A novel stability-enhanced Gaussian process variational autoencoder (SEGP-VAE) is proposed for indirectly training a low-dimensional linear time invariant (LTI) system, using high-dimensional video data. The mean and covariance function of the novel SEGP prior are derived from the definition of an LTI system, enabling the SEGP to capture the indirectly observed latent process using a combined probabilistic and interpretable physical model. The search space of LTI parameters is restricted to the set of semi-contracting systems via a complete and unconstrained parametrisation. As a result, the SEGP-VAE can be trained using unconstrained optimisation algorithms. Furthermore, this parametrisation prevents numerical issues caused by the presence of a non-Hurwitz state matrix. A case study applies SEGP-VAE to a dataset containing videos of spiralling particles. This highlights the benefits of the approach and the application-specific design choices that enabled accurate latent state predictions.
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.
University of California Santa Barbara (UCSB)（加州大学圣塔芭芭拉分校）
We develop data-driven methods for incorporating physical information for priors to learn parsimonious representations of nonlinear systems arising from parameterized PDEs and mechanics. Our approach is based on Variational Autoencoders (VAEs) for learning from observations nonlinear state space models. We develop ways to incorporate geometric and topological priors through general manifold latent space representations. We investigate the performance of our methods for learning low dimensional representations for the nonlinear Burgers equation and constrained mechanical systems.
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…
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 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 …
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…
Recently, variational autoencoders have been successfully used to learn a probabilistic prior over speech signals, which is then used to perform speech enhancement. However, variational autoencoders are trained on clean speech only, which results in a limited ability of extracting the speech signal from noisy speech compared to supervised approaches. In this paper, we propose to guide the variational autoencoder with a supervised classifier separately trained on noisy speech. The estimated label is a high-level categorical variable describing the speech signal (e.g. speech activity) allowing f…
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.
Karlsruhe Institute of Technology（卡尔斯鲁厄理工学院）；Nokia（诺基亚）
We evaluate the start-up of blind equalizers at critical working points, analyze the advantages and obstacles of commonly-used algorithms, and demonstrate how the recently-proposed variational autoencoder (VAE) based equalizers can improve bootstrapping.
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…
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.
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.
Adversarial attacks are malicious inputs that derail machine-learning models. We propose a scheme to attack autoencoders, as well as a quantitative evaluation framework that correlates well with the qualitative assessment of the attacks. We assess --- with statistically validated experiments --- the resistance to attacks of three variational autoencoders (simple, convolutional, and DRAW) in three datasets (MNIST, SVHN, CelebA), showing that both DRAW's recurrence and attention mechanism lead to better resistance. As autoencoders are proposed for compressing data --- a scenario in which their s…
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.
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 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…
Among likelihood-based approaches for deep generative modelling, variational autoencoders (VAEs) offer scalable amortized posterior inference and fast sampling. However, VAEs are also more and more outperformed by competing models such as normalizing flows (NFs), deep-energy models, or the new denoising diffusion probabilistic models (DDPMs). In this preliminary work, we improve VAEs by demonstrating how DDPMs can be used for modelling the prior distribution of the latent variables. The diffusion prior model improves upon Gaussian priors of classical VAEs and is competitive with NF-based prior…
King Abdullah University of Science and Technology（阿卜杜拉国王科技大学）
Variational autoencoders (VAE) often use Gaussian or category distribution to model the inference process. This puts a limit on variational learning because this simplified assumption does not match the true posterior distribution, which is usually much more sophisticated. To break this limitation and apply arbitrary parametric distribution during inference, this paper derives a \emph{semi-continuous} latent representation, which approximates a continuous density up to a prescribed precision, and is much easier to analyze than its continuous counterpart because it is fundamentally discrete. We…
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…
Seoul National University（首尔大学）；Samsung Electronics Co. Ltd.（三星电子株式会社）
In this paper, we propose Squeezed Convolutional Variational AutoEncoder (SCVAE) for anomaly detection in time series data for Edge Computing in Industrial Internet of Things (IIoT). The proposed model is applied to labeled time series data from UCI datasets for exact performance evaluation, and applied to real world data for indirect model performance comparison. In addition, by comparing the models before and after applying Fire Modules from SqueezeNet, we show that model size and inference times are reduced while similar levels of performance is maintained.
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.
Bielefeld University（比勒费尔德大学）；Australian Centre for Robotic Vision（澳大利亚机器人视觉中心）；Queensland University of Technology（昆士兰科技大学）
This contribution comprises the interplay between a multi-modal variational autoencoder and an environment to a perceived environment, on which an agent can act. Furthermore, we conclude our work with a comparison to curiosity-driven learning.
Recent increase in popularity of indoor climbing allows possible applications of deep learning algorthms to classify and generate climbing routes. In this work, we employ a variational autoencoder to climbing routes in a standardized training apparatus MoonBoard, a well-known training tool within the climbing community. By sampling the encoded latent space, it is observed that the algorithm can generate high quality climbing routes. 22 generated problems are uploaded to the Moonboard app for user review. This algorithm could serve as a first step to facilitate indoor climbing route setting.
Variational autoencoders employ an amortized inference model to approximate the posterior of latent variables. However, such amortized variational inference faces two challenges: (1) the limited posterior expressiveness of fully-factorized Gaussian assumption and (2) the amortization error of the inference model. We present a novel approach that addresses both challenges. First, we focus on ReLU networks with Gaussian output and illustrate their connection to probabilistic PCA. Building on this observation, we derive an iterative algorithm that finds the mode of the posterior and apply full-co…
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.
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.
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…
Computational design optimization in fluid dynamics usually requires to solve non-linear partial differential equations numerically. In this work, we explore a Bayesian optimization approach to minimize an object's drag coefficient in laminar flow based on predicting drag directly from the object shape. Jointly training an architecture combining a variational autoencoder mapping shapes to latent representations and Gaussian process regression allows us to generate improved shapes in the two dimensional case we consider.
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 Hong Kong University of Science and Technology（香港科技大学）；The Education University of Hong Kong（香港教育大学）
We investigate a variant of variational autoencoders where there is a superstructure of discrete latent variables on top of the latent features. In general, our superstructure is a tree structure of multiple super latent variables and it is automatically learned from data. When there is only one latent variable in the superstructure, our model reduces to one that assumes the latent features to be generated from a Gaussian mixture model. We call our model the latent tree variational autoencoder (LTVAE). Whereas previous deep learning methods for clustering produce only one partition of data, LT…
Stanford University（斯坦福大学）；Facebook AI Research（Facebook人工智能研究院）
Variational autoencoders (VAE) are directed generative models that learn factorial latent variables. As noted by Burda et al. (2015), these models exhibit the problem of factor over-pruning where a significant number of stochastic factors fail to learn anything and become inactive. This can limit their modeling power and their ability to learn diverse and meaningful latent representations. In this paper, we evaluate several methods to address this problem and propose a more effective model-based approach called the epitomic variational autoencoder (eVAE). The so-called epitomes of this model a…
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…
We propose a VAE for Transformers by developing a variational information bottleneck regulariser for Transformer embeddings. We formalise the embedding space of Transformer encoders as mixture probability distributions, and use Bayesian nonparametrics to derive a nonparametric variational information bottleneck (NVIB) for such attention-based embeddings. The variable number of mixture components supported by nonparametric methods captures the variable number of vectors supported by attention, and the exchangeability of our nonparametric distributions captures the permutation invariance of atte…
Recently introduced EASE algorithm presents a simple and elegant way, how to solve the top-N recommendation task. In this paper, we introduce Neural EASE to further improve the performance of this algorithm by incorporating techniques for training modern neural networks. Also, there is a growing interest in the recsys community to utilize variational autoencoders (VAE) for this task. We introduce deep autoencoder FLVAE benefiting from multiple non-linear layers without an information bottleneck while not overfitting towards the identity. We show how to learn FLVAE in parallel with Neural EASE …
Department of Computer Science, University of Toronto（多伦多大学计算机科学系）
Amortized inference allows latent-variable models trained via variational learning to scale to large datasets. The quality of approximate inference is determined by two factors: a) the capacity of the variational distribution to match the true posterior and b) the ability of the recognition network to produce good variational parameters for each datapoint. We examine approximate inference in variational autoencoders in terms of these factors. We find that divergence from the true posterior is often due to imperfect recognition networks, rather than the limited complexity of the approximating d…
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…
Department of Computer Science（计算机科学系）；Ecole Polytechnique（巴黎综合理工学院）；Palaiseau, FRANCE（帕莱索，法国（注：此为地址信息，按要求不应提取，此处原HTML可能存在格式错误，正确机构应为前两个））
In the original version of the Variational Autoencoder, Kingma et al. assume Gaussian distributions for the approximate posterior during the inference and for the output during the generative process. This assumptions are good for computational reasons, e.g. we can easily optimize the parameters of a neural network using the reparametrization trick and the KL divergence between two Gaussians can be computed in closed form. However it results in blurry images due to its difficulty to represent multimodal distributions. We show that using two adversarial networks, we can optimize the parameters …
A probability distribution allows practitioners to uncover hidden structure in the data and build models to solve supervised learning problems using limited data. The focus of this report is on Variational autoencoders, a method to learn the probability distribution of large complex datasets. The report provides a theoretical understanding of variational autoencoders and consolidates the current research in the field. The report is divided into multiple chapters, the first chapter introduces the problem, describes variational autoencoders and identifies key research directions in the field. Ch…
European Organization for Nuclear Research (CERN)（欧洲核子研究组织（CERN））；Laboratoire de Recherche en Informatique (LRI)（计算机科学研究实验室（LRI））；Université Paris-Saclay（巴黎萨克雷大学）
Exploiting the rapid advances in probabilistic inference, in particular variational Bayes and variational autoencoders (VAEs), for anomaly detection (AD) tasks remains an open research question. Previous works argued that training VAE models only with inliers is insufficient and the framework should be significantly modified in order to discriminate the anomalous instances. In this work, we exploit the deep conditional variational autoencoder (CVAE) and we define an original loss function together with a metric that targets hierarchically structured data AD. Our motivating application is a rea…
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…
The notion of disentangled autoencoders was proposed as an extension to the variational autoencoder by introducing a disentanglement parameter $β$, controlling the learning pressure put on the possible underlying latent representations. For certain values of $β$ this kind of autoencoders is capable of encoding independent input generative factors in separate elements of the code, leading to a more interpretable and predictable model behaviour. In this paper we quantify the effects of the parameter $β$ on the model performance and disentanglement. After training multiple models with the same va…
New York University（纽约大学）；Genentech（基因泰克）；NYU Langone Health（纽约大学朗格尼医学中心）
Domain adaptation and covariate shift are big issues in deep learning and they ultimately affect any causal inference algorithms that rely on deep neural networks. Causal effect variational autoencoder (CEVAE) is trained to predict the outcome given observational treatment data and it suffers from the distribution shift at test time. In this paper, we introduce uniform treatment variational autoencoders (UTVAE) that are trained with uniform treatment distribution using importance sampling and show that using uniform treatment over observational treatment distribution leads to better causal inf…
