45,112 research outputs found
Sliced Wasserstein Generative Models
In generative modeling, the Wasserstein distance (WD) has emerged as a useful
metric to measure the discrepancy between generated and real data
distributions. Unfortunately, it is challenging to approximate the WD of
high-dimensional distributions. In contrast, the sliced Wasserstein distance
(SWD) factorizes high-dimensional distributions into their multiple
one-dimensional marginal distributions and is thus easier to approximate. In
this paper, we introduce novel approximations of the primal and dual SWD.
Instead of using a large number of random projections, as it is done by
conventional SWD approximation methods, we propose to approximate SWDs with a
small number of parameterized orthogonal projections in an end-to-end deep
learning fashion. As concrete applications of our SWD approximations, we design
two types of differentiable SWD blocks to equip modern generative
frameworks---Auto-Encoders (AE) and Generative Adversarial Networks (GAN). In
the experiments, we not only show the superiority of the proposed generative
models on standard image synthesis benchmarks, but also demonstrate the
state-of-the-art performance on challenging high resolution image and video
generation in an unsupervised manner.Comment: This paper is accepted by CVPR 2019, accidentally uploaded as a new
submission (arXiv:1904.05408, which has been withdrawn). The code is
available at this https URL https:// github.com/musikisomorphie/swd.gi
Coding for Random Projections
The method of random projections has become very popular for large-scale
applications in statistical learning, information retrieval, bio-informatics
and other applications. Using a well-designed coding scheme for the projected
data, which determines the number of bits needed for each projected value and
how to allocate these bits, can significantly improve the effectiveness of the
algorithm, in storage cost as well as computational speed. In this paper, we
study a number of simple coding schemes, focusing on the task of similarity
estimation and on an application to training linear classifiers. We demonstrate
that uniform quantization outperforms the standard existing influential method
(Datar et. al. 2004). Indeed, we argue that in many cases coding with just a
small number of bits suffices. Furthermore, we also develop a non-uniform 2-bit
coding scheme that generally performs well in practice, as confirmed by our
experiments on training linear support vector machines (SVM)
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