Semi-supervised variational autoencoders (VAEs) have obtained strong results, but have also encountered the challenge that good ELBO values do not always imply accurate inference results. In this paper, we investigate and propose two causes of this problem: (1) The ELBO objective cannot utilize the label information directly. (2) A bottleneck value exists and continuing to optimize ELBO after this value will not improve inference accuracy. On the basis of the experiment results, we propose SHOT-VAE to address these problems without introducing additional prior knowledge. The SHOT-VAE offers two contributions: (1) A new ELBO approximation named smooth-ELBO that integrates the label predictive loss into ELBO. (2) An approximation based on optimal interpolation that breaks the ELBO value bottleneck by reducing the margin between ELBO and the data likelihood. The SHOT-VAE achieves good performance with a 25.30% error rate on CIFAR-100 with 10k labels and reduces the error rate to 6.11% on CIFAR-10 with 4k labels.
Posterior collapse in Variational Autoencoders (VAEs) arises when the variational posterior distribution closely matches the prior for a subset of latent variables. This paper presents a simple and intuitive explanation for posterior collapse through the analysis of linear VAEs and their direct correspondence with Probabilistic PCA (pPCA). We explain how posterior collapse may occur in pPCA due to local maxima in the log marginal likelihood. Unexpectedly, we prove that the ELBO objective for the linear VAE does not introduce additional spurious local maxima relative to log marginal likelihood.…
Czech Technical University in Prague（捷克布拉格技术大学）；Dresden University of Technology（德累斯顿工业大学）
The importance of Variational Autoencoders reaches far beyond standalone generative models -- the approach is also used for learning latent representations and can be generalized to semi-supervised learning. This requires a thorough analysis of their commonly known shortcomings: posterior collapse and approximation errors. This paper analyzes VAE approximation errors caused by the combination of the ELBO objective and encoder models from conditional exponential families, including, but not limited to, commonly used conditionally independent discrete and continuous models. We characterize subcl…
One of the challenges in training generative models such as the variational auto encoder (VAE) is avoiding posterior collapse. When the generator has too much capacity, it is prone to ignoring latent code. This problem is exacerbated when the dataset is small, and the latent dimension is high. The root of the problem is the ELBO objective, specifically the Kullback-Leibler (KL) divergence term in objective function \citep{zhao2019infovae}. This paper proposes a new objective function to replace the KL term with one that emulates the maximum mean discrepancy (MMD) objective. It also introduces …
Variational Auto-Encoders (VAEs) have shown great potential in the unsupervised learning of data distributions. An VAE trained on normal images is expected to only be able to reconstruct normal images, allowing the localization of anomalous pixels in an image via manipulating information within the VAE ELBO loss. The ELBO consists of KL divergence loss (image-wise) and reconstruction loss (pixel-wise). It is natural and straightforward to use the later as the predictor. However, usually local anomaly added to a normal image can deteriorate the whole reconstructed image, causing segmentation us…
University of Oxford（牛津大学）；Imperial College London（伦敦帝国学院）
A trade-off exists between reconstruction quality and the prior regularisation in the Evidence Lower Bound (ELBO) loss that Variational Autoencoder (VAE) models use for learning. There are few satisfactory approaches to deal with a balance between the prior and reconstruction objective, with most methods dealing with this problem through heuristics. In this paper, we show that the noise variance (often set as a fixed value) in the Gaussian likelihood p(x|z) for real-valued data can naturally act to provide such a balance. By learning this noise variance so as to maximise the ELBO loss, we auto…
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 …
Fraunhofer ITWM（弗劳恩霍夫工业数学研究所）；Technical University of Kaiserslautern（凯泽斯劳滕工业大学）
We consider a variational autoencoder (VAE) for binary data. Our main innovations are an interpretable lower bound for its training objective, a modified initialization and architecture of such a VAE that leads to faster training, and a decision support for finding the appropriate dimension of the latent space via using a PCA. Numerical examples illustrate our theoretical result and the performance of the new architecture.
We prove that the evidence lower bound (ELBO) employed by variational auto-encoders (VAEs) admits non-trivial solutions having constant posterior variances under certain mild conditions, removing the need to learn variances in the encoder. The proof follows from an unexpected journey through an array of topics: the closed form optimal decoder for Gaussian VAEs, a proof that the decoder is always smooth, a proof that the ELBO at its stationary points is equal to the exact log evidence, and the posterior variance is merely part of a stochastic estimator of the decoder Hessian. The penalty incurr…
Gatsby Computational Neuroscience Unit（盖茨比计算神经科学部）；University College London（伦敦大学学院）；Amazon Web Services（亚马逊云科技）
Score matching (SM) is a convenient method for training flexible probabilistic models, which is often preferred over the traditional maximum-likelihood (ML) approach. However, these models are less interpretable than normalized models; as such, training robustness is in general difficult to assess. We present a critical study of existing variational SM objectives, showing catastrophic failure on a wide range of datasets and network architectures. Our theoretical insights on the objectives emerge directly from their equivalent autoencoding losses when optimizing variational autoencoder (VAE) mo…
Multimodal variational autoencoders (VAEs) have shown promise as efficient generative models for weakly-supervised data. Yet, despite their advantage of weak supervision, they exhibit a gap in generative quality compared to unimodal VAEs, which are completely unsupervised. In an attempt to explain this gap, we uncover a fundamental limitation that applies to a large family of mixture-based multimodal VAEs. We prove that the sub-sampling of modalities enforces an undesirable upper bound on the multimodal ELBO and thereby limits the generative quality of the respective models. Empirically, we sh…
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…
Density-Informed VAE (DiVAE): Reliable Log-Prior Probability via Density Alignment Regularization
Department of Mathematics, Informatics and Geosciences, University of Trieste（特里埃斯特大学数学、信息学与地球科学系）；Laboratory of Data Engineering, Area Science Park, Trieste, Italy（数据工程实验室，特里埃斯特科学园）
National University of Singapore（新加坡国立大学）；Singapore Management University（新加坡管理大学）
VAE, or variational auto-encoder, compresses data into latent attributes, and generates new data of different varieties. VAE based on KL divergence has been considered as an effective technique for data augmentation. In this paper, we propose the use of Wasserstein distance as a measure of distributional similarity for the latent attributes, and show its superior theoretical lower bound (ELBO) compared with that of KL divergence under mild conditions. Using multiple experiments, we demonstrate that the new loss function exhibits better convergence property and generates artificial images that …
University of Torontoland（多伦多兰大学）；University of Edenborrow（伊甸伯勒大学）；HSE University（高等经济学院）；Skolkovo Institute of Science and Technology（斯科尔科沃科学技术研究院）；University of Oxford（牛津大学）；Centre de recherche Lagrange en mathematiques et calcul（拉格朗日数学与计算研究中心）
Variational auto-encoders (VAE) are popular deep latent variable models which are trained by maximizing an Evidence Lower Bound (ELBO). To obtain tighter ELBO and hence better variational approximations, it has been proposed to use importance sampling to get a lower variance estimate of the evidence. However, importance sampling is known to perform poorly in high dimensions. While it has been suggested many times in the literature to use more sophisticated algorithms such as Annealed Importance Sampling (AIS) and its Sequential Importance Sampling (SIS) extensions, the potential benefits broug…
Instance-Adaptive Parametrization for Amortized Variational Inference
Department of Electrical Engineering and Information Technology, University of Naples Federico II（那不勒斯费德里科二世大学电气工程与信息技术系）；Department of Information Engineering, Electrical Engineering, and Applied Mathematics, University of Salerno（萨勒诺大学信息工程、电气工程与应用数学系）
We present new intuitions and theoretical assessments of the emergence of disentangled representation in variational autoencoders. Taking a rate-distortion theory perspective, we show the circumstances under which representations aligned with the underlying generative factors of variation of data emerge when optimising the modified ELBO bound in $β$-VAE, as training progresses. From these insights, we propose a modification to the training regime of $β$-VAE, that progressively increases the information capacity of the latent code during training. This modification facilitates the robust learni…
Institute of Automation, Chinese Academy of Sciences（中国科学院自动化研究所）；School of Artificial Intelligence, University of Chinese Academy of Sciences（中国科学院大学人工智能学院）
Variational autoencoders (VAEs), as an important aspect of generative models, have received a lot of research interests and reached many successful applications. However, it is always a challenge to achieve the consistency between the learned latent distribution and the prior latent distribution when optimizing the evidence lower bound (ELBO), and finally leads to an unsatisfactory performance in data generation. In this paper, we propose a latent distribution consistency approach to avoid such substantial inconsistency between the posterior and prior latent distributions in ELBO optimizing. W…
Imperial College London（帝国理工学院）；Facebook AI Applied Research（Facebook人工智能应用研究部）；University College London（伦敦大学学院）
Recent work in unsupervised learning has focused on efficient inference and learning in latent variables models. Training these models by maximizing the evidence (marginal likelihood) is typically intractable. Thus, a common approximation is to maximize the Evidence Lower BOund (ELBO) instead. Variational autoencoders (VAE) are a powerful and widely-used class of generative models that optimize the ELBO efficiently for large datasets. However, the VAE's default Gaussian choice for the prior imposes a strong constraint on its ability to represent the true posterior, thereby degrading overall pe…
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 …
Variational autoencoder (VAE) is a very popular and well-investigated generative model in neural learning research. To leverage VAE in practical tasks dealing with a massive dataset of large dimensions, it is required to deal with the difficulty of building low variance evidence lower bounds (ELBO). Markov Chain Monte Carlo (MCMC) is an effective approach to tighten the ELBO for approximating the posterior distribution and Hamiltonian Variational Autoencoder (HVAE) is an effective MCMC inspired approach for constructing a low-variance ELBO that is amenable to the reparameterization trick. The …
KTH Royal Institute of Technology（瑞典皇家理工学院）；Science for Life Laboratory（生命科学实验室）；University of Edinburgh（爱丁堡大学）
In variational inference (VI), the marginal log-likelihood is estimated using the standard evidence lower bound (ELBO), or improved versions as the importance weighted ELBO (IWELBO). We propose the multiple importance sampling ELBO (MISELBO), a \textit{versatile} yet \textit{simple} framework. MISELBO is applicable in both amortized and classical VI, and it uses ensembles, e.g., deep ensembles, of independently inferred variational approximations. As far as we are aware, the concept of deep ensembles in amortized VI has not previously been established. We prove that MISELBO provides a tighter …
Harbin Institute of Technology（哈尔滨工业大学）；Beijing University of Civil Engineering and Architecture（北京建筑大学）
Being one of the most popular generative framework, variational autoencoders(VAE) are known to suffer from a phenomenon termed posterior collapse, i.e. the latent variational distributions collapse to the prior, especially when a strong decoder network is used. In this work, we analyze the latent representation of collapsed VAEs, and proposed a novel model, neighbor embedding VAE(NE-VAE), which explicitly constraints the encoder to encode inputs close in the input space to be close in the latent space. We observed that for VAE variants that report similar ELBO, KL divergence or even mutual inf…
When designing variational autoencoders (VAEs) or other types of latent space models, the dimensionality of the latent space is typically defined upfront. In this process, it is possible that the number of dimensions is under- or overprovisioned for the application at hand. In case the dimensionality is not predefined, this parameter is usually determined using time- and resource-consuming cross-validation. For these reasons we have developed a technique to shrink the latent space dimensionality of VAEs automatically and on-the-fly during training using Generalized ELBO with Constrained Optimi…
Zhejiang University（浙江大学）；China Electric Power Research Institute（中国电力科学研究院）
Insights in power grid pixel maps (PGPMs) refer to important facility operating states and unexpected changes in the power grid. Identifying insights helps analysts understand the collaboration of various parts of the grid so that preventive and correct operations can be taken to avoid potential accidents. Existing solutions for identifying insights in PGPMs are performed manually, which may be laborious and expertise-dependent. In this paper, we propose an interactive insight identification and annotation framework by leveraging an enhanced variational autoencoder (VAE). In particular, a new …
Technical University of Denmark（丹麦技术大学）；University of Copenhagen（哥本哈根大学）
A few-shot generative model should be able to generate data from a novel distribution by only observing a limited set of examples. In few-shot learning the model is trained on data from many sets from distributions sharing some underlying properties such as sets of characters from different alphabets or objects from different categories. We extend current latent variable models for sets to a fully hierarchical approach with an attention-based point to set-level aggregation and call our method SCHA-VAE for Set-Context-Hierarchical-Aggregation Variational Autoencoder. We explore likelihood-based…
University of California（加利福尼亚大学）；Tencent AI Lab（腾讯AI实验室）
Variational auto-encoder (VAE) is an effective neural network architecture to disentangle a speech utterance into speaker identity and linguistic content latent embeddings, then generate an utterance for a target speaker from that of a source speaker. This is possible by concatenating the identity embedding of the target speaker and the content embedding of the source speaker uttering a desired sentence. In this work, we propose to improve VAE models with self-attention and structural regularization (RGSM). Specifically, we found a suitable location of VAE's decoder to add a self-attention lay…
University of Oxford（牛津大学）；Alan Turing Institute for Data Science（艾伦·图灵数据科学研究所）
Variational Auto-Encoders (VAEs) have become very popular techniques to perform inference and learning in latent variable models as they allow us to leverage the rich representational power of neural networks to obtain flexible approximations of the posterior of latent variables as well as tight evidence lower bounds (ELBOs). Combined with stochastic variational inference, this provides a methodology scaling to large datasets. However, for this methodology to be practically efficient, it is necessary to obtain low-variance unbiased estimators of the ELBO and its gradients with respect to the p…
Department of Computer Science, National University of Singapore（新加坡国立大学计算机科学系）
We address the problem of unsupervised disentanglement of latent representations learnt via deep generative models. In contrast to current approaches that operate on the evidence lower bound (ELBO), we argue that statistical independence in the latent space of VAEs can be enforced in a principled hierarchical Bayesian manner. To this effect, we augment the standard VAE with an inverse-Wishart (IW) prior on the covariance matrix of the latent code. By tuning the IW parameters, we are able to encourage (or discourage) independence in the learnt latent dimensions. Extensive experimental results o…
Neural style transfer, allowing to apply the artistic style of one image to another, has become one of the most widely showcased computer vision applications shortly after its introduction. In contrast, related tasks in the music audio domain remained, until recently, largely untackled. While several style conversion methods tailored to musical signals have been proposed, most lack the 'one-shot' capability of classical image style transfer algorithms. On the other hand, the results of existing one-shot audio style transfer methods on musical inputs are not as compelling. In this work, we are …
Pro-t-VAE: Closed-Form Student's t Mixtures for Robust Prototype Discovery
Institute of Intelligent Information Processing, Shanxi University（山西大学智能信息处理研究所）；School of Medicine, Yale University（耶鲁大学医学院）；Boston Children’s Hospital, Harvard Medical School（哈佛医学院波士顿儿童医院）；Eli Lilly and Company（礼来公司）
The Variational AutoEncoder (VAE) learns simultaneously an inference and a generative model, but only one of these models can be learned at optimum, this behaviour is associated to the ELBO learning objective, that is optimised by a non-informative generator. In order to solve such an issue, we provide a learning objective, learning a maximal informative generator while maintaining bounded the network capacity: the Variational InfoMax (VIM). The contribution of the VIM derivation is twofold: an objective learning both an optimal inference and generative model and the explicit definition of the…
We propose a Text-to-Speech method to create an unseen expressive style using one utterance of expressive speech of around one second. Specifically, we enhance the disentanglement capabilities of a state-of-the-art sequence-to-sequence based system with a Variational AutoEncoder (VAE) and a Householder Flow. The proposed system provides a 22% KL-divergence reduction while jointly improving perceptual metrics over state-of-the-art. At synthesis time we use one example of expressive style as a reference input to the encoder for generating any text in the desired style. Perceptual MUSHRA evaluati…
Imperial College London（帝国理工学院）；University College London（伦敦大学学院）；City University of London（伦敦城市大学）
We propose a new model for relational VAE semi-supervision capable of balancing disentanglement and low complexity modelling of relations with different symbolic properties. We compare the relative benefits of relation-decoder complexity and latent space structure on both inductive and transductive transfer learning. Our results depict a complex picture where enforcing structure on semi-supervised representations can greatly improve zero-shot transductive transfer, but may be less favourable or even impact negatively the capacity for inductive transfer.
We present a new flavor of Variational Autoencoder (VAE) that interpolates seamlessly between unsupervised, semi-supervised and fully supervised learning domains. We show that unlabeled datapoints not only boost unsupervised tasks, but also the classification performance. Vice versa, every label not only improves classification, but also unsupervised tasks. The proposed architecture is simple: A classification layer is connected to the topmost encoder layer, and then combined with the resampled latent layer for the decoder. The usual evidence lower bound (ELBO) loss is supplemented with a supe…
Freie Universität Berlin（柏林自由大学）；BTU Cottbus-Senftenberg（科特布斯-森夫滕贝格工业大学）；dida Datenschmiede GmbH（迪达数据工坊有限公司）；University of Warwick（华威大学）；Universität Potsdam（波茨坦大学）；DeepMind（深度思维）；The Alan Turing Institute（艾伦·图灵研究所）
We analyse the properties of an unbiased gradient estimator of the ELBO for variational inference, based on the score function method with leave-one-out control variates. We show that this gradient estimator can be obtained using a new loss, defined as the variance of the log-ratio between the exact posterior and the variational approximation, which we call the $\textit{log-variance loss}$. Under certain conditions, the gradient of the log-variance loss equals the gradient of the (negative) ELBO. We show theoretically that this gradient estimator, which we call $\textit{VarGrad}$ due to its co…
Conditional generative models of high-dimensional images have many applications, but supervision signals from conditions to images can be expensive to acquire. This paper describes Diffusion-Decoding models with Contrastive representations (D2C), a paradigm for training unconditional variational autoencoders (VAEs) for few-shot conditional image generation. D2C uses a learned diffusion-based prior over the latent representations to improve generation and contrastive self-supervised learning to improve representation quality. D2C can adapt to novel generation tasks conditioned on labels or mani…
In this work, we present a novel neural network to generate high resolution images. We replace the decoder of VAE with a discriminator while using the encoder as it is. The encoder is fed data from a normal distribution while the generator is fed from a gaussian distribution. The combination from both is given to a discriminator which tells whether the generated image is correct or not. We evaluate our network on 3 different datasets: MNIST, LSUN and CelebA dataset. Our network beats the previous state of the art using MMD, SSIM, log likelihood, reconstruction error, ELBO and KL divergence as …
College of Information Science and Electronic Engineering, Zhejiang University（浙江大学信息与电子工程学院）；ZJU-League Research & Development Center（浙大-联队研发中心）；State Key Lab of CAD&CG, Zhejiang University（浙江大学CAD&CG国家重点实验室）；Zhejiang Provincial Key Laboratory of Information Processing, Communication and Networking（浙江省信息处理、通信与网络重点实验室）
Unsupervised meta-learning aims to learn the meta knowledge from unlabeled data and rapidly adapt to novel tasks. However, existing approaches may be misled by the context-bias (e.g. background) from the training data. In this paper, we abstract the unsupervised meta-learning problem into a Structural Causal Model (SCM) and point out that such bias arises due to hidden confounders. To eliminate the confounders, we define the priors are \textit{conditionally} independent, learn the relationships between priors and intervene on them with casual factorization. Furthermore, we propose Causal Meta …
Indian Institute of Science（印度科学学院）；Indian Institute of Technology Madras（印度理工学院马德拉斯分校）
Zero-shot learning is a new paradigm to classify objects from classes that are not available at training time. Zero-shot learning (ZSL) methods have attracted considerable attention in recent years because of their ability to classify unseen/novel class examples. Most of the existing approaches on ZSL works when all the samples from seen classes are available to train the model, which does not suit real life. In this paper, we tackle this hindrance by developing a generative replay-based continual ZSL (GRCZSL). The proposed method endows traditional ZSL to learn from streaming data and acquire…
