Generative adversarial network: Difference between revisions

<math display="block">L_G = \operatorname E_{x\sim \mu_G}[({\exp} \circ \sigma^{-1} \circ D) (x)]</math>where <math>\sigma</math> is the logistic function. When the discriminator is optimal, the generator gradient is the same as in [[maximum likelihood estimation]], even though GAN cannot perform maximum likelihood estimation ''itself''.<ref>{{cite arXiv |last=Goodfellow |first=Ian J. |date=2014-12-01 |title=On distinguishability criteria for estimating generative models |class=stat.ML |eprint=1412.6515 }}</ref><ref>{{Cite web |last=Goodfellow |first=Ian |date=2016-08-31 |title=Generative Adversarial Networks (GANs), Presentation at Berkeley Artificial Intelligence Lab |url=https://www.iangoodfellow.com/slides/2016-08-31-Berkeley.pdf |url-status=live |archive-url=https://web.archive.org/web/20220508101103/https://www.iangoodfellow.com/slides/2016-08-31-Berkeley.pdf |archive-date=8 May 2022}}</ref>

'''[[Hinge loss]] GAN''':<ref>{{cite arXiv |last1=Lim |first1=Jae Hyun |last2=Ye |first2=Jong Chul |date=2017-05-08 |title=Geometric GAN |class=stat.ML |eprint=1705.02894 }}</ref><math display="block"> L_D = -\operatorname E_{x\sim p_{\text{ref}}}\left[\min\left(0, -1 + D(x)\right)\right] -\operatorname E_{x\sim\mu_G}\left[\min\left(0, -1 - D\left(x\right)\right)\right] </math><math display="block"> L_{G}L_G = -\operatorname E_{x\sim \mu_G} [D(x)] </math>'''Least squares GAN:'''<ref>{{Cite journal |last1=Mao |first1=Xudong |last2=Li |first2=Qing |last3=Xie |first3=Haoran |last4=Lau |first4=Raymond Y. K. |last5=Wang |first5=Zhen |last6=Paul Smolley |first6=Stephen |date=2017 |title=Least Squares Generative Adversarial Networks |url=https://openaccess.thecvf.com/content_iccv_2017/html/Mao_Least_Squares_Generative_ICCV_2017_paper.html |pages=2794–2802}}</ref><math display="block">L_D = \operatorname E_{x\sim \mu_{\text{ref}}}[(D(x)-b)^2] + \operatorname E_{x\sim \mu_G}[(D(x)-a)^2]</math><math display="block">L_G = \operatorname E_{x\sim \mu_G}[(D(x)-c)^2]</math>where <math>a, b, c</math> are parameters to be chosen. The authors recommended <math>a = -1, b = 1, c = 0</math>.