Generative moment matching network (GMMN) is a deep generative model that differs from Generative Adversarial Network (GAN) by replacing the discriminator in GAN with a two-sample test based on kernel maximum mean discrepancy (MMD). Although some theoretical guarantees of MMD have been studied, the empirical performance of GMMN is still not as competitive as that of GAN on challenging and large benchmark datasets. The computational efficiency of GMMN is also less desirable in comparison with GAN, partially due to its requirement for a rather large batch size during the training. In this paper, we propose to improve both the model expressiveness of GMMN and its computational efficiency by introducing {\it adversarial kernel learning} techniques, as the replacement of a fixed Gaussian kernel in the original GMMN. The new approach combines the key ideas in both GMMN and GAN, hence we name it MMD-GAN. The new distance measure in MMD-GAN is a meaningful loss that enjoys the advantage of weak$^*$ topology and can be optimized via gradient descent with relatively small batch sizes. In our evaluation on multiple benchmark datasets, including MNIST, CIFAR-10, CelebA and LSUN, the performance of MMD-GAN significantly outperforms GMMN, and is competitive with other representative GAN works.

Different probabilistic (pseudo) metrics have been studied [ 5 - 8 ] under GAN framework.

The naive approach of extending GMMNs to conditional setting is to estimate a GMMN for each conditional distribution, and all these conditional distributions share parameters through the use of the same neural network. The problem of this approach is that each conditional distribution only has very few examples, and in the case of continuous domain for the conditioning variables, each conditional distribution may only have one single example, causing data sparsity problem. The proposed approach treats all the conditional distributions as a family and tries to match the model with the conditional embedding operator directly rather than matching each individual conditional distributions. The advantage of the proposed approach seems clear, but in some cases I can still see the naive approach do a reasonable job, for example in conditional generation where the conditioning variable takes one of 10 values as in MNIST. It would be interesting to compare to such a naive approach as a baseline.

Generative moment matching network (GMMN) is a deep generative model that differs from Generative Adversarial Network (GAN) by replacing the discriminator in GAN with a two-sample test based on kernel maximum mean discrepancy (MMD). Although some theoretical guarantees of MMD have been studied, the empirical performance of GMMN is still not as competitive as that of GAN on challenging and large benchmark datasets. The computational efficiency of GMMN is also less desirable in comparison with GAN, partially due to its requirement for a rather large batch size during the training. In this paper, we propose to improve both the model expressiveness of GMMN and its computational efficiency by introducing adversarial kernel learning techniques, as the replacement of a fixed Gaussian kernel in the original GMMN. The new approach combines the key ideas in both GMMN and GAN, hence we name it MMD GAN.

This paper examines an efficient method for quasi-random sampling of copulas in Monte Carlo computations. Traditional methods, like conditional distribution methods (CDM), have limitations when dealing with high-dimensional or implicit copulas, which refer to those that cannot be accurately represented by existing parametric copulas. Instead, this paper proposes the use of generative models, such as Generative Adversarial Networks (GANs), to generate quasi-random samples for any copula. GANs are a type of implicit generative models used to learn the distribution of complex data, thus facilitating easy sampling. In our study, GANs are employed to learn the mapping from a uniform distribution to copulas. Once this mapping is learned, obtaining quasi-random samples from the copula only requires inputting quasi-random samples from the uniform distribution. This approach offers a more flexible method for any copula. Additionally, we provide theoretical analysis of quasi-Monte Carlo estimators based on quasi-random samples of copulas. Through simulated and practical applications, particularly in the field of risk management, we validate the proposed method and demonstrate its superiority over various existing methods.

Generative moment matching networks (GMMNs) are suggested for modeling the cross-sectional dependence between stochastic processes. The stochastic processes considered are geometric Brownian motions and ARMA-GARCH models. Geometric Brownian motions lead to an application of pricing American basket call options under dependence and ARMA-GARCH models lead to an application of simulating predictive distributions. In both types of applications the benefit of using GMMNs in comparison to parametric dependence models is highlighted and the fact that GMMNs can produce dependent quasi-random samples with no additional effort is exploited to obtain variance reduction.

Generative moment matching networks (GMMNs) are introduced as dependence models for the joint innovation distribution of multivariate time series (MTS). Following the popular copula-GARCH approach for modeling dependent MTS data, a framework allowing us to take an alternative GMMN-GARCH approach is presented. First, ARMA-GARCH models are utilized to capture the serial dependence within each univariate marginal time series. Second, if the number of marginal time series is large, principal component analysis (PCA) is used as a dimension-reduction step. Last, the remaining cross-sectional dependence is modeled via a GMMN, our main contribution. GMMNs are highly flexible and easy to simulate from, which is a major advantage over the copula-GARCH approach. Applications involving yield curve modeling and the analysis of foreign exchange rate returns are presented to demonstrate the utility of our approach, especially in terms of producing better empirical predictive distributions and making better probabilistic forecasts. All results are reproducible with the demo GMMN_MTS_paper of the R package gnn.

Generative moment matching network (GMMN) is a deep generative model that differs from Generative Adversarial Network (GAN) by replacing the discriminator in GAN with a two-sample test based on kernel maximum mean discrepancy (MMD). Although some theoretical guarantees of MMD have been studied, the empirical performance of GMMN is still not as competitive as that of GAN on challenging and large benchmark datasets. The computational efficiency of GMMN is also less desirable in comparison with GAN, partially due to its requirement for a rather large batch size during the training. In this paper, we propose to improve both the model expressiveness of GMMN and its computational efficiency by introducing {\it adversarial kernel learning} techniques, as the replacement of a fixed Gaussian kernel in the original GMMN. The new approach combines the key ideas in both GMMN and GAN, hence we name it MMD-GAN.

This paper proposes a generative moment matching network (GMMN)-based post-filter that provides inter-utterance pitch variation for deep neural network (DNN)-based singing voice synthesis. The natural pitch variation of a human singing voice leads to a richer musical experience and is used in double-tracking, a recording method in which two performances of the same phrase are recorded and mixed to create a richer, layered sound. However, singing voices synthesized using conventional DNN-based methods never vary because the synthesis process is deterministic and only one waveform is synthesized from one musical score. To address this problem, we use a GMMN to model the variation of the modulation spectrum of the pitch contour of natural singing voices and add a randomized inter-utterance variation to the pitch contour generated by conventional DNN-based singing voice synthesis. Experimental evaluations suggest that 1) our approach can provide perceptible inter-utterance pitch variation while preserving speech quality. We extend our approach to double-tracking, and the evaluation demonstrates that 2) GMMN-based neural double-tracking is perceptually closer to natural double-tracking than conventional signal processing-based artificial double-tracking is.