Generative AutoEncoders require a chosen probability distribution in latent space, usually multivariate Gaussian. The original Variational AutoEncoder (VAE) uses randomness in encoder - causing problematic distortion, and overlaps in latent space for distinct inputs. It turned out unnecessary: we can instead use deterministic encoder with additional regularizer to ensure that sample distribution in latent space is close to the required. The original approach (WAE) uses Wasserstein metric, what required comparing with random sample and using an arbitrarily chosen kernel. Later CWAE finally derived a non-random analytic formula by averaging $L_2$ distance of Gaussian-smoothened sample over all 1D projections. However, these arbitrarily chosen regularizers do not lead to Gaussian distribution.
This article proposes approach for regularizers directly optimizing agreement between empirical distribution function and its desired CDF for chosen properties, for example radii and distances for Gaussian distribution, or coordinate-wise, to directly attract this distribution in latent space of AutoEncoder. We can also attract different distributions with this general approach, for example latent space uniform distribution on $[0,1]^D$ hypercube or torus would allow for data compression without entropy coding, increased density near codewords would optimize for the required quantization.
KTH Royal Institute of Technology（瑞典皇家理工学院）；Research Institutes of Sweden（瑞典研究机构）
Autoencoders and their variations provide unsupervised models for learning low-dimensional representations for downstream tasks. Without proper regularization, autoencoder models are susceptible to the overfitting problem and the so-called posterior collapse phenomenon. In this paper, we introduce a quantization-based regularizer in the bottleneck stage of autoencoder models to learn meaningful latent representations. We combine both perspectives of Vector Quantized-Variational AutoEncoders (VQ-VAE) and classical denoising regularization methods of neural networks. We interpret quantizers as r…
Invertible flow-based generative models are an effective method for learning to generate samples, while allowing for tractable likelihood computation and inference. However, the invertibility requirement restricts models to have the same latent dimensionality as the inputs. This imposes significant architectural, memory, and computational costs, making them more challenging to scale than other classes of generative models such as Variational Autoencoders (VAEs). We propose a generative model based on probability flows that does away with the bijectivity requirement on the model and only assume…
University of Oxford（牛津大学）；Universitat de València（瓦伦西亚大学）
Current adoption of machine learning in industrial, societal and economical activities has raised concerns about the fairness, equity and ethics of automated decisions. Predictive models are often developed using biased datasets and thus retain or even exacerbate biases in their decisions and recommendations. Removing the sensitive covariates, such as gender or race, is insufficient to remedy this issue since the biases may be retained due to other related covariates. We present a regularization approach to this problem that trades off predictive accuracy of the learned models (with respect to…
EURECOM（欧洲通信研究院）；University of California, Irvine（加州大学欧文分校）
Autoencoders and their variants are among the most widely used models in representation learning and generative modeling. However, autoencoder-based models usually assume that the learned representations are i.i.d. and fail to capture the correlations between the data samples. To address this issue, we propose a novel Sparse Gaussian Process Bayesian Autoencoder (SGPBAE) model in which we impose fully Bayesian sparse Gaussian Process priors on the latent space of a Bayesian Autoencoder. We perform posterior estimation for this model via stochastic gradient Hamiltonian Monte Carlo. We evaluate …
Pohang University of Science and Technology（浦项科技大学）
The variational autoencoder (VAE) is a generative model with continuous latent variables where a pair of probabilistic encoder (bottom-up) and decoder (top-down) is jointly learned by stochastic gradient variational Bayes. We first elaborate Gaussian VAE, approximating the local covariance matrix of the decoder as an outer product of the principal direction at a position determined by a sample drawn from Gaussian distribution. We show that this model, referred to as VAE-ROC, better captures the data manifold, compared to the standard Gaussian VAE where independent multivariate Gaussian was use…
University of Cambridge（剑桥大学）；The Alan Turing Institute（艾伦·图灵研究所）
Variational autoencoders (VAEs) are a powerful class of deep generative latent variable model for unsupervised representation learning on high-dimensional data. To ensure computational tractability, VAEs are often implemented with a univariate standard Gaussian prior and a mean-field Gaussian variational posterior distribution. This results in a vector-valued latent variables that are agnostic to the original data structure which might be highly correlated across and within multiple dimensions. We propose a tensor-variate extension to the VAE framework, the tensor-variate Gaussian process prio…
While the impact of variational inference (VI) on posterior inference in a fixed generative model is well-characterized, its role in regularizing a learned generative model when used in variational autoencoders (VAEs) is poorly understood. We study the regularizing effects of variational distributions on learning in generative models from two perspectives. First, we analyze the role that the choice of variational family plays in imparting uniqueness to the learned model by restricting the set of optimal generative models. Second, we study the regularization effect of the variational family on …
ETH Zürich（苏黎世联邦理工学院）；University of Cambridge（剑桥大学）；University of Warwick（华威大学）；University of California, Irvine（加州大学欧文分校）
Conventional variational autoencoders fail in modeling correlations between data points due to their use of factorized priors. Amortized Gaussian process inference through GP-VAEs has led to significant improvements in this regard, but is still inhibited by the intrinsic complexity of exact GP inference. We improve the scalability of these methods through principled sparse inference approaches. We propose a new scalable GP-VAE model that outperforms existing approaches in terms of runtime and memory footprint, is easy to implement, and allows for joint end-to-end optimization of all components…
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 …
Autoencoders provide a powerful framework for learning compressed representations by encoding all of the information needed to reconstruct a data point in a latent code. In some cases, autoencoders can "interpolate": By decoding the convex combination of the latent codes for two datapoints, the autoencoder can produce an output which semantically mixes characteristics from the datapoints. In this paper, we propose a regularization procedure which encourages interpolated outputs to appear more realistic by fooling a critic network which has been trained to recover the mixing coefficient from in…
This paper describes an entropy regularization term for vector quantization (VQ) based on the analysis of persistent homology of the VQ embeddings. Higher embedding entropy positively correlates with higher codebook utilization, mitigating overfit towards the identity and codebook collapse in VQ-based autoencoders [1]. We show that homology-constrained regularization is an effective way to increase entropy of the VQ process (approximated to input entropy) while preserving the approximated topology in the quantized latent space, averaged over mini batches. This work further explores some patter…
Complex multivariate time series arise in many fields, ranging from computer vision to robotics or medicine. Often we are interested in the independent underlying factors that give rise to the high-dimensional data we are observing. While many models have been introduced to learn such disentangled representations, only few attempt to explicitly exploit the structure of sequential data. We investigate the disentanglement properties of Gaussian process variational autoencoders, a class of models recently introduced that have been successful in different tasks on time series data. Our model explo…
Variation Autoencoder (VAE) has become a powerful tool in modeling the non-linear generative process of data from a low-dimensional latent space. Recently, several studies have proposed to use VAE for unsupervised clustering by using mixture models to capture the multi-modal structure of latent representations. This strategy, however, is ineffective when there are outlier data samples whose latent representations are meaningless, yet contaminating the estimation of key major clusters in the latent space. This exact problem arises in the context of resting-state fMRI (rs-fMRI) analysis, where c…
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…
Microsoft Research New England（微软新英格兰研究院）；Italian Institute for Genomic Medicine（意大利基因组医学研究所）；University of California, Berkeley（加州大学伯克利分校）
Variational autoencoders (VAE) are a powerful and widely-used class of models to learn complex data distributions in an unsupervised fashion. One important limitation of VAEs is the prior assumption that latent sample representations are independent and identically distributed. However, for many important datasets, such as time-series of images, this assumption is too strong: accounting for covariances between samples, such as those in time, can yield to a more appropriate model specification and improve performance in downstream tasks. In this work, we introduce a new model, the Gaussian Proc…
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…
An important property for deep neural networks is the ability to perform robust out-of-distribution detection on previously unseen data. This property is essential for safety purposes when deploying models for real world applications. Recent studies show that probabilistic generative models can perform poorly on this task, which is surprising given that they seek to estimate the likelihood of training data. To alleviate this issue, we propose the exponentially tilted Gaussian prior distribution for the Variational Autoencoder (VAE) which pulls points onto the surface of a hyper-sphere in laten…
Shanghai Jiao Tong University（上海交通大学）；Wuhan University（武汉大学）；University of California, Davis（加州大学戴维斯分校）
Recently, deep generative models have become increasingly popular in unsupervised anomaly detection. However, deep generative models aim at recovering the data distribution rather than detecting anomalies. Besides, deep generative models have the risk of overfitting training samples, which has disastrous effects on anomaly detection performance. To solve the above two problems, we propose a Self-adversarial Variational Autoencoder with a Gaussian anomaly prior assumption. We assume that both the anomalous and the normal prior distribution are Gaussian and have overlaps in the latent space. The…
University of Cambridge（剑桥大学）；ETH Zürich（苏黎世联邦理工学院）；Warwick University（华威大学）
Large, multi-dimensional spatio-temporal datasets are omnipresent in modern science and engineering. An effective framework for handling such data are Gaussian process deep generative models (GP-DGMs), which employ GP priors over the latent variables of DGMs. Existing approaches for performing inference in GP-DGMs do not support sparse GP approximations based on inducing points, which are essential for the computational efficiency of GPs, nor do they handle missing data -- a natural occurrence in many spatio-temporal datasets -- in a principled manner. We address these shortcomings with the de…
Max Planck Institute for Polymer Research（马克斯·普朗克聚合物研究所）；Koc University（科奇大学）
Extracting insight from the enormous quantity of data generated from molecular simulations requires the identification of a small number of collective variables whose corresponding low-dimensional free-energy landscape retains the essential features of the underlying system. Data-driven techniques provide a systematic route to constructing this landscape, without the need for extensive a priori intuition into the relevant driving forces. In particular, autoencoders are powerful tools for dimensionality reduction, as they naturally force an information bottleneck and, thereby, a low-dimensional…
In inference, open-set classification is to either classify a sample into a known class from training or reject it as an unknown class. Existing deep open-set classifiers train explicit closed-set classifiers, in some cases disjointly utilizing reconstruction, which we find dilutes the latent representation's ability to distinguish unknown classes. In contrast, we train our model to cooperatively learn reconstruction and perform class-based clustering in the latent space. With this, our Gaussian mixture variational autoencoder (GMVAE) achieves more accurate and robust open-set classification r…
University of Bologna（博洛尼亚大学）；Department of Informatics: Science and Engineering (DISI)（信息学系：科学与工程（DISI））
In the loss function of Variational Autoencoders there is a well known tension between two components: the reconstruction loss, improving the quality of the resulting images, and the Kullback-Leibler divergence, acting as a regularizer of the latent space. Correctly balancing these two components is a delicate issue, easily resulting in poor generative behaviours. In a recent work, Dai and Wipf obtained a sensible improvement by allowing the network to learn the balancing factor during training, according to a suitable loss function. In this article, we show that learning can be replaced by a …
We study a variant of the variational autoencoder model (VAE) with a Gaussian mixture as a prior distribution, with the goal of performing unsupervised clustering through deep generative models. We observe that the known problem of over-regularisation that has been shown to arise in regular VAEs also manifests itself in our model and leads to cluster degeneracy. We show that a heuristic called minimum information constraint that has been shown to mitigate this effect in VAEs can also be applied to improve unsupervised clustering performance with our model. Furthermore we analyse the effect of …
A neural network regularizer (e.g., weight decay) boosts performance by explicitly penalizing the complexity of a network. In this paper, we penalize inferior network activations -- feature embeddings -- which in turn regularize the network's weights implicitly. We propose singular value maximization (SVMax) to learn a more uniform feature embedding. The SVMax regularizer supports both supervised and unsupervised learning. Our formulation mitigates model collapse and enables larger learning rates. We evaluate the SVMax regularizer using both retrieval and generative adversarial networks. We le…
Max Planck Institute of Intelligent Systems（马克斯·普朗克智能系统研究所）；IBM Research AI（IBM研究院人工智能部门）
Susceptibility of deep neural networks to adversarial attacks poses a major theoretical and practical challenge. All efforts to harden classifiers against such attacks have seen limited success. Two distinct categories of samples to which deep networks are vulnerable, "adversarial samples" and "fooling samples", have been tackled separately so far due to the difficulty posed when considered together. In this work, we show how one can address them both under one unified framework. We tie a discriminative model with a generative model, rendering the adversarial objective to entail a conflict. Ou…
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…
Montreal Institute for Learning Algorithms（蒙特利尔学习算法研究所）；University of Montreal（蒙特利尔大学）
Denoising autoencoders (DAE) are trained to reconstruct their clean inputs with noise injected at the input level, while variational autoencoders (VAE) are trained with noise injected in their stochastic hidden layer, with a regularizer that encourages this noise injection. In this paper, we show that injecting noise both in input and in the stochastic hidden layer can be advantageous and we propose a modified variational lower bound as an improved objective function in this setup. When input is corrupted, then the standard VAE lower bound involves marginalizing the encoder conditional distrib…
Technical University of Denmark（丹麦技术大学）；Research Institutes of Sweden（瑞典研究院）；Max Planck Institute for Intelligent Systems（马克斯·普朗克智能系统研究所）
Variational Autoencoders (VAEs) represent the given data in a low-dimensional latent space, which is generally assumed to be Euclidean. This assumption naturally leads to the common choice of a standard Gaussian prior over continuous latent variables. Recent work has, however, shown that this prior has a detrimental effect on model capacity, leading to subpar performance. We propose that the Euclidean assumption lies at the heart of this failure mode. To counter this, we assume a Riemannian structure over the latent space, which constitutes a more principled geometric view of the latent codes,…
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…
Regularized autoencoders learn the latent codes, a structure with the regularization under the distribution, which enables them the capability to infer the latent codes given observations and generate new samples given the codes. However, they are sometimes ambiguous as they tend to produce reconstructions that are not necessarily faithful reproduction of the inputs. The main reason is to enforce the learned latent code distribution to match a prior distribution while the true distribution remains unknown. To improve the reconstruction quality and learn the latent space a manifold structure, t…
User attributes, such as gender and education, face severe incompleteness in social networks. In order to make this kind of valuable data usable for downstream tasks like user profiling and personalized recommendation, attribute inference aims to infer users' missing attribute labels based on observed data. Recently, variational autoencoder (VAE), an end-to-end deep generative model, has shown promising performance by handling the problem in a semi-supervised way. However, VAEs can easily suffer from over-fitting and over-smoothing when applied to attribute inference. To be specific, VAE imple…
Singapore University of Technology and Design（新加坡科技设计大学）；Institute of High Performance Computing, A*STAR（新加坡科技研究局高性能计算研究所）；Yong Siew Toh Conservatory of Music, National University of Singapore（新加坡大学杨秀桃音乐学院）
In this paper, we learn disentangled representations of timbre and pitch for musical instrument sounds. We adapt a framework based on variational autoencoders with Gaussian mixture latent distributions. Specifically, we use two separate encoders to learn distinct latent spaces for timbre and pitch, which form Gaussian mixture components representing instrument identity and pitch, respectively. For reconstruction, latent variables of timbre and pitch are sampled from corresponding mixture components, and are concatenated as the input to a decoder. We show the model efficacy by latent space visu…
Boltzmann machines are powerful distributions that have been shown to be an effective prior over binary latent variables in variational autoencoders (VAEs). However, previous methods for training discrete VAEs have used the evidence lower bound and not the tighter importance-weighted bound. We propose two approaches for relaxing Boltzmann machines to continuous distributions that permit training with importance-weighted bounds. These relaxations are based on generalized overlapping transformations and the Gaussian integral trick. Experiments on the MNIST and OMNIGLOT datasets show that these r…
High dimensional data is often assumed to be concentrated on or near a low-dimensional manifold. Autoencoders (AE) is a popular technique to learn representations of such data by pushing it through a neural network with a low dimension bottleneck while minimizing a reconstruction error. Using high capacity AE often leads to a large collection of minimizers, many of which represent a low dimensional manifold that fits the data well but generalizes poorly. Two sources of bad generalization are: extrinsic, where the learned manifold possesses extraneous parts that are far from the data; and intri…
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…
Scientific Computing and Imaging Institute（科学计算与成像研究所）；University of Utah（犹他大学）
Unsupervised representation learning via generative modeling is a staple to many computer vision applications in the absence of labeled data. Variational Autoencoders (VAEs) are powerful generative models that learn representations useful for data generation. However, due to inherent challenges in the training objective, VAEs fail to learn useful representations amenable for downstream tasks. Regularization-based methods that attempt to improve the representation learning aspect of VAEs come at a price: poor sample generation. In this paper, we explore this representation-generation trade-off …
University of Waterloo（滑铁卢大学）；ByteDance AI Lab（字节跳动人工智能实验室）
The variational autoencoder (VAE) imposes a probabilistic distribution (typically Gaussian) on the latent space and penalizes the Kullback--Leibler (KL) divergence between the posterior and prior. In NLP, VAEs are extremely difficult to train due to the problem of KL collapsing to zero. One has to implement various heuristics such as KL weight annealing and word dropout in a carefully engineered manner to successfully train a VAE for text. In this paper, we propose to use the Wasserstein autoencoder (WAE) for probabilistic sentence generation, where the encoder could be either stochastic or de…
Cosmic microwave background radiation (CMB) is critical to the understanding of the early universe and precise estimation of cosmological constants. Due to the contamination of thermal dust noise in the galaxy, the CMB map that is an image on the two-dimensional sphere has missing observations, mainly concentrated on the equatorial region. The noise of the CMB map has a significant impact on the estimation precision for cosmological parameters. Inpainting the CMB map can effectively reduce the uncertainty of parametric estimation. In this paper, we propose a deep learning-based variational aut…
Queen’s University（女王大学）；Azad University（阿扎德大学）；University of Leeds（利兹大学）；KU Leuven（荷语鲁汶大学）；Shenzhen University（深圳大学）
In large studies involving multi protocol Magnetic Resonance Imaging (MRI), it can occur to miss one or more sub-modalities for a given patient owing to poor quality (e.g. imaging artifacts), failed acquisitions, or hallway interrupted imaging examinations. In some cases, certain protocols are unavailable due to limited scan time or to retrospectively harmonise the imaging protocols of two independent studies. Missing image modalities pose a challenge to segmentation frameworks as complementary information contributed by the missing scans is then lost. In this paper, we propose a novel model, …
University of Oxford（牛津大学）；UCL（伦敦大学学院）；The Alan Turing Institute（艾伦·图灵研究所）
In this work we study Variational Autoencoders (VAEs) from the perspective of harmonic analysis. By viewing a VAE's latent space as a Gaussian Space, a variety of measure space, we derive a series of results that show that the encoder variance of a VAE controls the frequency content of the functions parameterised by the VAE encoder and decoder neural networks. In particular we demonstrate that larger encoder variances reduce the high frequency content of these functions. Our analysis allows us to show that increasing this variance effectively induces a soft Lipschitz constraint on the decoder …
Department of Chemical and Biomolecular Engineering, University of Maryland（马里兰大学化学与生物分子工程系）
Conformational sampling of biomolecules using molecular dynamics simulations often produces large amount of high dimensional data that makes it difficult to interpret using conventional analysis techniques. Dimensionality reduction methods are thus required to extract useful and relevant information. Here we devise a machine learning method, Gaussian mixture variational autoencoder (GMVAE) that can simultaneously perform dimensionality reduction and clustering of biomolecular conformations in an unsupervised way. We show that GMVAE can learn a reduced representation of the free energy landscap…
Sapienza University of Rome（罗马第一大学）；Cardiff University（卡迪夫大学）；Technical University of Munich（慕尼黑工业大学）
In machine learning, novelty detection is the task of identifying novel unseen data. During training, only samples from the normal class are available. Test samples are classified as normal or abnormal by assignment of a novelty score. Here we propose novelty detection methods based on training variational autoencoders (VAEs) on normal data. Since abnormal samples are not used during training, we define novelty metrics based on the (partially complementary) assumptions that the VAE is less capable of reconstructing abnormal samples well; that abnormal samples more strongly violate the VAE regu…
