A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2020; you can also visit the original URL.
The file type is application/pdf.
Filters
Wasserstein Distance to Independence Models
[article]
2020
arXiv
pre-print
Preserved Fulltext
Other Versions
Given any data distribution, we seek to minimize its Wasserstein distance to a fixed independence model. The solution to this optimization problem is a piecewise algebraic function of the data. ...
An independence model for discrete random variables is a Segre-Veronese variety in a probability simplex. ...
In Sections 4 and 5, we compute the vectors f and δ for Wasserstein distance to the independence models. Section 6 features numerical experiments. ...
arXiv:2003.06725v2
fatcat:e6mu2ny6vneyho4qbqheui5s64
Comparison of Maximum Likelihood and GAN-based training of Real NVPs
[article]
2017
arXiv
pre-print
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2020; you can also visit the original URL.
The file type is application/pdf.
We show that an independent critic trained to approximate Wasserstein distance between the validation set and the generator distribution helps detect overfitting. ...
We then compare the generated samples, exact log-probability densities and approximate Wasserstein distances. ...
It would be possible to use auto-regressive discriminators (Oord et al., 2016) to decompose the large KL divergence to multiple smaller terms: ...
arXiv:1705.05263v1
fatcat:tjxqumbrybenhgwzknqqqw3f3a
The Cramer Distance as a Solution to Biased Wasserstein Gradients
[article]
2017
arXiv
pre-print
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2019; you can also visit the original URL.
The file type is application/pdf.
Leveraging insights from probabilistic forecasting we propose an alternative to the Wasserstein metric, the Cram\'er distance. ...
The value of being sensitive to this geometry has been demonstrated, among others, in ordinal regression and generative modelling. ...
how the Cramér distance compares to the 1-Wasserstein metric, we consider modelling the discrete distribution P depicted in Figure 1 (left). ...
arXiv:1705.10743v1
fatcat:rfgqmom5qfeq7mnea7fnxtmlbu
Orthogonal Estimation of Wasserstein Distances
[article]
2019
arXiv
pre-print
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2020; you can also visit the original URL.
The file type is application/pdf.
Other Versions
In this paper, we propose a new variant of sliced Wasserstein distance, study the use of orthogonal coupling in Monte Carlo estimation of Wasserstein distances and draw connections with stratified sampling ...
Wasserstein distances are increasingly used in a wide variety of applications in machine learning. ...
Due to the close connections between various Wasserstein distance measures, we propose to set D(·, ·) as either sliced Wasserstein distance or projected Wasserstein distance. ...
arXiv:1903.03784v2
fatcat:5va23hq3fffa5h6bjjzppfpwia
Gaussian Word Embedding with a Wasserstein Distance Loss
[article]
2018
arXiv
pre-print
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2019; you can also visit the original URL.
The file type is application/pdf.
Other Versions
Therefore, with the aim of representing words in a highly efficient way, we propose to operate a Gaussian word embedding model with a loss function based on the Wasserstein distance. ...
The Wasserstein distance provides a natural notion of dissimilarity with probability measures and has a closed-form solution when measuring the distance between two Gaussian distributions. ...
embedding model (Vilnis and McCallum 2014) , Wasserstein Distance Gaussian model, and Wasserstein Distance Gaussian model with external information, respectively. ...
arXiv:1808.07016v7
fatcat:stvuzzcngbhrnm7iqfcet45kyy
Optimal Transport to a Variety
[article]
2020
arXiv
pre-print
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2020; you can also visit the original URL.
The file type is application/pdf.
Other Versions
A detailed analysis is given for the two bit independence model. ...
We study the problem of minimizing the Wasserstein distance between a probability distribution and an algebraic variety. ...
What we are interested in is the minimum Wasserstein distance from µ to any point ν in the independence model M. ...
arXiv:1909.11716v2
fatcat:d4uetu6fvfapte3tjjsgbhi55i
Wasserstein Training of Restricted Boltzmann Machines
2016
Neural Information Processing Systems
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2022; you can also visit the original URL.
The file type is application/pdf.
We derive a gradient of that distance with respect to the model parameters. Minimization of this new objective leads to generative models with different statistical properties. ...
This metric between observations can then be used to define the Wasserstein distance between the distribution induced by the Boltzmann machine on the one hand, and that given by the training sample on ...
Correspondence to GM, KRM and MC. ...
dblp:conf/nips/MontavonMC16
fatcat:xjb3lsmp3jfz5hid4iq2bf6pja
On a prior based on the Wasserstein information matrix
[article]
2022
arXiv
pre-print
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2022; you can also visit the original URL.
The file type is application/pdf.
Other Versions
We present sufficient conditions for the propriety of the posterior distribution for general classes of models. ...
We introduce a prior for the parameters of univariate continuous distributions, based on the Wasserstein information matrix, which is invariant under reparameterisations. ...
The last expression is proportional to the marginal likelihood associated to a normal sampling model together with the Wasserstein prior. ...
arXiv:2202.03217v3
fatcat:rv4b3krc3jgc3hdsjwa6ugqnau
Improved Image Wasserstein Attacks and Defenses
[article]
2020
arXiv
pre-print
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2020; you can also visit the original URL.
The file type is application/pdf.
A recently proposed Wasserstein distance-bounded threat model is a promising alternative that limits the perturbation to pixel mass movements. ...
Perturbations in the real-world, however, rarely exhibit the pixel independence that ℓ_p threat models assume. ...
One reason behind this is the p threat model perturbs each pixel independently, while the Wasserstein threat model does not. ...
arXiv:2004.12478v1
fatcat:gvh3phuqovd5zi7jphbfy7taae
Reproducibility of radiomic features using network analysis and its application in Wasserstein k-means clustering
2021
Journal of Medical Imaging
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2021; you can also visit the original URL.
The file type is application/pdf.
The reliability and reproducibility of those radiomic features were further validated on phantom data using the Wasserstein distance. ...
an independent dataset. ...
The use of unstable features in predictive modeling can lead to failure in validating the models on independent data. ...
doi:10.1117/1.jmi.8.3.031904
pmid:33954225
pmcid:PMC8085581
fatcat:wjg3br6zhffoblf6ixbdffpcue
OUP accepted manuscript
2019
Information and Inference A Journal of the IMA
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2021; you can also visit the original URL.
The file type is application/pdf.
Our results are motivated by recent applications of minimum Wasserstein estimators to complex generative models. ...
Statistical inference can be performed by minimizing, over the parameter space, the Wasserstein distance between model distributions and the empirical distribution of the data. ...
If ζ goes to zero, the dual-Sinkhorn divergence goes to the Wasserstein distance. If ζ goes to infinity, it converges to the energy distance (Ramdas et al., 2017) . ...
doi:10.1093/imaiai/iaz003
fatcat:s6umcdcc6rfzbjrrd2borgpdpm
Wasserstein Neural Processes
[article]
2020
arXiv
pre-print
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2020; you can also visit the original URL.
The file type is application/pdf.
Other Versions
Neural Processes (NPs) are a class of models that learn a mapping from a context set of input-output pairs to a distribution over functions. ...
We also show that this drawback is solved by using approximations of Wasserstein distance which calculates optimal transport distances even for distributions of disjoint support. ...
Since the Wasserstein distance is defined independent of likelihood, the WNP model still finds the proper fit of parameters given the data as seen in (fig 2) . ...
arXiv:1910.00668v2
fatcat:63pnwx3fsnd6teaoktl6yk3o4e
Reproducibility test of radiomics using network analysis and Wasserstein K-means algorithm
[article]
2019
bioRxiv
pre-print
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2020; you can also visit the original URL.
The file type is application/pdf.
Purpose: To construct robust and validated radiomic predictive models, the development of a reliable method that can identify reproducible radiomic features robust to varying image acquisition methods ...
For phantom data, the Wasserstein distance on a largest common network component from the lung cancer data was much smaller than the Wasserstein distance on the same network using random radiomic features ...
This has led many radiomic models built using a dataset to be unsuccessful in subsequent external validation on independent data [6] . ...
doi:10.1101/773168
fatcat:nnfsjrbjozgnzgdw5wjica4nt4
Image Hashing by Minimizing Discrete Component-wise Wasserstein Distance
[article]
2020
arXiv
pre-print
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2020; you can also visit the original URL.
The file type is application/pdf.
Other Versions
set of easy-to-compute one-dimensional Wasserstein distances. ...
Specifically, by exploiting the desired properties of the hash function in the low-dimensional, discrete space, our method efficiently estimates a better variant of Wasserstein distance by averaging a ...
Secondly, the OT-estimate of the Wasserstein distance requires an exponential number of samples to generalize (or to achieve a good estimate of the distance) [2] . ...
arXiv:2003.00134v3
fatcat:x3rwu23p3ndy3hzth37p27o4di
Permutation invariant networks to learn Wasserstein metrics
[article]
2021
arXiv
pre-print
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2021; you can also visit the original URL.
The file type is application/pdf.
Other Versions
In this work, we use a permutation invariant network to map samples from probability measures into a low-dimensional space such that the Euclidean distance between the encoded samples reflects the Wasserstein ...
We show that our network can generalize to correctly compute distances between unseen densities. ...
Acknowledgements The first author wants to thank Alexander Cloninger for helpful suggestions and for suggesting to study the geometry of the Wasserstein space by simple translations and scalings. ...
arXiv:2010.05820v4
fatcat:eald6qab2rg37ld5nm6gmr2pn4
« Previous
Showing results 1 — 15 out of 12,402 results