Generative Moment Matching Networks (1502.02761v1)

Abstract: We consider the problem of learning deep generative models from data. We formulate a method that generates an independent sample via a single feedforward pass through a multilayer perceptron, as in the recently proposed generative adversarial networks (Goodfellow et al., 2014). Training a generative adversarial network, however, requires careful optimization of a difficult minimax program. Instead, we utilize a technique from statistical hypothesis testing known as maximum mean discrepancy (MMD), which leads to a simple objective that can be interpreted as matching all orders of statistics between a dataset and samples from the model, and can be trained by backpropagation. We further boost the performance of this approach by combining our generative network with an auto-encoder network, using MMD to learn to generate codes that can then be decoded to produce samples. We show that the combination of these techniques yields excellent generative models compared to baseline approaches as measured on MNIST and the Toronto Face Database.

• The paper introduces a novel generative model using Maximum Mean Discrepancy to match data moments, achieving more stable training compared to GANs.
• It integrates auto-encoders to harness latent representations, enhancing generative performance on benchmarks like MNIST and TFD.
• Empirical evaluations show that the GMMN+AE model outperforms baselines in log-likelihood metrics while delivering smoother transitions along the data manifold.

Generative Moment Matching Networks

The paper entitled "Generative Moment Matching Networks" introduces a novel deep generative model leveraging maximum mean discrepancy (MMD) for training purposes. The proposed generative moment matching networks (GMMNs) aim to simplify the training of generative models by avoiding the intricacies of minimax optimization associated with generative adversarial networks (GANs).

Summary and Core Contributions

The key contributions of the paper can be summarized as follows:

1. GMMNs and MMD Objective:
   • GMMNs utilize a technique from statistical hypothesis testing known as MMD for training the generative models.
   • The MMD criterion involves matching all statistical moments between the model-generated samples and the original dataset samples, enabling the reduction of the discrepancy between these two distributions.
   • The kernel trick applied in this context permits the implicit computation of high-dimensional feature mappings, essential for efficiently measuring discrepancies between distributions.
2. Integration with Auto-Encoder Networks:
   • The authors propose enhancing the generative capacity of GMMNs by integrating them with auto-encoder networks (GMMN+AE).
   • The combined model involves training an auto-encoder and subsequently utilizing MMD to learn the generative model in the auto-encoder's latent code space.
   • This integration leverages the representational power of auto-encoders, leading to improved generative performance.

Network Architecture and Training Methodology

The GMMN involves a multilayer perceptron (MLP) architecture where samples from a simple uniform distribution are deterministically mapped to data space. The training procedure focuses on minimizing the MMD loss, which inherently matches the moments between the empirical data distribution and the generated samples, leading to a simpler and more stable training process compared to GANs.

The enhanced GMMN+AE model operates in the code space of a pretrained auto-encoder. This approach capitalizes on the rich, low-dimensional representations learned by the auto-encoder, making the generative task more tractable and effective.

Experimental Validation

The empirical validation of the proposed models was conducted on two benchmark datasets: MNIST and the Toronto Face Dataset (TFD). The key observations from the experimental results include:

• Quantitative Results: The GMMN+AE outperformed the baseline models, including GANs, in terms of log-likelihood of the test datasets under Gaussian Parzen window estimation.
  • For MNIST, GMMN+AE achieved a log-likelihood of 282 ± 2, whereas GANs achieved 225 ± 2.
  • For TFD, the performance of GMMN+AE was 2204 ± 20, compared to 2057 ± 26 for GANs.
• Qualitative Results: The samples generated by GMMN+AE were visually appealing and exhibited smooth transitions across the data manifold, as confirmed by interpolation tests in the code space.

Theoretical and Practical Implications

The proposed GMMNs offer significant advancements in the domain of deep generative models:

1. Theoretical Implications:
   • The use of MMD provides a robust statistical framework for training generative models, which can be more stable and less cumbersome than minimax objectives.
   • The ability to match all moments between distributions could potentially lead to better performance in generating realistic samples.
2. Practical Implications:
   • The GMMN+AE model demonstrates that bootstrapping with auto-encoders can significantly enhance the generative capabilities, making it a practical choice for complex, high-dimensional data.
   • The simplicity in training through straightforward backpropagation makes GMMNs more accessible and easier to implement compared to more intricate generative models like GANs.

Future Directions

Several promising avenues for future research emerge from this paper:

1. Advanced MMD Estimators:
   • Exploring alternative MMD estimators, such as linear-time or random feature-based methods, could reduce computational overhead and enhance scalability.
2. Joint Training Schemes:
   • Investigating joint training schemes where the auto-encoder and GMMN are trained simultaneously might result in more cohesive generative models.
3. Extension to Complex Datasets:
   • Applying GMMN+AE to more complex datasets, possibly incorporating convolutional architectures, could expand its applicability to broader and more challenging domains, such as high-resolution image generation.

The paper sets a strong foundation for utilizing MMD in deep generative models, providing insights into both the theoretical grounding and practical implementation strategies.