Variational Autoencoder is a scalable method for learning latent variable models of complex data. It employs a clear objective that can be easily optimized. However, it does not explicitly measure the quality of learned representations. We propose a Variational Mutual Information Maximization Framework for VAE to address this issue. It provides an objective that maximizes the mutual information between latent codes and observations. The objective acts as a regularizer that forces VAE to not ignore the latent code and allows one to select particular components of it to be most informative with respect to the observations. On top of that, the proposed framework provides a way to evaluate mutual information between latent codes and observations for a fixed VAE model.
Korea Advanced Institute of Science and Technology（韩国科学技术院）
Learning interpretable and disentangled representations of data is a key topic in machine learning research. Variational Autoencoder (VAE) is a scalable method for learning directed latent variable models of complex data. It employs a clear and interpretable objective that can be easily optimized. However, this objective does not provide an explicit measure for the quality of latent variable representations which may result in their poor quality. We propose Variational Mutual Information Maximization Framework for VAE to address this issue. In comparison to other methods, it provides an explic…
Variational autoencoders (VAEs) have ushered in a new era of unsupervised learning methods for complex distributions. Although these techniques are elegant in their approach, they are typically not useful for representation learning. In this work, we propose a simple yet powerful class of VAEs that simultaneously result in meaningful learned representations. Our solution is to combine traditional VAEs with mutual information maximization, with the goal to enhance amortized inference in VAEs using Information Theoretic techniques. We call this approach InfoMax-VAE, and such an approach can sign…
Universidad de la República（共和国大学）；CNRS & Université de Paris（法国国家科学研究中心与巴黎大学）；Sorbonne Université（索邦大学）
In this paper we address the problem of solving ill-posed inverse problems in imaging where the prior is a neural generative model. Specifically we consider the decoupled case where the prior is trained once and can be reused for many different log-concave degradation models without retraining. Whereas previous MAP-based approaches to this problem lead to highly non-convex optimization algorithms, our approach computes the joint (space-latent) MAP that naturally leads to alternate optimization algorithms and to the use of a stochastic encoder to accelerate computations. The resulting technique…
In this paper, we provide an information-theoretic interpretation of the Vector Quantized-Variational Autoencoder (VQ-VAE). We show that the loss function of the original VQ-VAE can be derived from the variational deterministic information bottleneck (VDIB) principle. On the other hand, the VQ-VAE trained by the Expectation Maximization (EM) algorithm can be viewed as an approximation to the variational information bottleneck(VIB) principle.
Training deep generative models with maximum likelihood remains a challenge. The typical workaround is to use variational inference (VI) and maximize a lower bound to the log marginal likelihood of the data. Variational auto-encoders (VAEs) adopt this approach. They further amortize the cost of inference by using a recognition network to parameterize the variational family. Amortized VI scales approximate posterior inference in deep generative models to large datasets. However it introduces an amortization gap and leads to approximate posteriors of reduced expressivity due to the problem known…
In this work, we have proposed a generative model, called VAE-KRnet, for density estimation or approximation, which combines the canonical variational autoencoder (VAE) with our recently developed flow-based generative model, called KRnet. VAE is used as a dimension reduction technique to capture the latent space, and KRnet is used to model the distribution of the latent variable. Using a linear model between the data and the latent variable, we show that VAE-KRnet can be more effective and robust than the canonical VAE. VAE-KRnet can be used as a density model to approximate either data distr…
Rice University（莱斯大学）；Aix-Marseille Univ（艾克斯-马赛大学）；Université de Toulon（土伦大学）；CNRS（法国国家科学研究中心）
Deep Generative Networks (DGNs) with probabilistic modeling of their output and latent space are currently trained via Variational Autoencoders (VAEs). In the absence of a known analytical form for the posterior and likelihood expectation, VAEs resort to approximations, including (Amortized) Variational Inference (AVI) and Monte-Carlo (MC) sampling. We exploit the Continuous Piecewise Affine (CPA) property of modern DGNs to derive their posterior and marginal distributions as well as the latter's first moments. These findings enable us to derive an analytical Expectation-Maximization (EM) algo…
Recently, an audio-visual speech generative model based on variational autoencoder (VAE) has been proposed, which is combined with a nonnegative matrix factorization (NMF) model for noise variance to perform unsupervised speech enhancement. When visual data is clean, speech enhancement with audio-visual VAE shows a better performance than with audio-only VAE, which is trained on audio-only data. However, audio-visual VAE is not robust against noisy visual data, e.g., when for some video frames, speaker face is not frontal or lips region is occluded. In this paper, we propose a robust unsupervi…
University of Tübingen（蒂宾根大学）；Max Planck Institute for Intelligent Systems（马克斯·普朗克智能系统研究所）；University of Cambridge（剑桥大学）；Amazon Web Services（亚马逊云服务）
Variational autoencoders (VAEs) are a popular framework for modeling complex data distributions; they can be efficiently trained via variational inference by maximizing the evidence lower bound (ELBO), at the expense of a gap to the exact (log-)marginal likelihood. While VAEs are commonly used for representation learning, it is unclear why ELBO maximization would yield useful representations, since unregularized maximum likelihood estimation cannot invert the data-generating process. Yet, VAEs often succeed at this task. We seek to elucidate this apparent paradox by studying nonlinear VAEs in …
Institute of Informatics and Telecommunications（信息与通信研究所）
Learning disentangled representations without supervision or inductive biases, often leads to non-interpretable or undesirable representations. On the other hand, strict supervision requires detailed knowledge of the true generative factors, which is not always possible. In this paper, we consider weak supervision by means of high-level labels that are not assumed to be explicitly related to the ground truth factors. Such labels, while being easier to acquire, can also be used as inductive biases for algorithms to learn more interpretable or alternative disentangled representations. To this en…
Deep neural networks with discrete latent variables offer the promise of better symbolic reasoning, and learning abstractions that are more useful to new tasks. There has been a surge in interest in discrete latent variable models, however, despite several recent improvements, the training of discrete latent variable models has remained challenging and their performance has mostly failed to match their continuous counterparts. Recent work on vector quantized autoencoders (VQ-VAE) has made substantial progress in this direction, with its perplexity almost matching that of a VAE on datasets such…
Learning disentangled and interpretable representations is an important step towards accomplishing comprehensive data representations on the manifold. In this paper, we propose a novel representation learning algorithm which combines the inference abilities of Variational Autoencoders (VAE) with the generalization capability of Generative Adversarial Networks (GAN). The proposed model, called InfoVAEGAN, consists of three networks~: Encoder, Generator and Discriminator. InfoVAEGAN aims to jointly learn discrete and continuous interpretable representations in an unsupervised manner by using two…
Auto-encoding Variational Bayes (AEVB) is a powerful and general algorithm for fitting latent variable models (a promising direction for unsupervised learning), and is well-known for training the Variational Auto-Encoder (VAE). In this tutorial, we focus on motivating AEVB from the classic Expectation Maximization (EM) algorithm, as opposed to from deterministic auto-encoders. Though natural and somewhat self-evident, the connection between EM and AEVB is not emphasized in the recent deep learning literature, and we believe that emphasizing this connection can improve the community's understan…
UvA-Bosch-Deltalab（阿姆斯特丹大学-博世-德尔塔实验室）；NEC Labs（日本电气实验室）；Facebook AI Research（脸书人工智能研究院）
Despite recent successes in synthesizing faces and bedrooms, existing generative models struggle to capture more complex image types, potentially due to the oversimplification of their latent space constructions. To tackle this issue, building on Variational Autoencoders (VAEs), we integrate recurrent connections across channels to both inference and generation steps, allowing the high-level features to be captured in global-to-local, coarse-to-fine manners. Combined with adversarial loss, our channel-recurrent VAE-GAN (crVAE-GAN) outperforms VAE-GAN in generating a diverse spectrum of high re…
A new approach for blind channel equalization and decoding, variational inference, and variational autoencoders (VAEs) in particular, is introduced. We first consider the reconstruction of uncoded data symbols transmitted over a noisy linear intersymbol interference (ISI) channel, with an unknown impulse response, without using pilot symbols. We derive an approximate maximum likelihood estimate to the channel parameters and reconstruct the transmitted data. We demonstrate significant and consistent improvements in the error rate of the reconstructed symbols, compared to existing blind equaliza…
Variational autoencoders (VAEs) have recently been used for unsupervised disentanglement learning of complex density distributions. Numerous variants exist to encourage disentanglement in latent space while improving reconstruction. However, none have simultaneously managed the trade-off between attaining extremely low reconstruction error and a high disentanglement score. We present a generalized framework to handle this challenge under constrained optimization and demonstrate that it outperforms state-of-the-art existing models as regards disentanglement while balancing reconstruction. We in…
In this paper, we investigate the problem of learning disentangled representations. Given a pair of images sharing some attributes, we aim to create a low-dimensional representation which is split into two parts: a shared representation that captures the common information between the images and an exclusive representation that contains the specific information of each image. To address this issue, we propose a model based on mutual information estimation without relying on image reconstruction or image generation. Mutual information maximization is performed to capture the attributes of data …
Romanian Institute of Science and Technology（罗马尼亚科学与技术研究院）；Max Planck Institute for Mathematics in the Sciences（马克斯·普朗克数学科学研究所）
In this paper we propose two novel bounds for the log-likelihood based on Kullback-Leibler and the Rényi divergences, which can be used for variational inference and in particular for the training of Variational AutoEncoders. Our proposal is motivated by the difficulties encountered in training VAEs on continuous datasets with high contrast images, such as those with handwritten digits and characters, where numerical issues often appear unless noise is added, either to the dataset during training or to the generative model given by the decoder. The new bounds we propose, which are obtained fro…
Fast gradient-free activation maximization for neurons in spiking neural networks
Laboratory of Neuronal Intelligence, Institute for Advanced Brain Studies, Lomonosov Moscow State University（神经智能实验室，先进脑科学研究所，洛蒙诺索夫莫斯科国立大学）；Artificial Intelligence Research Institute (AIRI)（人工智能研究所）；Skolkovo Institute of Science and Technology（斯克罗夫科技研究院）；HSE University Moscow, Russia（莫斯科高等经济大学，俄罗斯）
Physically Interpretable Representation Learning with Gaussian Mixture Variational AutoEncoder (GM-VAE)
Institute for Computational and Mathematical Engineering, Stanford University（计算与数学工程研究所，斯坦福大学）；Department of Mechanical Engineering, Stanford University（机械工程系，斯坦福大学）；National Renewable Energy Laboratory（国家可再生能源实验室）；Ann and H.J. Smead Department of Aerospace Engineering Sciences, University of Colorado, Boulder（安与H.J.斯迈德航空航天工程科学系，科罗拉多大学，博尔德）
Agency Lab（机构实验室）；Independent University Bangladesh（孟加拉国独立大学）
Decomposition of the evidence lower bound (ELBO) objective of VAE used for density estimation revealed the deficiency of VAE for representation learning and suggested ways to improve the model. In this paper, we investigate whether we can get similar insights by decomposing the ELBO for semi-supervised classification using VAE model. Specifically, we show that mutual information between input and class labels decreases during maximization of ELBO objective. We propose a method to address this issue. We also enforce cluster assumption to aid in classification. Experiments on a diverse datasets …
Information Sciences Institute（信息科学研究所）；University of Southern California（南加利福尼亚大学）
Advances in unsupervised learning enable reconstruction and generation of samples from complex distributions, but this success is marred by the inscrutability of the representations learned. We propose an information-theoretic approach to characterizing disentanglement and dependence in representation learning using multivariate mutual information, also called total correlation. The principle of total Cor-relation Ex-planation (CorEx) has motivated successful unsupervised learning applications across a variety of domains, but under some restrictive assumptions. Here we relax those restrictions…
School of Astronautics, Beihang University（北京航空航天大学宇航学院）
Disentanglement learning aims to construct independent and interpretable latent variables in which generative models are a popular strategy. InfoGAN is a classic method via maximizing Mutual Information (MI) to obtain interpretable latent variables mapped to the target space. However, it did not emphasize independent characteristic. To explicitly infer latent variables with inter-independence, we propose a novel GAN-based disentanglement framework via embedding Orthogonal Basis Expansion (OBE) into InfoGAN network (Inference-InfoGAN) in an unsupervised way. Under the OBE module, one set of ort…
Cross-domain disentanglement is the problem of learning representations partitioned into domain-invariant and domain-specific representations, which is a key to successful domain transfer or measuring semantic distance between two domains. Grounded in information theory, we cast the simultaneous learning of domain-invariant and domain-specific representations as a joint objective of multiple information constraints, which does not require adversarial training or gradient reversal layers. We derive a tractable bound of the objective and propose a generative model named Interaction Information A…
This is a tutorial and survey paper on factor analysis, probabilistic Principal Component Analysis (PCA), variational inference, and Variational Autoencoder (VAE). These methods, which are tightly related, are dimensionality reduction and generative models. They assume that every data point is generated from or caused by a low-dimensional latent factor. By learning the parameters of distribution of latent space, the corresponding low-dimensional factors are found for the sake of dimensionality reduction. For their stochastic and generative behaviour, these models can also be used for generatio…
Dynamical variational autoencoders (DVAEs) are a class of deep generative models with latent variables, dedicated to model time series of high-dimensional data. DVAEs can be considered as extensions of the variational autoencoder (VAE) that include temporal dependencies between successive observed and/or latent vectors. Previous work has shown the interest of using DVAEs over the VAE for speech spectrograms modeling. Independently, the VAE has been successfully applied to speech enhancement in noise, in an unsupervised noise-agnostic set-up that requires neither noise samples nor noisy speech …
In this paper, we are interested in audio-visual speech separation given a single-channel audio recording as well as visual information (lips movements) associated with each speaker. We propose an unsupervised technique based on audio-visual generative modeling of clean speech. More specifically, during training, a latent variable generative model is learned from clean speech spectrograms using a variational auto-encoder (VAE). To better utilize the visual information, the posteriors of the latent variables are inferred from mixed speech (instead of clean speech) as well as the visual data. Th…
