Nonparametric Density Estimation under Adversarial Losses release_bu34qw73cjdovoc2lb3vc2ob7y

by Shashank Singh, Ananya Uppal, Boyue Li, Chun-Liang Li, Manzil Zaheer, Barnabás Póczos

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abstracts [{'sha1': 'c8e9b28ee26bcaae0c8f2a2c28f50082bf7634e4', 'content': 'We study minimax convergence rates of nonparametric density estimation under\na large class of loss functions called "adversarial losses", which, besides\nclassical L^p losses, includes maximum mean discrepancy (MMD),\nWasserstein distance, and total variation distance. These losses are closely\nrelated to the losses encoded by discriminator networks in generative\nadversarial networks (GANs). In a general framework, we study how the choice of\nloss and the assumed smoothness of the underlying density together determine\nthe minimax rate. We also discuss implications for training GANs based on deep\nReLU networks, and more general connections to learning implicit generative\nmodels in a minimax statistical sense.', 'mimetype': 'text/plain', 'lang': 'en'}, {'sha1': 'b7180367e38f38899269e78e451bbbae4af59e93', 'content': 'We study minimax convergence rates of nonparametric density estimation under\na large class of loss functions called "adversarial losses", which, besides\nclassical $\\mathcal{L}^p$ losses, includes maximum mean discrepancy (MMD),\nWasserstein distance, and total variation distance. These losses are closely\nrelated to the losses encoded by discriminator networks in generative\nadversarial networks (GANs). In a general framework, we study how the choice of\nloss and the assumed smoothness of the underlying density together determine\nthe minimax rate. We also discuss implications for training GANs based on deep\nReLU networks, and more general connections to learning implicit generative\nmodels in a minimax statistical sense.', 'mimetype': 'application/x-latex', 'lang': 'en'}]
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release_date 2018-10-28
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title Nonparametric Density Estimation under Adversarial Losses
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arxiv.base_id 1805.08836
arxiv.categories ['math.ST', 'cs.IT', 'math.IT', 'stat.ML', 'stat.TH']