Sliced Generative Models

In this paper we discuss a class of  AutoEncoder based generative models based on one dimensional sliced approach. The idea is based on the reduction of the discrimination between samples to one-dimensional case.

Our experiments show that methods can be divided into two groups. First consists of methods which are a modification of standard normality tests, while the second is based on classical distances between samples.

It turns out that both groups are correct generative models, but the second one gives a slightly faster decrease rate of Frechet Inception Distance (FID).

[1] H. Cramér and H.Wold. Some theorems on distribution functions. London Math. Soc., 11:290-294, 1936.

[2] M. Hazewinkel, ed. Kolmogorov-Smirnov test. Encyclopedia of Mathematics. Springer Science+Business Media B.V. / Kluwer Academic Publishers, 2001.

[3] N. Henze. Invariant tests for multivariate normality: a critical review. Statist. Papers, 43(4):467-506, 2002.

[4] M. Heusel, H. Ramsauer, T. Unterthiner, B. Nessler, G. Klambauer, and S. Hochreiter. Gans trained by a two time-scale update rule converge to a nash equilibrium. arXiv:1706.08500, 2017.

[5] D.P. Kingma and M.Welling. Auto-encoding variational bayes. arXiv:1312.6114, 2014.

[6] S. Kolouri, P.E. Pope, C.E. Martin, and G.K. Rohde. Sliced wasserstein autoencoders. 2018.

[7] M. Mazur and P. Kościelniak. On some goodness of fit tests for normality based on the optimal transport distance. submitted.

[8] A. Palmer, D. Dey, and J. Bi. Reforming generative autoencoders via goodnessoffit hypothesis testing. UAI, 2018.

[9] B.W. Silverman. Density estimation for statistics and data analysis. Monographs on Statistics and Applied Probability. Chapman & Hall, London, 1986.

[10] Jacek Tabor, Szymon Knop, Przemysław Spurek, Igor Podolak, Marcin Mazur, and Stanisław Jastrz¦bski. Cramer-wold autoencoder. arXiv preprint arXiv:1805.09235, 2018.

[11] I. Tolstikhin, O. Bousquet, S. Gelly, and B. Schoelkopf. Wasserstein autoencoders. arXiv preprint arXiv:1711.01558, 2017.