Generative Adversarial Nets from a Density Ratio Estimation Perspective

By Masatoshi Uehara, Issei Sato, Masahiro Suzuki, Kotaro Nakayama, Yutaka Matsuo. 2016

106 citations recorded by the source corpus.

Generative adversarial networks (GANs) are successful deep generative models. GANs are based on a two-player minimax game. However, the objective function derived in the original motivation is changed to obtain stronger gradients when learning the generator. We propose a novel algorithm that repeats the density ratio estimation and f-divergence minimization. Our algorithm offers a new perspective toward the understanding of GANs and is able to make use of multiple viewpoints obtained in the research of density ratio estimation, e.g. what divergence is stable and relative density ratio is useful.

Subfields: Artificial Intelligence, Computer Vision and Pattern Recognition, Statistical and Nonlinear Physics, Generative Models

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Citations in the corpus

Spectral Normalization for Generative Adversarial Networks (2018, background): “For example, (Nowozin et al., 2016; Uehara et al., 2016; Mohamed & Laksh-minarayanan, 2017) revealed that the training of the discriminator amounts to the training of a good estimator for the density ratio between the model distribution and the target.”
Conditional Image Synthesis with Auxiliary Classifier GANs (2016, background): “Moreover, a theoretical understanding of GANs is an on-going research topic (Uehara et al., 2016; Mohamed & Lakshminarayanan, 2016).”
Group invariance principles for causal generative models (2017, methodology): “However, as discussed in [Goodfellow et al., 2014; Uehara et al., 2016], it is heuristically preferable to maximize instead EX∼pg [log(D(X))] .”
Learning in Implicit Generative Models (2016, methodology): “One approximation suggested by Uehara et al. (2016) is to assume p ∗ ≈ r φ q θ , i.e. assume a near-optimal ratio, which reduces the f -divergence to: As a result, the last two terms in equation (21) cancel, leaving a generative loss that can be used for learning.”
Generative Multi-Adversarial Networks (2016, methodology): “Nowozin et al. (2016) and then Uehara et al. (2016) extended the JSD perspective on GANs to more general divergences, speciﬁcally f -divergences and then Bregman-divergences respectively.”
GANS for Sequences of Discrete Elements with the Gumbel-softmax Distribution (2016, methodology): “Further, we believe that incorporating recent advances in GANs such as training GANs using variational divergence minimization [10] or via density ratio estimation [13] could yield further improvements.”
Variational Approaches for Auto-Encoding Generative Adversarial Networks (2017, background): “GANs are based on an underlying principle of density ratio estimation [27, 38] and thus provide us with an important tool for overcoming intractable distributions.”
Improved generator objectives for GANs (2016, methodology): “Given samples from p and an estimate of the density ratio at each point, we can compute an estimate of the f -divergence, f G between p and q : where G f D ,f G is the generator objective, f G is the f -divergence targeted for the generator, and f D the f -divergence targeted for the discriminator.…”
Deep and Hierarchical Implicit Models (2017, background): “It is a key idea in GANs (Mohamed & Lakshminarayanan, 2016; Uehara et al., 2016), and similar ideas have rearisen in statistics and physics (Gutmann et al.”
Discriminator Contrastive Divergence: Semi-Amortized Generative Modeling by Exploring Energy of the Discriminator (2020, background): “The discriminator in f -GANs serves as a density ratio estimator [37].”
Likelihood-free MCMC with Amortized Approximate Ratio Estimators (2019, background): “…2015; Mohamed & Lakshmi-narayanan, 2016; Gutmann et al., 2017; Dutta et al., 2016; Tran et al., 2017; Brehmer et al., 2020) and is especially prominent in the area of Generative Adversarial Networks ( GAN s) (Goodfellow et al., 2014; Uehara et al., 2016; Turner et al., 2018; Azadi et al., 2018).”
Adversarial Message Passing For Graphical Models (2016, background): “Furthermore, it was clariﬁed in concurrent work very much in the same spirit with our paper such as [2] and [3] that Generative Adversarial Networks can be seen as a form of inference on ratios of partition functions, with early links towards training generative models.”
Hierarchical Implicit Models and Likelihood-Free Variational Inference (2017, background): “It is a key idea in GANs [35, 54], and similar ideas have rearisen in statistics and physics [19, 8].”
Under Review as a Conference Paper at Iclr 2017 Learning in Implicit Generative Models (2017, methodology): “We can generalise (16) to loss functions beyond the squared error using the Bregman divergence for density ratio estimation (Sugiyama et al., 2012a; Uehara et al., 2016), and is the unifying tool exploited in previous work (Reid and Williamson, 2011; Sriperumbudur et al.”
HP-GAN: Probabilistic 3D Human Motion Prediction via GAN (2017, background): “Recent literature[1, 10, 25, 37, 29, 22] tries to improve GAN training and provide a theoretical guaranty for its convergence.”
Understanding the Effectiveness of Lipschitz Constraint in Training of GANs via Gradient Analysis (2018, background): “Please also refer to our Appendix for a more comprehensive understanding, where we include: extended discussions on why Euclidean distance is important; how to efficiently enforcing the Lipschitz constraint; when f∗(x) is no-differentiable and how it behaves in practice; discussion on related work [”
Importance Weighted Hierarchical Variational Inference (2019, background): “…(Mescheder et al., 2017; Shi et al., 2017; Tran et al., 2017), for example, via the Density Ratio Estimation trick (Goodfellow et al., 2014; Uehara et al., 2016; Mohamed and Lakshminarayanan, 2016), typically estimate the densities indirectly utilizing an auxiliary critic and hide…”