Principal Component Analysis (PCA) minimizes the reconstruction error given a class of linear models of fixed component dimensionality. Probabilistic PCA adds a probabilistic structure by learning the probability distribution of the PCA latent space weights, thus creating a generative model. Autoencoders (AE) minimize the reconstruction error in a class of nonlinear models of fixed latent space dimensionality and outperform PCA at fixed dimensionality. Here, we introduce the Probabilistic Autoencoder (PAE) that learns the probability distribution of the AE latent space weights using a normalizing flow (NF). The PAE is fast and easy to train and achieves small reconstruction errors, high sample quality, and good performance in downstream tasks. We compare the PAE to Variational AE (VAE), showing that the PAE trains faster, reaches a lower reconstruction error, and produces good sample quality without requiring special tuning parameters or training procedures. We further demonstrate that the PAE is a powerful model for performing the downstream tasks of probabilistic image reconstruction in the context of Bayesian inference of inverse problems for inpainting and denoising applications. Finally, we identify latent space density from NF as a promising outlier detection metric.
We introduce and demonstrate the variational autoencoder (VAE) for probabilistic non-negative matrix factorisation (PAE-NMF). We design a network which can perform non-negative matrix factorisation (NMF) and add in aspects of a VAE to make the coefficients of the latent space probabilistic. By restricting the weights in the final layer of the network to be non-negative and using the non-negative Weibull distribution we produce a probabilistic form of NMF which allows us to generate new data and find a probability distribution that effectively links the latent and input variables. We demonstrat…
University of California, Berkeley（加州大学伯克利分校）；Lawrence Berkeley National Laboratory（劳伦斯伯克利国家实验室）；Sorbonne Université（索邦大学）；Université de Paris（巴黎大学）；University of Washington（华盛顿大学）
We construct a physically-parameterized probabilistic autoencoder (PAE) to learn the intrinsic diversity of type Ia supernovae (SNe Ia) from a sparse set of spectral time series. The PAE is a two-stage generative model, composed of an Auto-Encoder (AE) which is interpreted probabilistically after training using a Normalizing Flow (NF). We demonstrate that the PAE learns a low-dimensional latent space that captures the nonlinear range of features that exists within the population, and can accurately model the spectral evolution of SNe Ia across the full range of wavelength and observation times…
School of Informatics（信息学院）；University of Edinburgh（爱丁堡大学）；Alan Turing Institute（艾伦·图灵研究所）
Latent variable models can be used to probabilistically "fill-in" missing data entries. The variational autoencoder architecture (Kingma and Welling, 2014; Rezende et al., 2014) includes a "recognition" or "encoder" network that infers the latent variables given the data variables. However, it is not clear how to handle missing data variables in this network. The factor analysis (FA) model is a basic autoencoder, using linear encoder and decoder networks. We show how to calculate exactly the latent posterior distribution for the factor analysis (FA) model in the presence of missing data, and n…
(T.A.E.) 2 Faculty of Physics, Ludwig -Maximilians-Universit \"a t M \"u nchen, Geschwister-Scholl-Platz 1, 80539 M \"u nchen, Germany
Neural Networks play a growing role in many science disciplines, including physics. Variational Autoencoders (VAEs) are neural networks that are able to represent the essential information of a high dimensional data set in a low dimensional latent space, which have a probabilistic interpretation. In particular the so-called encoder network, the first part of the VAE, which maps its input onto a position in latent space, additionally provides uncertainty information in terms of a variance around this position. In this work, an extension to the Autoencoder architecture is introduced, the FisherN…
Probabilistic models with discrete latent variables naturally capture datasets composed of discrete classes. However, they are difficult to train efficiently, since backpropagation through discrete variables is generally not possible. We present a novel method to train a class of probabilistic models with discrete latent variables using the variational autoencoder framework, including backpropagation through the discrete latent variables. The associated class of probabilistic models comprises an undirected discrete component and a directed hierarchical continuous component. The discrete compon…
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…
Any autoencoder network can be turned into a generative model by imposing an arbitrary prior distribution on its hidden code vector. Variational Autoencoder (VAE) [2] uses a KL divergence penalty to impose the prior, whereas Adversarial Autoencoder (AAE) [1] uses {\it generative adversarial networks} GAN [3]. GAN trades the complexities of {\it sampling} algorithms with the complexities of {\it searching} Nash equilibrium in minimax games. Such minimax architectures get trained with the help of data examples and gradients flowing through a generator and an adversary. A straightforward modifica…
Disentangled Latent Spaces for Reduced Order Models using Deterministic Autoencoders
Institute for Fluid Dynamics and Ship Theory, Hamburg University of Technology（汉堡工业大学流体动力学与船舶理论研究所）；Institute of Mathematics, Hamburg University of Technology（汉堡工业大学数学研究所）
The paper addresses the problem of finding the causal direction between two associated variables. The proposed solution is to build an autoencoder of their joint distribution and to maximize its estimation capacity relative to both the marginal distributions. It is shown that the resulting two capacities cannot, in general, be equal. This leads to a new criterion for causal discovery: the higher capacity is consistent with the unconstrained choice of a distribution representing the cause while the lower capacity reflects the constraints imposed by the mechanism on the distribution of the effec…
We present VAEL, a neuro-symbolic generative model integrating variational autoencoders (VAE) with the reasoning capabilities of probabilistic logic (L) programming. Besides standard latent subsymbolic variables, our model exploits a probabilistic logic program to define a further structured representation, which is used for logical reasoning. The entire process is end-to-end differentiable. Once trained, VAEL can solve new unseen generation tasks by (i) leveraging the previously acquired knowledge encoded in the neural component and (ii) exploiting new logical programs on the structured laten…
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.
Variational Autoencoders (VAEs) have experienced recent success as data-generating models by using simple architectures that do not require significant fine-tuning of hyperparameters. However, VAEs are known to suffer from over-regularization which can lead to failure to escape local maxima. This phenomenon, known as posterior collapse, prevents learning a meaningful latent encoding of the data. Recent methods have mitigated this issue by deterministically moment-matching an aggregated posterior distribution to an aggregate prior. However, abandoning a probabilistic framework (and thus relying…
Duke University（杜克大学）；Infinia ML Inc.（Infinia ML公司）
A new algorithmic framework is proposed for learning autoencoders of data distributions. We minimize the discrepancy between the model and target distributions, with a \emph{relational regularization} on the learnable latent prior. This regularization penalizes the fused Gromov-Wasserstein (FGW) distance between the latent prior and its corresponding posterior, allowing one to flexibly learn a structured prior distribution associated with the generative model. Moreover, it helps co-training of multiple autoencoders even if they have heterogeneous architectures and incomparable latent spaces. W…
University of Oxford（牛津大学）；Microsoft Research（微软研究院）
We would like to learn a representation of the data which decomposes an observation into factors of variation which we can independently control. Specifically, we want to use minimal supervision to learn a latent representation that reflects the semantics behind a specific grouping of the data, where within a group the samples share a common factor of variation. For example, consider a collection of face images grouped by identity. We wish to anchor the semantics of the grouping into a relevant and disentangled representation that we can easily exploit. However, existing deep probabilistic mod…
pAE: An Efficient Autoencoder Architecture for Modeling the Lateral Geniculate Nucleus by Integrating Feedforward and Feedback Streams in Human Visual System
Stanford University（斯坦福大学）；Broad Institute of MIT and Harvard（麻省理工学院与哈佛大学布罗德研究所）
Autoencoders are a deep learning model for representation learning. When trained to minimize the distance between the data and its reconstruction, linear autoencoders (LAEs) learn the subspace spanned by the top principal directions but cannot learn the principal directions themselves. In this paper, we prove that $L_2$-regularized LAEs are symmetric at all critical points and learn the principal directions as the left singular vectors of the decoder. We smoothly parameterize the critical manifold and relate the minima to the MAP estimate of probabilistic PCA. We illustrate these results empir…
Probabilistic deep learning is deep learning that accounts for uncertainty, both model uncertainty and data uncertainty. It is based on the use of probabilistic models and deep neural networks. We distinguish two approaches to probabilistic deep learning: probabilistic neural networks and deep probabilistic models. The former employs deep neural networks that utilize probabilistic layers which can represent and process uncertainty; the latter uses probabilistic models that incorporate deep neural network components which capture complex non-linear stochastic relationships between the random va…
Wide accessibility of imaging and profile sensors in modern industrial systems created an abundance of high-dimensional sensing variables. This led to a a growing interest in the research of high-dimensional process monitoring. However, most of the approaches in the literature assume the in-control population to lie on a linear manifold with a given basis (i.e., spline, wavelet, kernel, etc) or an unknown basis (i.e., principal component analysis and its variants), which cannot be used to efficiently model profiles with a nonlinear manifold which is common in many real-life cases. We propose d…
NTT Network Technology Laboratories, NTT Corporation（NTT公司NTT网络技术实验室）；Faculty of Natural Sciences, International Christian University（国际基督教大学自然科学学院）
Anomaly detection using dimensionality reduction has been an essential technique for monitoring multidimensional data. Although deep learning-based methods have been well studied for their remarkable detection performance, their interpretability is still a problem. In this paper, we propose a novel algorithm for estimating the dimensions contributing to the detected anomalies by using variational autoencoders (VAEs). Our algorithm is based on an approximative probabilistic model that considers the existence of anomalies in the data, and by maximizing the log-likelihood, we estimate which dimen…
MSS-PAE: Saving Autoencoder-based Outlier Detection from Unexpected Reconstruction
School of Marine Science and Technology, Northwestern Polytechnical University（西北工业大学海洋科学与技术学院）；Faculty of Technology, University of Turku（图尔库大学技术学院）；School of Computing, University of Eastern Finland（东芬兰大学计算机学院）；Engineering Cluster, Singapore Institute of Technology（新加坡理工学院工程集群）
Multi-label classification is the challenging task of predicting the presence and absence of multiple targets, involving representation learning and label correlation modeling. We propose a novel framework for multi-label classification, Multivariate Probit Variational AutoEncoder (MPVAE), that effectively learns latent embedding spaces as well as label correlations. MPVAE learns and aligns two probabilistic embedding spaces for labels and features respectively. The decoder of MPVAE takes in the samples from the embedding spaces and models the joint distribution of output targets under a Multi…
Ensemble Visualization With Variational Autoencoder
Institute of Medical Technology, Peking University Health Science Center（北京大学健康科学中心医学技术研究所）；National Institute of Health Data Science, Peking University（北京大学健康数据科学国家研究院）；Center for Machine Learning Research, Peking University（北京大学机器学习研究中心）
We develop a novel probabilistic generative model based on the variational autoencoder approach. Notable aspects of our architecture are: a novel way of specifying the latent variables prior, and the introduction of an ordinality enforcing unit. We describe how to do supervised, unsupervised and semi-supervised learning, and nominal and ordinal classification, with the model. We analyze generative properties of the approach, and the classification effectiveness under nominal and ordinal classification, using two benchmark datasets. Our results show that our model can achieve comparable results…
FUJITSU LABORATORIES LTD.（富士通实验室有限公司）；Fujitsu R&D Center Co., Ltd.（富士通研发中心有限公司）
To analyze high-dimensional and complex data in the real world, deep generative models, such as variational autoencoder (VAE) embed data in a low-dimensional space (latent space) and learn a probabilistic model in the latent space. However, they struggle to accurately reproduce the probability distribution function (PDF) in the input space from that in the latent space. If the embedding were isometric, this issue can be solved, because the relation of PDFs can become tractable. To achieve isometric property, we propose Rate- Distortion Optimization guided autoencoder inspired by orthonormal tr…
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 Oxford（牛津大学）；Alan Turing Institute（艾伦·图灵研究所）
We make inroads into understanding the robustness of Variational Autoencoders (VAEs) to adversarial attacks and other input perturbations. While previous work has developed algorithmic approaches to attacking and defending VAEs, there remains a lack of formalization for what it means for a VAE to be robust. To address this, we develop a novel criterion for robustness in probabilistic models: $r$-robustness. We then use this to construct the first theoretical results for the robustness of VAEs, deriving margins in the input space for which we can provide guarantees about the resulting reconstru…
While unsupervised variational autoencoders (VAE) have become a powerful tool in neuroimage analysis, their application to supervised learning is under-explored. We aim to close this gap by proposing a unified probabilistic model for learning the latent space of imaging data and performing supervised regression. Based on recent advances in learning disentangled representations, the novel generative process explicitly models the conditional distribution of latent representations with respect to the regression target variable. Performing a variational inference procedure on this model leads to j…
Alfréd Rényi Institute of Mathematics（阿尔弗雷德·雷尼数学研究所）；Eötvös Loránd University（厄特沃什·罗兰大学）
Modern deep artificial neural networks have achieved great success in the domain of computer vision and beyond. However, their application to many real-world tasks is undermined by certain limitations, such as overconfident uncertainty estimates on out-of-distribution data or performance deterioration under data distribution shifts. Several types of deep learning models used for density estimation through probabilistic generative modeling have been shown to fail to detect out-of-distribution samples by assigning higher likelihoods to anomalous data. We investigate this failure mode in Variatio…
Monash University（莫纳什大学）；Indian Institute of Technology, Kanpur（印度理工学院坎普尔分校）；The University of Texas at Austin（德克萨斯大学奥斯汀分校）
Many applications, such as text modelling, high-throughput sequencing, and recommender systems, require analysing sparse, high-dimensional, and overdispersed discrete (count-valued or binary) data. Although probabilistic matrix factorisation and linear/nonlinear latent factor models have enjoyed great success in modelling such data, many existing models may have inferior modelling performance due to the insufficient capability of modelling overdispersion in count-valued data and model misspecification in general. In this paper, we comprehensively study these issues and propose a variational au…
Center for the Neural Basis of Cognition, Machine Learning Department（认知神经基础中心，机器学习系）；Carnegie Mellon University（卡内基梅隆大学）
The variational autoencoder (VAE) is a popular probabilistic generative model. However, one shortcoming of VAEs is that the latent variables cannot be discrete, which makes it difficult to generate data from different modes of a distribution. Here, we propose an extension of the VAE framework that incorporates a classifier to infer the discrete class of the modeled data. To model sequential data, we can combine our Classifying VAE with a recurrent neural network such as an LSTM. We apply this model to algorithmic music generation, where our model learns to generate musical sequences in differe…
Variational inference for latent variable models is prevalent in various machine learning problems, typically solved by maximizing the Evidence Lower Bound (ELBO) of the true data likelihood with respect to a variational distribution. However, freely enriching the family of variational distribution is challenging since the ELBO requires variational likelihood evaluations of the latent variables. In this paper, we propose a novel framework to enrich the variational family by incorporating auxiliary variables to the variational family. The resulting inference network doesn't require density eval…
Deep neural networks have made breakthroughs in a wide range of visual understanding tasks. A typical challenge that hinders their real-world applications is that unknown samples may be fed into the system during the testing phase, but traditional deep neural networks will wrongly recognize these unknown samples as one of the known classes. Open set recognition (OSR) is a potential solution to overcome this problem, where the open set classifier should have the flexibility to reject unknown samples and meanwhile maintain high classification accuracy in known classes. Probabilistic generative m…
The task of predicting stochastic behaviors of road agents in diverse environments is a challenging problem for autonomous driving. To best understand scene contexts and produce diverse possible future states of the road agents adaptively in different environments, a prediction model should be probabilistic, multi-modal, context-driven, and general. We present Conditionalizing Variational AutoEncoders via Hypernetworks (CVAE-H); a conditional VAE that extensively leverages hypernetwork and performs generative tasks for high-dimensional problems like the prediction task. We first evaluate CVAE-…
In this paper, we present an unsupervised probabilistic model and associated estimation algorithm for multi-object tracking (MOT) based on a dynamical variational autoencoder (DVAE), called DVAE-UMOT. The DVAE is a latent-variable deep generative model that can be seen as an extension of the variational autoencoder for the modeling of temporal sequences. It is included in DVAE-UMOT to model the objects' dynamics, after being pre-trained on an unlabeled synthetic dataset of single-object trajectories. Then the distributions and parameters of DVAE-UMOT are estimated on each multi-object sequence…
Multi-way data analysis has become an essential tool for capturing underlying structures in higher-order data sets where standard two-way analysis techniques often fail to discover the hidden correlations between variables in multi-way data. We propose a multi-objective variational autoencoder (MVA) method for smart infrastructure damage detection and diagnosis in multi-way sensing data based on the reconstruction probability of autoencoder deep neural network (ADNN). Our method fuses data from multiple sensors in one ADNN at which informative features are being extracted and utilized for dama…
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…
University of Toronto（多伦多大学）；Google Brain（谷歌大脑）；OpenAI
In this paper, we propose the "adversarial autoencoder" (AAE), which is a probabilistic autoencoder that uses the recently proposed generative adversarial networks (GAN) to perform variational inference by matching the aggregated posterior of the hidden code vector of the autoencoder with an arbitrary prior distribution. Matching the aggregated posterior to the prior ensures that generating from any part of prior space results in meaningful samples. As a result, the decoder of the adversarial autoencoder learns a deep generative model that maps the imposed prior to the data distribution. We sh…
The Alan Turing Institute（艾伦·图灵研究所）；University of Edinburgh（爱丁堡大学）
Recent advances in deep generative models have led to impressive results in a variety of application domains. Motivated by the possibility that deep learning models might memorize part of the input data, there have been increased efforts to understand how memorization arises. In this work, we extend a recently proposed measure of memorization for supervised learning (Feldman, 2019) to the unsupervised density estimation problem and adapt it to be more computationally efficient. Next, we present a study that demonstrates how memorization can occur in probabilistic deep generative models such as…
Probabilistic models with hierarchical-latent-variable structures provide state-of-the-art results amongst non-autoregressive, unsupervised density-based models. However, the most common approach to training such models based on Variational Autoencoders (VAEs) often fails to leverage deep-latent hierarchies; successful approaches require complex inference and optimisation schemes. Optimal Transport is an alternative, non-likelihood-based framework for training generative models with appealing theoretical properties, in principle allowing easier training convergence between distributions. In th…
Quantile Regression, Variational Autoencoders, and Diffusion Models for Uncertainty Quantification: A Spatial Analysis of Sub-seasonal Wind Speed Prediction
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…
VAE-MS: An Asymmetric Variational Autoencoder for Mutational Signature Extraction
Center for Clinical Data Science（临床数据科学中心）；Aalborg University（奥胡斯大学）；Aalborg University Hospital（奥胡斯大学医院）；Nuffield Department of Surgical Sciences（外科科学努尔菲尔德部门）；University of Oxford（牛津大学）；Nuffield Department of Women’s and Reproductive Health（妇女和生殖健康努尔菲尔德部门）
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…
University of Michigan（密歇根大学）；Columbia University（哥伦比亚大学）
Variational autoencoders model high-dimensional data by positing low-dimensional latent variables that are mapped through a flexible distribution parametrized by a neural network. Unfortunately, variational autoencoders often suffer from posterior collapse: the posterior of the latent variables is equal to its prior, rendering the variational autoencoder useless as a means to produce meaningful representations. Existing approaches to posterior collapse often attribute it to the use of neural networks or optimization issues due to variational approximation. In this paper, we consider posterior …
Xiaomi AI Lab（小米人工智能实验室）；Chinese University of Hong Kong（香港中文大学）
Variational Auto-Encoder (VAE) has been widely applied as a fundamental generative model in machine learning. For complex samples like imagery objects or scenes, however, VAE suffers from the dimensional dilemma between reconstruction precision that needs high-dimensional latent codes and probabilistic inference that favors a low-dimensional latent space. By virtue of high-dimensional geometry, we propose a very simple algorithm, called Spherical Auto-Encoder (SAE), completely different from existing VAEs to address the issue. SAE is in essence the vanilla autoencoder with spherical normalizat…
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…
Université Paris Est（巴黎东部大学）；École des Ponts ParisTech（巴黎高科桥路学校）
Deep learning on graphs has become a popular research topic with many applications. However, past work has concentrated on learning graph embedding tasks, which is in contrast with advances in generative models for images and text. Is it possible to transfer this progress to the domain of graphs? We propose to sidestep hurdles associated with linearization of such discrete structures by having a decoder output a probabilistic fully-connected graph of a predefined maximum size directly at once. Our method is formulated as a variational autoencoder. We evaluate on the challenging task of molecul…
University of Oxford（牛津大学）；Alan Turing Institute（艾伦·图灵研究所）；University of Birmingham（伯明翰大学）；University of Manchester（曼彻斯特大学）
Variational Autoencoders (VAEs) provide a flexible and scalable framework for non-linear dimensionality reduction. However, in application domains such as genomics where data sets are typically tabular and high-dimensional, a black-box approach to dimensionality reduction does not provide sufficient insights. Common data analysis workflows additionally use clustering techniques to identify groups of similar features. This usually leads to a two-stage process, however, it would be desirable to construct a joint modelling framework for simultaneous dimensionality reduction and clustering of feat…
University of Edinburgh（爱丁堡大学）；University of Amsterdam（阿姆斯特丹大学）
Variational autoencoders (VAEs) are a standard framework for inducing latent variable models that have been shown effective in learning text representations as well as in text generation. The key challenge with using VAEs is the {\it posterior collapse} problem: learning tends to converge to trivial solutions where the generators ignore latent variables. In our Levenstein VAE, we propose to replace the evidence lower bound (ELBO) with a new objective which is simple to optimize and prevents posterior collapse. Intuitively, it corresponds to generating a sequence from the autoencoder and encour…
