The variational autoencoder (VAE; Kingma, Welling (2014)) is a recently proposed generative model pairing a top-down generative network with a bottom-up recognition network which approximates posterior inference. It typically makes strong assumptions about posterior inference, for instance that the posterior distribution is approximately factorial, and that its parameters can be approximated with nonlinear regression from the observations. As we show empirically, the VAE objective can lead to overly simplified representations which fail to use the network's entire modeling capacity. We present the importance weighted autoencoder (IWAE), a generative model with the same architecture as the VAE, but which uses a strictly tighter log-likelihood lower bound derived from importance weighting. In the IWAE, the recognition network uses multiple samples to approximate the posterior, giving it increased flexibility to model complex posteriors which do not fit the VAE modeling assumptions. We show empirically that IWAEs learn richer latent space representations than VAEs, leading to improved test log-likelihood on density estimation benchmarks.
Other researchers have derived log-probability lower bounds by way of importance sampling. and avoided recognition networks entirely, instead performing inference using importance sampling from the prior. presented a variety of graphical model inference algorithms based on importance weighting. Reweighted wake-sleep (RWS) of @cite_2 is another recognition network approach which combines the original wake-sleep algorithm with updates to the generative network equivalent to gradient ascent on our bound @math . However, interpret this update as following a biased estimate of @math , whereas we interpret it as following an unbiased estimate of @math . The IWAE also differs from RWS in that the generative and recognition networks are trained to maximize a single objective, @math . By contrast, the @math -wake and sleep steps of RWS do not appear to be related to @math . Finally, the IWAE differs from RWS in that it makes use of the reparameterization trick.
@cite_2
2294427751 2687693326 2963275229 2963981733
We present a pattern recognition framework to improve committee machines of deep convolutional neural networks (deep CNNs) and its application to static facial expression recognition in the wild (SFEW). In order to generate enough diversity of decisions, we trained multiple deep CNNs by varying network architectures, input normalization, and weight initialization as well as by adopting several learning strategies to use large external databases. Moreover, with these deep models, we formed hierarchical committees using the validation-accuracy-based exponentially-weighted average (VA-Expo-WA) rule. Through extensive experiments, the great strengths of our committee machines were demonstrated in both structural and decisional ways. On the SFEW2.0 dataset released for the 3rd Emotion Recognition in the Wild (EmotiW) sub-challenge, a test accuracy of 57.3 was obtained from the best single deep CNN, while the single-level committees yielded 58.3 and 60.5 with the simple average rule and with the VA-Expo-WA rule, respectively. Our final submission based on the 3-level hierarchy using the VA-Expo-WA achieved 61.6 , significantly higher than the SFEW baseline of 39.1 . Generative Adversarial Networks (GANs) excel at creating realistic images with complex models for which maximum likelihood is infeasible. However, the convergence of GAN training has still not been proved. We propose a two time-scale update rule (TTUR) for training GANs with stochastic gradient descent on arbitrary GAN loss functions. TTUR has an individual learning rate for both the discriminator and the generator. Using the theory of stochastic approximation, we prove that the TTUR converges under mild assumptions to a stationary local Nash equilibrium. The convergence carries over to the popular Adam optimization, for which we prove that it follows the dynamics of a heavy ball with friction and thus prefers flat minima in the objective landscape. For the evaluation of the performance of GANs at image generation, we introduce the "Frechet Inception Distance" (FID) which captures the similarity of generated images to real ones better than the Inception Score. In experiments, TTUR improves learning for DCGANs and Improved Wasserstein GANs (WGAN-GP) outperforming conventional GAN training on CelebA, CIFAR-10, SVHN, LSUN Bedrooms, and the One Billion Word Benchmark. Abstract: The variational autoencoder (VAE; Kingma, Welling (2014)) is a recently proposed generative model pairing a top-down generative network with a bottom-up recognition network which approximates posterior inference. It typically makes strong assumptions about posterior inference, for instance that the posterior distribution is approximately factorial, and that its parameters can be approximated with nonlinear regression from the observations. As we show empirically, the VAE objective can lead to overly simplified representations which fail to use the network's entire modeling capacity. We present the importance weighted autoencoder (IWAE), a generative model with the same architecture as the VAE, but which uses a strictly tighter log-likelihood lower bound derived from importance weighting. In the IWAE, the recognition network uses multiple samples to approximate the posterior, giving it increased flexibility to model complex posteriors which do not fit the VAE modeling assumptions. We show empirically that IWAEs learn richer latent space representations than VAEs, leading to improved test log-likelihood on density estimation benchmarks. Generative Adversarial Networks (GANs) excel at creating realistic images with complex models for which maximum likelihood is infeasible. However, the convergence of GAN training has still not been proved. We propose a two time-scale update rule (TTUR) for training GANs with stochastic gradient descent on arbitrary GAN loss functions. TTUR has an individual learning rate for both the discriminator and the generator. Using the theory of stochastic approximation, we prove that the TTUR converges under mild assumptions to a stationary local Nash equilibrium. The convergence carries over to the popular Adam optimization, for which we prove that it follows the dynamics of a heavy ball with friction and thus prefers flat minima in the objective landscape. For the evaluation of the performance of GANs at image generation, we introduce the Frechet Inception Distance'' (FID) which captures the similarity of generated images to real ones better than the Inception Score. In experiments, TTUR improves learning for DCGANs and Improved Wasserstein GANs (WGAN-GP) outperforming conventional GAN training on CelebA, CIFAR-10, SVHN, LSUN Bedrooms, and the One Billion Word Benchmark.