1,579 research outputs found
Entropy-regularized Optimal Transport Generative Models
We investigate the use of entropy-regularized optimal transport (EOT) cost in
developing generative models to learn implicit distributions. Two generative
models are proposed. One uses EOT cost directly in an one-shot optimization
problem and the other uses EOT cost iteratively in an adversarial game. The
proposed generative models show improved performance over contemporary models
for image generation on MNSIT
Scalable Unbalanced Optimal Transport using Generative Adversarial Networks
Generative adversarial networks (GANs) are an expressive class of neural
generative models with tremendous success in modeling high-dimensional
continuous measures. In this paper, we present a scalable method for unbalanced
optimal transport (OT) based on the generative-adversarial framework. We
formulate unbalanced OT as a problem of simultaneously learning a transport map
and a scaling factor that push a source measure to a target measure in a
cost-optimal manner. In addition, we propose an algorithm for solving this
problem based on stochastic alternating gradient updates, similar in practice
to GANs. We also provide theoretical justification for this formulation,
showing that it is closely related to an existing static formulation by Liero
et al. (2018), and perform numerical experiments demonstrating how this
methodology can be applied to population modeling
Learning Generative Models with Sinkhorn Divergences
The ability to compare two degenerate probability distributions (i.e. two
probability distributions supported on two distinct low-dimensional manifolds
living in a much higher-dimensional space) is a crucial problem arising in the
estimation of generative models for high-dimensional observations such as those
arising in computer vision or natural language. It is known that optimal
transport metrics can represent a cure for this problem, since they were
specifically designed as an alternative to information divergences to handle
such problematic scenarios. Unfortunately, training generative machines using
OT raises formidable computational and statistical challenges, because of (i)
the computational burden of evaluating OT losses, (ii) the instability and lack
of smoothness of these losses, (iii) the difficulty to estimate robustly these
losses and their gradients in high dimension. This paper presents the first
tractable computational method to train large scale generative models using an
optimal transport loss, and tackles these three issues by relying on two key
ideas: (a) entropic smoothing, which turns the original OT loss into one that
can be computed using Sinkhorn fixed point iterations; (b) algorithmic
(automatic) differentiation of these iterations. These two approximations
result in a robust and differentiable approximation of the OT loss with
streamlined GPU execution. Entropic smoothing generates a family of losses
interpolating between Wasserstein (OT) and Maximum Mean Discrepancy (MMD), thus
allowing to find a sweet spot leveraging the geometry of OT and the favorable
high-dimensional sample complexity of MMD which comes with unbiased gradient
estimates. The resulting computational architecture complements nicely standard
deep network generative models by a stack of extra layers implementing the loss
function
Learning Generative Models across Incomparable Spaces
Generative Adversarial Networks have shown remarkable success in learning a
distribution that faithfully recovers a reference distribution in its entirety.
However, in some cases, we may want to only learn some aspects (e.g., cluster
or manifold structure), while modifying others (e.g., style, orientation or
dimension). In this work, we propose an approach to learn generative models
across such incomparable spaces, and demonstrate how to steer the learned
distribution towards target properties. A key component of our model is the
Gromov-Wasserstein distance, a notion of discrepancy that compares
distributions relationally rather than absolutely. While this framework
subsumes current generative models in identically reproducing distributions,
its inherent flexibility allows application to tasks in manifold learning,
relational learning and cross-domain learning.Comment: International Conference on Machine Learning (ICML
Likelihood Training of Schr\"odinger Bridge using Forward-Backward SDEs Theory
Schr\"odinger Bridge (SB) is an entropy-regularized optimal transport problem
that has received increasing attention in deep generative modeling for its
mathematical flexibility compared to the Scored-based Generative Model (SGM).
However, it remains unclear whether the optimization principle of SB relates to
the modern training of deep generative models, which often rely on constructing
log-likelihood objectives.This raises questions on the suitability of SB models
as a principled alternative for generative applications. In this work, we
present a novel computational framework for likelihood training of SB models
grounded on Forward-Backward Stochastic Differential Equations Theory - a
mathematical methodology appeared in stochastic optimal control that transforms
the optimality condition of SB into a set of SDEs. Crucially, these SDEs can be
used to construct the likelihood objectives for SB that, surprisingly,
generalizes the ones for SGM as special cases. This leads to a new optimization
principle that inherits the same SB optimality yet without losing applications
of modern generative training techniques, and we show that the resulting
training algorithm achieves comparable results on generating realistic images
on MNIST, CelebA, and CIFAR10. Our code is available at
https://github.com/ghliu/SB-FBSDE
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