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Improving GANs Using Optimal Transport
We present Optimal Transport GAN (OT-GAN), a variant of generative adver...
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First Order Generative Adversarial Networks
GANs excel at learning high dimensional distributions, but they can upda...
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Many Paths to Equilibrium: GANs Do Not Need to Decrease a Divergence At Every Step
Generative adversarial networks (GANs) are a family of generative models...
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f-GAN: Training Generative Neural Samplers using Variational Divergence Minimization
Generative neural samplers are probabilistic models that implement sampl...
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Generative Learning With Euler Particle Transport
We propose an Euler particle transport (EPT) approach for generative lea...
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Sliced Iterative Generator
We introduce the Sliced Iterative Generator (SIG), an iterative generati...
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An adaptive transport framework for joint and conditional density estimation
We propose a general framework to robustly characterize joint and condit...
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ACT: Asymptotic Conditional Transport
We propose conditional transport (CT) as a new divergence to measure the difference between two probability distributions. The CT divergence consists of the expected cost of a forward CT, which constructs a navigator to stochastically transport a data point of one distribution to the other distribution, and that of a backward CT which reverses the transport direction. To apply it to the distributions whose probability density functions are unknown but random samples are accessible, we further introduce asymptotic CT (ACT), whose estimation only requires access to mini-batch based discrete empirical distributions. Equipped with two navigators that amortize the computation of conditional transport plans, the ACT divergence comes with unbiased sample gradients that are straightforward to compute, making it amenable to mini-batch stochastic gradient descent based optimization. When applied to train a generative model, the ACT divergence is shown to strike a good balance between mode covering and seeking behaviors and strongly resist mode collapse. To model high-dimensional data, we show that it is sufficient to modify the adversarial game of an existing generative adversarial network (GAN) to a game played by a generator, a forward navigator, and a backward navigator, which try to minimize a distribution-to-distribution transport cost by optimizing both the distribution of the generator and conditional transport plans specified by the navigators, versus a critic that does the opposite by inflating the point-to-point transport cost. On a wide variety of benchmark datasets for generative modeling, substituting the default statistical distance of an existing GAN with the ACT divergence is shown to consistently improve the performance.
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