Learning to Draw Samples: With Application to Amortized MLE for Generative Adversarial Learning

TL;DR

The paper tackles efficient probabilistic inference when the target distribution is known only up to a normalization constant. It introduces Amortized SVGD, training a neural sampler to mimic Stein variational dynamics so that the sampler can rapidly generate samples for many related tasks without computing the proposal density. Building on this, SteinGAN couples the neural sampler with an energy-based model to perform amortized MLE in a GAN-like framework, achieving realistic image synthesis and competitive performance on multiple datasets. This approach automates sampler design, leverages a principled kernelized Stein discrepancy to maintain diversity, and demonstrates practical gains in both sample quality and downstream predictive tasks. The work lays groundwork for automatic, task-adaptive probabilistic inference and fast inner-loop optimization in deep energy models.

Abstract

We propose a simple algorithm to train stochastic neural networks to draw samples from given target distributions for probabilistic inference. Our method is based on iteratively adjusting the neural network parameters so that the output changes along a Stein variational gradient that maximumly decreases the KL divergence with the target distribution. Our method works for any target distribution specified by their unnormalized density function, and can train any black-box architectures that are differentiable in terms of the parameters we want to adapt. As an application of our method, we propose an amortized MLE algorithm for training deep energy model, where a neural sampler is adaptively trained to approximate the likelihood function. Our method mimics an adversarial game between the deep energy model and the neural sampler, and obtains realistic-looking images competitive with the state-of-the-art results.

Figures (5)

• Figure 1: MNIST images generated by DCGAN and our SteinGAN. We use the joint model in \ref{['equ:pxy']} to allow us to generate images for each digit. We set $m = 0.2$.
• Figure 2: Results on CIFAR-10. "500 Duplicate" denotes 500 images randomly subsampled from the training set, each duplicated 100 times. Upper: images simulated by DCGAN and SteinGAN (based on joint model \ref{['equ:pxy']}) conditional on each category. Middle: inception scores for samples generated by various methods (all with 50,000 images) on inception models trained on ImageNet and CIFAR-10, respectively. Lower: testing accuracy on real testing set when using 50,000 simulated images to train ResNets for classification. SteinGAN achieves higher testing accuracy than DCGAN. We set $m=1$ and $\gamma=0.8$.
• Figure 3: Results on CelebA. Upper: images generated by DCGAN and our SteinGAN. Lower: images generated by SteinGAN when performing a random walk $\xi\gets \xi + 0.01\times\mathrm{Uniform}([-1,1])$ on the random input $\xi$; we can see that a man with glasses and black hair gradually changes to a woman with blonde hair. See Figure \ref{['fig:facemore']} for more examples.
• Figure 4: Images generated by DCGAN and our SteinGAN on LSUN.
• Figure 5: More images generated by SteinGAN on CelebA.