7,900 research outputs found
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
Geometrical Insights for Implicit Generative Modeling
Learning algorithms for implicit generative models can optimize a variety of
criteria that measure how the data distribution differs from the implicit model
distribution, including the Wasserstein distance, the Energy distance, and the
Maximum Mean Discrepancy criterion. A careful look at the geometries induced by
these distances on the space of probability measures reveals interesting
differences. In particular, we can establish surprising approximate global
convergence guarantees for the -Wasserstein distance,even when the
parametric generator has a nonconvex parametrization.Comment: this version fixes a typo in a definitio
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
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