A wide range of systems exhibit high dimensional incomplete data. Accurate estimation of the missing data is often desired, and is crucial for many downstream analyses. Many state-of-the-art recovery methods involve supervised learning using datasets containing full observations. In contrast, we focus on unsupervised estimation of missing image data, where no full observations are available - a common situation in practice. Unsupervised imputation methods for images often employ a simple linear subspace to capture correlations between data dimensions, omitting more complex relationships. In this work, we introduce a general probabilistic model that describes sparse high dimensional imaging data as being generated by a deep non-linear embedding. We derive a learning algorithm using a variational approximation based on convolutional neural networks and discuss its relationship to linear imputation models, the variational auto encoder, and deep image priors. We introduce sparsity-aware network building blocks that explicitly model observed and missing data. We analyze proposed sparsity-aware network building blocks, evaluate our method on public domain imaging datasets, and conclude by showing that our method enables imputation in an important real-world problem involving medical images. The code is freely available as part of the |neuron| library at this http URL.
Variational Bayes auto-encoders (VAEs) and similar models have been used to learn probabilistic generative models, often in the context of images @cite_16 @cite_40 @cite_2 . Similarly, deep denoising auto-encoders use neural networks to obtain embeddings that are robust to noise @cite_52 . Our method builds on these recent developments to approximate subspaces using neural networks. Importantly, we show that a principled treatment of a sparsity model leads to important and intuitive differences from the VAE.
@cite_40 @cite_16 @cite_52 @cite_2
2952584433 2579277680 2952673310 2769521316
The recently developed variational autoencoders (VAEs) have proved to be an effective confluence of the rich representational power of neural networks with Bayesian methods. However, most work on VAEs use a rather simple prior over the latent variables such as standard normal distribution, thereby restricting its applications to relatively simple phenomena. In this work, we propose hierarchical nonparametric variational autoencoders, which combines tree-structured Bayesian nonparametric priors with VAEs, to enable infinite flexibility of the latent representation space. Both the neural parameters and Bayesian priors are learned jointly using tailored variational inference. The resulting model induces a hierarchical structure of latent semantic concepts underlying the data corpus, and infers accurate representations of data instances. We apply our model in video representation learning. Our method is able to discover highly interpretable activity hierarchies, and obtain improved clustering accuracy and generalization capacity based on the learned rich representations. Variational Autoencoders (VAEs) are expressive latent variable models that can be used to learn complex probability distributions from training data. However, the quality of the resulting model crucially relies on the expressiveness of the inference model. We introduce Adversarial Variational Bayes (AVB), a technique for training Variational Autoencoders with arbitrarily expressive inference models. We achieve this by introducing an auxiliary discriminative network that allows to rephrase the maximum-likelihood-problem as a two-player game, hence establishing a principled connection between VAEs and Generative Adversarial Networks (GANs). We show that in the nonparametric limit our method yields an exact maximum-likelihood assignment for the parameters of the generative model, as well as the exact posterior distribution over the latent variables given an observation. Contrary to competing approaches which combine VAEs with GANs, our approach has a clear theoretical justification, retains most advantages of standard Variational Autoencoders and is easy to implement. Variational Autoencoders (VAEs) are expressive latent variable models that can be used to learn complex probability distributions from training data. However, the quality of the resulting model crucially relies on the expressiveness of the inference model. We introduce Adversarial Variational Bayes (AVB), a technique for training Variational Autoencoders with arbitrarily expressive inference models. We achieve this by introducing an auxiliary discriminative network that allows to rephrase the maximum-likelihood-problem as a two-player game, hence establishing a principled connection between VAEs and Generative Adversarial Networks (GANs). We show that in the nonparametric limit our method yields an exact maximum-likelihood assignment for the parameters of the generative model, as well as the exact posterior distribution over the latent variables given an observation. Contrary to competing approaches which combine VAEs with GANs, our approach has a clear theoretical justification, retains most advantages of standard Variational Autoencoders and is easy to implement. Generative models, such as variational auto-encoders (VAE) and generative adversarial networks (GAN), have been immensely successful in approximating image statistics in computer vision. VAEs are useful for unsupervised feature learning, while GANs alleviate supervision by penalizing inaccurate samples using an adversarial game. In order to utilize benefits of these two approaches, we combine the VAE under an adversarial setup with auxiliary label information. We show that factorizing the latent space to separate the information needed for reconstruction (a continuous space) from the information needed for image attribute classification (a discrete space), enables the capability to edit specific attributes of an image.