a penalized form of the Wasserstein distance between the model distribution and the target distribution, which leads to a different regularizer than the one used by the Variational Auto-Encoder  ...  We compare our algorithm with several other techniques and show that it is a generalization of adversarial auto-encoders (AAE).  ...  The authors also thank Josip Djolonga, Carlos Riquelme, and Paul Rubenstein for carrying out extended experimental evaluations (bigWAE and bigVAE) reported in Table 1 and Section D.  ... 
arXiv:1711.01558v4 fatcat:qdhtlfdzvjgr7j2sxz7cpmuqy4

Model-based Reconstruction with Learning: From Unsupervised to Supervised and Beyond [article]

Zhishen Huang and Siqi Ye and Michael T. McCann and Saiprasad Ravishankar
2021 arXiv   pre-print
This review includes many recent methods based on unsupervised learning, and supervised learning, as well as a framework to combine multiple types of learned models together.  ...  ., in magnetic resonance imaging and tomographic modalities) and exploit models of the imaging system's physics together with statistical models of measurements, noise and often relatively simple object  ...  primal-dual methods [1] , where proximal operators are realized by a parametrized residual neural network with the parameters learned from training; iterative reweighted least squares [4] , where the  ... 
arXiv:2103.14528v1 fatcat:kxzugqnnijdwfn62jwrl45zmge

Energy-Based Sequence GANs for Recommendation and Their Connection to Imitation Learning [article]

Jaeyoon Yoo, Heonseok Ha, Jihun Yi, Jongha Ryu, Chanju Kim, Jung-Woo Ha, Young-Han Kim, Sungroh Yoon
2017 arXiv   pre-print
Recommender systems aim to find an accurate and efficient mapping from historic data of user-preferred items to a new item that is to be liked by a user.  ...  Towards this goal, energy-based sequence generative adversarial nets (EB-SeqGANs) are adopted for recommendation by learning a generative model for the time series of user-preferred items.  ...  E P [f (S, A)] = E P E [f (S, A)] (7) where H (P) denotes the entropy of P. Due to Slater's condition strong duality holds, and one can obtain primal and dual solutions from KKT condition [4] .  ... 
arXiv:1706.09200v1 fatcat:j7bep3vgurcend7axrjk5i3o3m

Unsupervised Deep Learning Methods for Biological Image Reconstruction and Enhancement [article]

Mehmet Akçakaya, Burhaneddin Yaman, Hyungjin Chung, Jong Chul Ye
2021 arXiv   pre-print
In this paper, we overview these approaches from a coherent perspective in the context of classical inverse problems, and discuss their applications to biological imaging, including electron, fluorescence  ...  and deconvolution microscopy, optical diffraction tomography and functional neuroimaging.  ...  Similar to f -GAN, rather than solving the complicated primal problem, a dual problem is solved.  ... 
arXiv:2105.08040v2 fatcat:56gnjk7y45a7jifx4s6npb6zxy

Deep learning in photoacoustic imaging: a review

Handi Deng, Hui Qiao, Qionghai Dai, Cheng Ma
2021 Journal of Biomedical Optics  
We provide (i) a comprehensive overview of the DL techniques that have been applied in PAI, (ii) references for designing DL models for various PAI tasks, and (iii) a summary of the future challenges and  ...  When applied in PAI, DL can effectively process images, improve reconstruction quality, fuse information, and assist quantitative analysis. DL has become a powerful tool in PAI.  ...  The authors would like to thank Youwei Bao and Xiangxiu Zhang for assistance with figure copyright application.  ... 
doi:10.1117/1.jbo.26.4.040901 pmid:33837678 pmcid:PMC8033250 fatcat:uwutps2wfbfztfo6bvbv6g5f6y

Model-Based Domain Generalization [article]

Alexander Robey and George J. Pappas and Hamed Hassani
2021 arXiv   pre-print
Toward addressing this challenge, we consider the domain generalization problem, wherein predictors are trained using data drawn from a family of related training domains and then evaluated on a distinct  ...  We show that under a natural model of data generation and a concomitant invariance condition, the domain generalization problem is equivalent to an infinite-dimensional constrained statistical learning  ...  This architecture comprises two GANs and two autoencoding networks.  ... 
arXiv:2102.11436v5 fatcat:vsl7jcofe5dw3jndbtvuph24cu

Geometric Losses for Distributional Learning [article]

Arthur Mensch, Mathieu Blondel, Gabriel Peyré (DMA, CNRS)
2019 arXiv   pre-print
a metric or cost between classes.  ...  Building upon recent advances in entropy-regularized optimal transport, and upon Fenchel duality between measures and continuous functions , we propose a generalization of the logistic loss that incorporates  ...  Acknowledgements The work of A. Mensch and G. Peyré has been supported by the European Research Council (ERC project NORIA). A. Mensch thanks Jean Feydy and Thibault Séjourné for fruitful discussions.  ... 
arXiv:1905.06005v1 fatcat:bp4o56snqnfkfol5lywlfvp3fy

A Tutorial on Ultra-Reliable and Low-Latency Communications in 6G: Integrating Domain Knowledge into Deep Learning [article]

Changyang She and Chengjian Sun and Zhouyou Gu and Yonghui Li and Chenyang Yang and H. Vincent Poor and Branka Vucetic
2021 arXiv   pre-print
In particular, a holistic framework that takes into account latency, reliability, availability, scalability, and decision making under uncertainty is lacking.  ...  We first provide some background of URLLC and review promising network architectures and deep learning frameworks for 6G.  ...  in terms of lower BLER Part II: Primal-dual Method for Radio Resource Allocation (Constrained Functional Optimization) Year Reference Summary Performance 2019 [63] The primal-dual method is  ... 
arXiv:2009.06010v2 fatcat:kusavm5a45h2vazoyu6k3q2dxe

Moreau-Yosida f-divergences [article]

Dávid Terjék
2021 arXiv   pre-print
Hellinger, Jensen-Shannon, Jeffreys, triangular discrimination and total variation divergences as GANs trained on CIFAR-10, leading to competitive results and a simple solution to the problem of uniqueness  ...  The corresponding variational formulas provide a generalization of a number of recent results, novel special cases of interest and a relaxation of the hard Lipschitz constraint.  ...  URL 8333-a-primal-dual-link-between-gans-and-autoencoders. Jost, J. and Li-Jost, X. Calculus of Variations. Cambridge Studies in Advanced Mathematics.  ... 
arXiv:2102.13416v2 fatcat:qn3y27yxirdihbeulitinlbkfe

Microgrid management with weather-based forecasting of energy generation, consumption and prices [article]

Jonathan Dumas
2021 arXiv   pre-print
It is divided into two main parts to propose directions to address both research questions (1) a forecasting part; (2) a planning and control part.  ...  A high share of renewables is challenging for power systems that have been designed and sized for dispatchable units.  ...  called the primal, and another LP problem, called the dual.  ... 
arXiv:2107.01034v7 fatcat:c5a7d2w2uzez3par3q6gs3elaq

Learning Robust Visual-semantic Mapping for Zero-shot Learning [article]

Jingcai Guo
2021 arXiv   pre-print
In this thesis, we explore effective ways to mitigate the domain shift problem and learn a robust mapping function between the visual and semantic feature spaces.  ...  In ZSL, the common practice is to train a mapping function between the visual and semantic feature spaces with labeled seen class examples.  ...  DASCN [126] proposes two GAN networks, namely the primal GAN and dual GAN in a unified framework, for generalized zero-shot recognition. Schonfeld et al.  ... 
arXiv:2104.05668v1 fatcat:uq5msriuovettbwar46qzjfcbm
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