Does a Variational AutoEncoder (VAE) consistently encode typical samples generated from its decoder? This paper shows that the perhaps surprising answer to this question is `No'; a (nominally trained) VAE does not necessarily amortize inference for typical samples that it is capable of generating. We study the implications of this behaviour on the learned representations and also the consequences of fixing it by introducing a notion of self consistency. Our approach hinges on an alternative construction of the variational approximation distribution to the true posterior of an extended VAE model with a Markov chain alternating between the encoder and the decoder. The method can be used to train a VAE model from scratch or given an already trained VAE, it can be run as a post processing step in an entirely self supervised way without access to the original training data. Our experimental analysis reveals that encoders trained with our self-consistency approach lead to representations that are robust (insensitive) to perturbations in the input introduced by adversarial attacks. We provide experimental results on the ColorMnist and CelebA benchmark datasets that quantify the properties of the learned representations and compare the approach with a baseline that is specifically trained for the desired property.
Recent state-of-the-art autoencoder based generative models have an encoder-decoder structure and learn a latent representation with a pre-defined distribution that can be sampled from. Implementing the encoder networks of these models in a stochastic manner provides a natural and common approach to avoid overfitting and enforce a smooth decoder function. However, we show that for stochastic encoders, simultaneously attempting to enforce a distribution constraint and minimising an output distortion leads to a reduction in generative and reconstruction quality. In addition, attempting to enforc…
We propose a new family of optimization criteria for variational auto-encoding models, generalizing the standard evidence lower bound. We provide conditions under which they recover the data distribution and learn latent features, and formally show that common issues such as blurry samples and uninformative latent features arise when these conditions are not met. Based on these new insights, we propose a new sequential VAE model that can generate sharp samples on the LSUN image dataset based on pixel-wise reconstruction loss, and propose an optimization criterion that encourages unsupervised l…
University of Minnesota（明尼苏达大学）；Duke Kunshan University（昆山杜克大学）
We propose a new method for novelty detection that can tolerate high corruption of the training points, whereas previous works assumed either no or very low corruption. Our method trains a robust variational autoencoder (VAE), which aims to generate a model for the uncorrupted training points. To gain robustness to high corruption, we incorporate the following four changes to the common VAE: 1. Extracting crucial features of the latent code by a carefully designed dimension reduction component for distributions; 2. Modeling the latent distribution as a mixture of Gaussian low-rank inliers and …
Technical University of Denmark（丹麦技术大学）；University of Copenhagen（哥本哈根大学）；Twitter
We present an autoencoder that leverages learned representations to better measure similarities in data space. By combining a variational autoencoder with a generative adversarial network we can use learned feature representations in the GAN discriminator as basis for the VAE reconstruction objective. Thereby, we replace element-wise errors with feature-wise errors to better capture the data distribution while offering invariance towards e.g. translation. We apply our method to images of faces and show that it outperforms VAEs with element-wise similarity measures in terms of visual fidelity. …
The model order of a wireless channel plays an important role for a variety of applications in communications engineering, e.g., it represents the number of resolvable incident wavefronts with non-negligible power incident from a transmitter to a receiver. Areas such as direction of arrival estimation leverage the model order to analyze the multipath components of channel state information. In this work, we propose to use a variational autoencoder to group unlabeled channel state information with respect to the model order in the variational autoencoder latent space in an unsupervised manner. …
Washington University in St. Louis（圣路易斯华盛顿大学）；Illinois Institute of Technology（伊利诺伊理工学院）
We introduce a deep learning method to simulate the motion of particles trapped in a chaotic recirculating flame. The Lagrangian trajectories of particles, captured using a high-speed camera and subsequently reconstructed in 3-dimensional space, were used to train a variational autoencoder (VAE) which comprises multiple layers of convolutional neural networks. We show that the trajectories, which are statistically representative of those determined in experiments, can be generated using the VAE network. The performance of our model is evaluated with respect to the accuracy and generalization o…
Variational Autoencoding Discrete Diffusion with Enhanced Dimensional Correlations Modeling
School of Mathematical Sciences, Peking University（北京大学数学科学学院）；Center for Statistical Science, Peking University（北京大学统计科学中心）；Academy of Mathematics and Systems Science, Chinese Academy of Sciences（中国科学院数学与系统科学研究院）；Huawei Foundation Model Dept（华为基金会模型部门）；The Chinese University of Hong Kong, Shenzhen（香港中文大学（深圳））
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…
Parameterized mathematical models play a central role in understanding and design of complex information systems. However, they often cannot take into account the intricate interactions innate to such systems. On the contrary, purely data-driven approaches do not need explicit mathematical models for data generation and have a wider applicability at the cost of interpretability. In this paper, we consider the design of a one-bit compressive variational autoencoder, and propose a novel hybrid model-based and data-driven methodology that allows us not only to design the sensing matrix and the qu…
A large number of objectives have been proposed to train latent variable generative models. We show that many of them are Lagrangian dual functions of the same primal optimization problem. The primal problem optimizes the mutual information between latent and visible variables, subject to the constraints of accurately modeling the data distribution and performing correct amortized inference. By choosing to maximize or minimize mutual information, and choosing different Lagrange multipliers, we obtain different objectives including InfoGAN, ALI/BiGAN, ALICE, CycleGAN, beta-VAE, adversarial auto…
Google（谷歌公司）；Universiteit van Amsterdam（阿姆斯特丹大学）；Qualcomm（高通公司）
Variational autoencoders provide a principled framework for learning deep latent-variable models and corresponding inference models. In this work, we provide an introduction to variational autoencoders and some important extensions.
Shanghai Jiao Tong University（上海交通大学）；University of Technology Sydney（悉尼科技大学）
Learning in the latent variable model is challenging in the presence of the complex data structure or the intractable latent variable. Previous variational autoencoders can be low effective due to the straightforward encoder-decoder structure. In this paper, we propose a variational composite autoencoder to sidestep this issue by amortizing on top of the hierarchical latent variable model. The experimental results confirm the advantages of our model.
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.
RETINA-AI Health, Inc.（RETINA-AI健康公司）；MD Anderson Cancer Center（MD安德森癌症中心）
In Bayesian machine learning, the posterior distribution is typically computationally intractable, hence variational inference is often required. In this approach, an evidence lower bound on the log likelihood of data is maximized during training. Variational Autoencoders (VAE) are one important example where variational inference is utilized. In this tutorial, we derive the variational lower bound loss function of the standard variational autoencoder. We do so in the instance of a gaussian latent prior and gaussian approximate posterior, under which assumptions the Kullback-Leibler term in th…
This work gives an in-depth derivation of the trainable evidence lower bound obtained from the marginal joint log-Likelihood with the goal of training a Multi-Modal Variational Autoencoder (M$^2$VAE).
The recognition network in deep latent variable models such as variational autoencoders (VAEs) relies on amortized inference for efficient posterior approximation that can scale up to large datasets. However, this technique has also been demonstrated to select suboptimal variational parameters, often resulting in considerable additional error called the amortization gap. To close the amortization gap and improve the training of the generative model, recent works have introduced an additional refinement step that applies stochastic variational inference (SVI) to improve upon the variational par…
This paper presents an infinite variational autoencoder (VAE) whose capacity adapts to suit the input data. This is achieved using a mixture model where the mixing coefficients are modeled by a Dirichlet process, allowing us to integrate over the coefficients when performing inference. Critically, this then allows us to automatically vary the number of autoencoders in the mixture based on the data. Experiments show the flexibility of our method, particularly for semi-supervised learning, where only a small number of training samples are available.
Variational autoencoders learn unsupervised data representations, but these models frequently converge to minima that fail to preserve meaningful semantic information. For example, variational autoencoders with autoregressive decoders often collapse into autodecoders, where they learn to ignore the encoder input. In this work, we demonstrate that adding an auxiliary decoder to regularize the latent space can prevent this collapse, but successful auxiliary decoding tasks are domain dependent. Auxiliary decoders can increase the amount of semantic information encoded in the latent space and visi…
We propose Information Theoretic-Learning (ITL) divergence measures for variational regularization of neural networks. We also explore ITL-regularized autoencoders as an alternative to variational autoencoding bayes, adversarial autoencoders and generative adversarial networks for randomly generating sample data without explicitly defining a partition function. This paper also formalizes, generative moment matching networks under the ITL framework.
With the recent advance of geometric deep learning, neural networks have been extensively used for data in non-Euclidean domains. In particular, hyperbolic neural networks have proved successful in processing hierarchical information of data. However, many hyperbolic neural networks are numerically unstable during training, which precludes using complex architectures. This crucial problem makes it difficult to build hyperbolic generative models for real and complex data. In this work, we propose a hyperbolic generative network in which we design novel architecture and layers to improve stabili…
Samsung AI Center Moscow（三星莫斯科人工智能中心）；Samsung-HSE Laboratory（三星-高等经济学院实验室）
We propose a single neural probabilistic model based on variational autoencoder that can be conditioned on an arbitrary subset of observed features and then sample the remaining features in "one shot". The features may be both real-valued and categorical. Training of the model is performed by stochastic variational Bayes. The experimental evaluation on synthetic data, as well as feature imputation and image inpainting problems, shows the effectiveness of the proposed approach and diversity of the generated samples.
Generative models of graphs are well-known, but many existing models are limited in scalability and expressivity. We present a novel sequential graphical variational autoencoder operating directly on graphical representations of data. In our model, the encoding and decoding of a graph as is framed as a sequential deconstruction and construction process, respectively, enabling the the learning of a latent space. Experiments on a cycle dataset show promise, but highlight the need for a relaxation of the distribution over node permutations.
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…
University of Florida（佛罗里达大学）；NEC Laboratories Europe（NEC欧洲实验室）
Although substantial efforts have been made to learn disentangled representations under the variational autoencoder (VAE) framework, the fundamental properties to the dynamics of learning of most VAE models still remain unknown and under-investigated. In this work, we first propose a novel learning objective, termed the principle-of-relevant-information variational autoencoder (PRI-VAE), to learn disentangled representations. We then present an information-theoretic perspective to analyze existing VAE models by inspecting the evolution of some critical information-theoretic quantities across t…
University of Copenhagen（哥本哈根大学）；Aalto University（阿尔托大学）；Technical University of Denmark（丹麦技术大学）
Variational Autoencoders are powerful models for unsupervised learning. However deep models with several layers of dependent stochastic variables are difficult to train which limits the improvements obtained using these highly expressive models. We propose a new inference model, the Ladder Variational Autoencoder, that recursively corrects the generative distribution by a data dependent approximate likelihood in a process resembling the recently proposed Ladder Network. We show that this model provides state of the art predictive log-likelihood and tighter log-likelihood lower bound compared t…
In recent years Variation Autoencoders have become one of the most popular unsupervised learning of complicated distributions.Variational Autoencoder (VAE) provides more efficient reconstructive performance over a traditional autoencoder. Variational auto enocders make better approximaiton than MCMC. The VAE defines a generative process in terms of ancestral sampling through a cascade of hidden stochastic layers. They are a directed graphic models. Variational autoencoder is trained to maximise the variational lower bound. Here we are trying maximise the likelihood and also at the same time we…
In just three years, Variational Autoencoders (VAEs) have emerged as one of the most popular approaches to unsupervised learning of complicated distributions. VAEs are appealing because they are built on top of standard function approximators (neural networks), and can be trained with stochastic gradient descent. VAEs have already shown promise in generating many kinds of complicated data, including handwritten digits, faces, house numbers, CIFAR images, physical models of scenes, segmentation, and predicting the future from static images. This tutorial introduces the intuitions behind VAEs, e…
We propose a molecular generative model based on the conditional variational autoencoder for de novo molecular design. It is specialized to control multiple molecular properties simultaneously by imposing them on a latent space. As a proof of concept, we demonstrate that it can be used to generate drug-like molecules with five target properties. We were also able to adjust a single property without changing the others and to manipulate it beyond the range of the dataset.
Recently proposed normalizing flow models such as Glow have been shown to be able to generate high quality, high dimensional images with relatively fast sampling speed. Due to their inherently restrictive architecture, however, it is necessary that they are excessively deep in order to train effectively. In this paper we propose to combine Glow with an underlying variational autoencoder in order to counteract this issue. We demonstrate that our proposed model is competitive with Glow in terms of image quality and test likelihood while requiring far less time for training.
A standard Variational Autoencoder, with a Euclidean latent space, is structurally incapable of capturing topological properties of certain datasets. To remove topological obstructions, we introduce Diffusion Variational Autoencoders with arbitrary manifolds as a latent space. A Diffusion Variational Autoencoder uses transition kernels of Brownian motion on the manifold. In particular, it uses properties of the Brownian motion to implement the reparametrization trick and fast approximations to the KL divergence. We show that the Diffusion Variational Autoencoder is capable of capturing topolog…
A new form of the variational autoencoder (VAE) is proposed, based on the symmetric Kullback-Leibler divergence. It is demonstrated that learning of the resulting symmetric VAE (sVAE) has close connections to previously developed adversarial-learning methods. This relationship helps unify the previously distinct techniques of VAE and adversarially learning, and provides insights that allow us to ameliorate shortcomings with some previously developed adversarial methods. In addition to an analysis that motivates and explains the sVAE, an extensive set of experiments validate the utility of the …
The problem of learning a manifold structure on a dataset is framed in terms of a generative model, to which we use ideas behind autoencoders (namely adversarial/Wasserstein autoencoders) to fit deep neural networks. From a machine learning perspective, the resulting structure, an atlas of a manifold, may be viewed as a combination of dimensionality reduction and "fuzzy" clustering.
LTCI, Télécom Paris, Institut Polytechnique de Paris（巴黎理工学院巴黎电信学院LTCI实验室）
This paper investigates a novel algorithmic approach to data representation based on kernel methods. Assuming that the observations lie in a Hilbert space X, the introduced Kernel Autoencoder (KAE) is the composition of mappings from vector-valued Reproducing Kernel Hilbert Spaces (vv-RKHSs) that minimizes the expected reconstruction error. Beyond a first extension of the autoencoding scheme to possibly infinite dimensional Hilbert spaces, KAE further allows to autoencode any kind of data by choosing X to be itself a RKHS. A theoretical analysis of the model is carried out, providing a general…
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…
University of Amsterdam（阿姆斯特丹大学）；eScience Center（电子科学中心）；ASTRON, the Netherlands Institute for Radio Astronomy（荷兰射电天文研究所（ASTRON））
We show that using nearest neighbours in the latent space of autoencoders (AE) significantly improves performance of semi-supervised novelty detection in both single and multi-class contexts. Autoencoding methods detect novelty by learning to differentiate between the non-novel training class(es) and all other unseen classes. Our method harnesses a combination of the reconstructions of the nearest neighbours and the latent-neighbour distances of a given input's latent representation. We demonstrate that our nearest-latent-neighbours (NLN) algorithm is memory and time efficient, does not requir…
Ruhr University Bochum（波鸿鲁尔大学）；Bucknell University（巴克内尔大学）
Traditional computational authorship attribution describes a classification task in a closed-set scenario. Given a finite set of candidate authors and corresponding labeled texts, the objective is to determine which of the authors has written another set of anonymous or disputed texts. In this work, we propose a probabilistic autoencoding framework to deal with this supervised classification task. More precisely, we are extending a variational autoencoder (VAE) with embedded Gaussian mixture model to a Student-$t$ mixture model. Autoencoders have had tremendous success in learning latent repre…
The paper presents the application of Variational Autoencoders (VAE) for data dimensionality reduction and explorative analysis of mass spectrometry imaging data (MSI). The results confirm that VAEs are capable of detecting the patterns associated with the different tissue sub-types with performance than standard approaches.
Through training on unlabeled data, anomaly detection has the potential to impact computer-aided diagnosis by outlining suspicious regions. Previous work on deep-learning-based anomaly detection has primarily focused on the reconstruction error. We argue instead, that pixel-wise anomaly ratings derived from a Variational Autoencoder based score approximation yield a theoretically better grounded and more faithful estimate. In our experiments, Variational Autoencoder gradient-based rating outperforms other approaches on unsupervised pixel-wise tumor detection on the BraTS-2017 dataset with a RO…
The slowness principle is a concept inspired by the visual cortex of the brain. It postulates that the underlying generative factors of a quickly varying sensory signal change on a slower time scale. Unsupervised learning of intermediate representations utilizing abundant unlabeled sensory data can be leveraged to perform data-efficient supervised downstream regression. In this paper, we propose a general formulation of slowness for unsupervised representation learning adding a slowness regularization term to the estimate lower bound of the beta-VAE to encourage temporal similarity in observat…
Harvard University（哈佛大学）；Massachusetts Institute of Technology（麻省理工学院）
Amortized variational inference (AVI) replaces instance-specific local inference with a global inference network. While AVI has enabled efficient training of deep generative models such as variational autoencoders (VAE), recent empirical work suggests that inference networks can produce suboptimal variational parameters. We propose a hybrid approach, to use AVI to initialize the variational parameters and run stochastic variational inference (SVI) to refine them. Crucially, the local SVI procedure is itself differentiable, so the inference network and generative model can be trained end-to-end…
Variational autoencoders often assume isotropic Gaussian priors and mean-field posteriors, hence do not exploit structure in scenarios where we may expect similarity or consistency across latent variables. Gaussian process variational autoencoders alleviate this problem through the use of a latent Gaussian process, but lead to a cubic inference time complexity. We propose a more scalable extension of these models by leveraging the independence of the auxiliary features, which is present in many datasets. Our model factorizes the latent kernel across these features in different dimensions, lead…
A key advance in learning generative models is the use of amortized inference distributions that are jointly trained with the models. We find that existing training objectives for variational autoencoders can lead to inaccurate amortized inference distributions and, in some cases, improving the objective provably degrades the inference quality. In addition, it has been observed that variational autoencoders tend to ignore the latent variables when combined with a decoding distribution that is too flexible. We again identify the cause in existing training criteria and propose a new class of obj…
MPI Tübingen（图宾根马普研究所）；Microsoft Research Cambridge（微软剑桥研究院）；ETH Zürich（苏黎世联邦理工学院）
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 VA…
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.
This paper introduces the Descriptive Variational Autoencoder (DVAE), an unsupervised and end-to-end trainable neural network for predicting vehicle trajectories that provides partial interpretability. The novel approach is based on the architecture and objective of common variational autoencoders. By introducing expert knowledge within the decoder part of the autoencoder, the encoder learns to extract latent parameters that provide a graspable meaning in human terms. Such an interpretable latent space enables the validation by expert defined rule sets. The evaluation of the DVAE is performed …
University of California Santa Barbara（加州大学圣巴巴拉分校）
Variational language models seek to estimate the posterior of latent variables with an approximated variational posterior. The model often assumes the variational posterior to be factorized even when the true posterior is not. The learned variational posterior under this assumption does not capture the dependency relationships over latent variables. We argue that this would cause a typical training problem called posterior collapse observed in all other variational language models. We propose Gaussian Copula Variational Autoencoder (VAE) to avert this problem. Copula is widely used to model co…
We formulate learning of a binary autoencoder as a biconvex optimization problem which learns from the pairwise correlations between encoded and decoded bits. Among all possible algorithms that use this information, ours finds the autoencoder that reconstructs its inputs with worst-case optimal loss. The optimal decoder is a single layer of artificial neurons, emerging entirely from the minimax loss minimization, and with weights learned by convex optimization. All this is reflected in competitive experimental results, demonstrating that binary autoencoding can be done efficiently by conveying…
We present an approach to quantify and compare the privacy-accuracy trade-off for differentially private Variational Autoencoders. Our work complements previous work in two aspects. First, we evaluate the the strong reconstruction MI attack against Variational Autoencoders under differential privacy. Second, we address the data scientist's challenge of setting privacy parameter epsilon, which steers the differential privacy strength and thus also the privacy-accuracy trade-off. In our experimental study we consider image and time series data, and three local and central differential privacy me…
Variational autoencoders trained to minimize the reconstruction error are sensitive to the posterior collapse problem, that is the proposal posterior distribution is always equal to the prior. We propose a novel regularization method based on fraternal dropout to prevent posterior collapse. We evaluate our approach using several metrics and observe improvements in all the tested configurations.
The current practice of manually processing features for high-dimensional and heterogeneous aviation data is labor-intensive, does not scale well to new problems, and is prone to information loss, affecting the effectiveness and maintainability of machine learning (ML) procedures. This research explored an unsupervised learning method, autoencoder, to extract effective features for aviation machine learning problems. The study explored variants of autoencoders with the aim of forcing the learned representations of the input to assume useful properties. A flight track anomaly detection autoenco…
Recently, the standard variational autoencoder has been successfully used to learn a probabilistic prior over speech signals, which is then used to perform speech enhancement. Variational autoencoders have then been conditioned on a label describing a high-level speech attribute (e.g. speech activity) that allows for a more explicit control of speech generation. However, the label is not guaranteed to be disentangled from the other latent variables, which results in limited performance improvements compared to the standard variational autoencoder. In this work, we propose to use an adversarial…
