Some Theoretical Properties of GANs
Generative Adversarial Networks (GANs) are a class of generative algorithms that have been shown to produce state-of-the art samples, especially in the domain of image creation. The fundamental principle of GANs is to approximate the unknown distribution of a given data set by optimizing an objectiv...
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| creator | Biau, G Cadre, B Sangnier, M Tanielian, U |
| description | Generative Adversarial Networks (GANs) are a class of generative algorithms
that have been shown to produce state-of-the art samples, especially in the
domain of image creation. The fundamental principle of GANs is to approximate
the unknown distribution of a given data set by optimizing an objective
function through an adversarial game between a family of generators and a
family of discriminators. In this paper, we offer a better theoretical
understanding of GANs by analyzing some of their mathematical and statistical
properties. We study the deep connection between the adversarial principle
underlying GANs and the Jensen-Shannon divergence, together with some
optimality characteristics of the problem. An analysis of the role of the
discriminator family via approximation arguments is also provided. In addition,
taking a statistical point of view, we study the large sample properties of the
estimated distribution and prove in particular a central limit theorem. Some of
our results are illustrated with simulated examples. |
| doi_str_mv | 10.48550/arxiv.1803.07819 |
| format | Article |
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that have been shown to produce state-of-the art samples, especially in the
domain of image creation. The fundamental principle of GANs is to approximate
the unknown distribution of a given data set by optimizing an objective
function through an adversarial game between a family of generators and a
family of discriminators. In this paper, we offer a better theoretical
understanding of GANs by analyzing some of their mathematical and statistical
properties. We study the deep connection between the adversarial principle
underlying GANs and the Jensen-Shannon divergence, together with some
optimality characteristics of the problem. An analysis of the role of the
discriminator family via approximation arguments is also provided. In addition,
taking a statistical point of view, we study the large sample properties of the
estimated distribution and prove in particular a central limit theorem. Some of
our results are illustrated with simulated examples.</description><identifier>DOI: 10.48550/arxiv.1803.07819</identifier><language>eng</language><subject>Computer Science - Learning ; Statistics - Machine Learning</subject><creationdate>2018-03</creationdate><rights>http://arxiv.org/licenses/nonexclusive-distrib/1.0</rights><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>228,230,780,885</link.rule.ids><linktorsrc>$$Uhttps://arxiv.org/abs/1803.07819$$EView_record_in_Cornell_University$$FView_record_in_$$GCornell_University$$Hfree_for_read</linktorsrc><backlink>$$Uhttps://doi.org/10.48550/arXiv.1803.07819$$DView paper in arXiv$$Hfree_for_read</backlink></links><search><creatorcontrib>Biau, G</creatorcontrib><creatorcontrib>Cadre, B</creatorcontrib><creatorcontrib>Sangnier, M</creatorcontrib><creatorcontrib>Tanielian, U</creatorcontrib><title>Some Theoretical Properties of GANs</title><description>Generative Adversarial Networks (GANs) are a class of generative algorithms
that have been shown to produce state-of-the art samples, especially in the
domain of image creation. The fundamental principle of GANs is to approximate
the unknown distribution of a given data set by optimizing an objective
function through an adversarial game between a family of generators and a
family of discriminators. In this paper, we offer a better theoretical
understanding of GANs by analyzing some of their mathematical and statistical
properties. We study the deep connection between the adversarial principle
underlying GANs and the Jensen-Shannon divergence, together with some
optimality characteristics of the problem. An analysis of the role of the
discriminator family via approximation arguments is also provided. In addition,
taking a statistical point of view, we study the large sample properties of the
estimated distribution and prove in particular a central limit theorem. Some of
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that have been shown to produce state-of-the art samples, especially in the
domain of image creation. The fundamental principle of GANs is to approximate
the unknown distribution of a given data set by optimizing an objective
function through an adversarial game between a family of generators and a
family of discriminators. In this paper, we offer a better theoretical
understanding of GANs by analyzing some of their mathematical and statistical
properties. We study the deep connection between the adversarial principle
underlying GANs and the Jensen-Shannon divergence, together with some
optimality characteristics of the problem. An analysis of the role of the
discriminator family via approximation arguments is also provided. In addition,
taking a statistical point of view, we study the large sample properties of the
estimated distribution and prove in particular a central limit theorem. Some of
our results are illustrated with simulated examples.</abstract><doi>10.48550/arxiv.1803.07819</doi><oa>free_for_read</oa></addata></record> |
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| subjects | Computer Science - Learning Statistics - Machine Learning |
| title | Some Theoretical Properties of GANs |
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