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Global Guarantees for Enforcing Deep Generative Priors by Empirical Risk [article]

Paul Hand, Vladislav Voroninski
2018 arXiv   pre-print
We examine the theoretical properties of enforcing priors provided by generative deep neural networks via empirical risk minimization.  ...  of enforcing deep generative priors and a rigorous understanding of non-linear inverse problems.  ...  Acknowledgment PH is partially supported by NSF Grant DMS-1464525.  ... 
arXiv:1705.07576v3 fatcat:7zvv7paszbcubnoabbntizunvu

Theoretical Issues in Deep Networks: Approximation, Optimization and Generalization [article]

Tomaso Poggio, Andrzej Banburski, Qianli Liao
2019 arXiv   pre-print
It covers the following questions: 1) representation power of deep networks 2) optimization of the empirical risk 3) generalization properties of gradient descent techniques --- why the expected error  ...  Our approach, which is supported by several independent new results, offers a solution to the puzzle about generalization performance of deep overparametrized ReLU networks, uncovering the origin of the  ...  It covers the following questions: 1) representation power of deep networks 2) optimization of the empirical risk 3) generalization properties of gradient descent techniques -how can deep networks generalize  ... 
arXiv:1908.09375v1 fatcat:mozi3aotovhmpdd2kzimyi5lbu

A Likelihood-Free Inference Framework for Population Genetic Data using Exchangeable Neural Networks

Jeffrey Chan, Valerio Perrone, Jeffrey P Spence, Paul A Jenkins, Sara Mathieson, Yun S Song
2018 Advances in Neural Information Processing Systems  
Recent work in population genetics has centered on designing inference methods for relatively simple model classes, and few scalable general-purpose inference techniques exist for more realistic, complex  ...  These challenges are traditionally tackled by likelihood-free methods that use scientific simulators to generate datasets and reduce them to hand-designed, permutation-invariant summary statistics, often  ...  Acknowledgements We thank Ben Graham for helpful discussions and Yuval Simons for his suggestion to use the decile.  ... 
pmid:33244210 pmcid:PMC7687905 fatcat:ugwufqi7ijfetfrqjmb2kiznpm

FETA: Fairness Enforced Verifying, Training, and Predicting Algorithms for Neural Networks [article]

Kiarash Mohammadi, Aishwarya Sivaraman, Golnoosh Farnadi
2022 arXiv   pre-print
Contrary to prior work that enforces fairness only on points around test or train data, we are able to enforce and guarantee fairness on all points in the input domain.  ...  A popular approach for enforcing fairness is to translate a fairness notion into constraints over the parameters of the model.  ...  Acknowledgments and Disclosure of Funding Funding support for project activities has been partially provided by Canada CIFAR AI Chair, Google scholar award, and NSERC Discovery Grants program.  ... 
arXiv:2206.00553v1 fatcat:d6aj65n35vgh5cam362qxinzp4

Phase Consistent Ecological Domain Adaptation

Yanchao Yang, Dong Lao, Ganesh Sundaramoorthi, Stefano Soatto
2020 2020 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR)  
Incorporating these two priors in a standard domain adaptation framework improves performance across the board in the most common unsupervised domain adaptation benchmarks for semantic segmentation. 1  ...  The first criterion, inspired by visual psychophysics, is that the map between the two image domains be phase-preserving.  ...  Acknowledgements Research supported by ARO W911NF-17-1-0304 and ONR N00014-19-1-2066. Dong Lao is supported by KAUST through the VCC Center Competitive Funding.  ... 
doi:10.1109/cvpr42600.2020.00903 dblp:conf/cvpr/YangLSS20 fatcat:vlnypnij3zf67j3ody5gud2yca

Phase Consistent Ecological Domain Adaptation [article]

Yanchao Yang, Dong Lao, Ganesh Sundaramoorthi, Stefano Soatto
2020 arXiv   pre-print
Incorporating these two priors in a standard domain adaptation framework improves performance across the board in the most common unsupervised domain adaptation benchmarks for semantic segmentation.  ...  The first criterion, inspired by visual psychophysics, is that the map between the two image domains be phase-preserving.  ...  Acknowledgements Research supported by ARO W911NF-17-1-0304 and ONR N00014-19-1-2066. Dong Lao is supported by KAUST through the VCC Center Competitive Funding.  ... 
arXiv:2004.04923v1 fatcat:kt5qeiilivavpbfavsxjem56by

Nonasymptotic Guarantees for Spiked Matrix Recovery with Generative Priors [article]

Jorio Cocola, Paul Hand, Vladislav Voroninski
2020 arXiv   pre-print
Enforcing additional prior information on the rank-one component is often key to guaranteeing good recovery performance.  ...  Specifically, we establish a favorable global optimization landscape for a nonlinear least squares objective, provided the number of samples is on the order of the dimensionality of the input to the generative  ...  Global guarantees for enforcing deep generative priors by empirical risk, 2017. [30] Paul Hand and Vladislav Voroninski.  ... 
arXiv:2006.07953v2 fatcat:bj2chmc5uvhk5kgn3wdfymbaiy

A Likelihood-Free Inference Framework for Population Genetic Data using Exchangeable Neural Networks [article]

Jeffrey Chan, Valerio Perrone, Jeffrey P Spence, Paul A Jenkins, Sara Mathieson, Yun S Song
2018 bioRxiv   pre-print
Inference for population genetics models is hindered by computationally intractable likelihoods.  ...  We leverage access to scientific simulators to learn such likelihood-free function mappings, and establish a general framework for inference in a variety of simulation-based tasks.  ...  Acknowledgements We thank Ben Graham for helpful discussions and Yuval Simons for his suggestion to use the decile.  ... 
doi:10.1101/267211 fatcat:hofwzezsqfaybjrztesvjqe3ti

Neural Proximal Gradient Descent for Compressive Imaging [article]

Morteza Mardani, Qingyun Sun, Shreyas Vasawanala, Vardan Papyan, Hatef Monajemi, John Pauly, David Donoho
2018 arXiv   pre-print
Our architecture significantly outperforms conventional non-recurrent deep ResNets by 2dB SNR; it is also trained much more rapidly. 3.  ...  Learning a good inverse mapping from training data faces severe challenges, including: (i) scarcity of training data; (ii) need for plausible reconstructions that are physically feasible; (iii) need for  ...  Joseph Cheng for fruitful discussions and their feedback about the MRI reconstruction and software implementation.  ... 
arXiv:1806.03963v1 fatcat:nd2yiahcd5bprj7lkpwparnsza

Toward Learning Trustworthily from Data Combining Privacy, Fairness, and Explainability: An Application to Face Recognition

Danilo Franco, Luca Oneto, Nicolò Navarin, Davide Anguita
2021 Entropy  
For this purpose, in this work, we work toward the development of systems able to ensure trustworthiness by delivering privacy, fairness, and explainability by design.  ...  ., gender, ethnicity, political/sexual orientation), or require one to provide an explanation for a decision, are daily undermined by the use of increasingly complex and less understandable yet more accurate  ...  and to the right of explanation, and by risks of attacks in current artificial intelligence systems.  ... 
doi:10.3390/e23081047 fatcat:vl5q3ys6xbha7oxgj4ba67mkne

Physics-Informed Probabilistic Learning of Linear Embeddings of Non-linear Dynamics With Guaranteed Stability [article]

Shaowu Pan, Karthik Duraisamy
2019 arXiv   pre-print
The Koopman operator has emerged as a powerful tool for the analysis of nonlinear dynamical systems as it provides coordinate transformations to globally linearize the dynamics.  ...  We then enforce a structural parameterization that renders the realization of the Koopman operator provably stable.  ...  Computing resources were provided by the NSF via grant 1531752 MRI: Acquisition of Conflux, A Novel Platform for Data-Driven Computational Physics.  ... 
arXiv:1906.03663v4 fatcat:52gjlmkjcvanzj53htpdbwlkvq

Rate-Optimal Denoising with Deep Neural Networks [article]

Reinhard Heckel, Wen Huang, Paul Hand, Vladislav Voroninski
2019 arXiv   pre-print
We also demonstrate in numerical experiments that this denoising performance is, indeed, achieved by generative priors learned from data.  ...  Deep neural networks provide state-of-the-art performance for image denoising, where the goal is to recover a near noise-free image from a noisy observation.  ...  Acknowledgements RH is partially supported by a NSF Grant ISS-1816986 and PH is partially supported by a NSF CAREER Grant DMS-1848087 as well as NSF Grant DMS-1464525, and the authors would like to  ... 
arXiv:1805.08855v2 fatcat:flvt4fg5ebchtnf4kxfd4sgivq

A Survey on Differentially Private Machine Learning [Review Article]

Maoguo Gong, Yu Xie, Ke Pan, Kaiyuan Feng, A.K. Qin
2020 IEEE Computational Intelligence Magazine  
in prior works.  ...  O d / 1 3 compared to ( ) O d for Summary. Output and objective perturbation are common techniques in differential private empirical risk mini mization.  ... 
doi:10.1109/mci.2020.2976185 fatcat:72lxqnelszctfghmhdhdi3bk44

Toward a System Design Science [chapter]

Joseph Sifakis
2014 Lecture Notes in Computer Science  
The second, proceduralization, generates an executable description for realizing the anticipated behavior by executing sequences of elementary functions.  ...  For some application areas, they can be formalized by using logics.  ...  They allow correctness almost for free. Notice that property enforcement enables designers to ensure that compositions of components meet a specific global requirement.  ... 
doi:10.1007/978-3-642-54848-2_15 fatcat:4g2ky252ezfdlihl7ig7xbteze

A Likelihood-Free Inference Framework for Population Genetic Data using Exchangeable Neural Networks [article]

Jeffrey Chan, Valerio Perrone, Jeffrey P. Spence, Paul A. Jenkins, Sara Mathieson, Yun S. Song
2018 arXiv   pre-print
Recent work in population genetics has centered on designing inference methods for relatively simple model classes, and few scalable general-purpose inference techniques exist for more realistic, complex  ...  These challenges are traditionally tackled by likelihood-free methods that use scientific simulators to generate datasets and reduce them to hand-designed, permutation-invariant summary statistics, often  ...  More formally, define the Bayes risk for prior π(θ) as Rπ∗ = inf T Ex Eθ∼π [l(θ, T (x)], with l being the loss function and T an estimator.  ... 
arXiv:1802.06153v2 fatcat:uv63a54qrfghzgotg5q3l2cv2a
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