Jointly identifying a mixture of discrete and continuous factors of variability without supervision is a key problem in unraveling complex phenomena. Variational inference has emerged as a promising method to learn interpretable mixture representations. However, posterior approximation in high-dimensional latent spaces, particularly for discrete factors remains challenging. Here, we propose an unsupervised variational framework using multiple interacting networks called cpl-mixVAE that scales well to high-dimensional discrete settings. In this framework, the mixture representation of each network is regularized by imposing a consensus constraint on the discrete factor. We justify the use of this framework by providing both theoretical and experimental results. Finally, we use the proposed method to jointly uncover discrete and continuous factors of variability describing gene expression in a single-cell transcriptomic dataset profiling more than a hundred cortical neuron types.
Samsung AI Center（三星人工智能中心）；Rutgers University（罗格斯大学）
Inference networks of traditional Variational Autoencoders (VAEs) are typically amortized, resulting in relatively inaccurate posterior approximation compared to instance-wise variational optimization. Recent semi-amortized approaches were proposed to address this drawback; however, their iterative gradient update procedures can be computationally demanding. To address these issues, in this paper we introduce an accurate amortized inference algorithm. We propose a novel recursive mixture estimation algorithm for VAEs that iteratively augments the current mixture with new components so as to ma…
Multi-label classification (MLC) is a prediction task where each sample can have more than one label. We propose a novel contrastive learning boosted multi-label prediction model based on a Gaussian mixture variational autoencoder (C-GMVAE), which learns a multimodal prior space and employs a contrastive loss. Many existing methods introduce extra complex neural modules like graph neural networks to capture the label correlations, in addition to the prediction modules. We find that by using contrastive learning in the supervised setting, we can exploit label information effectively in a data-d…
Physically Interpretable Representation Learning with Gaussian Mixture Variational AutoEncoder (GM-VAE)
Institute for Computational and Mathematical Engineering, Stanford University（计算与数学工程研究所，斯坦福大学）；Department of Mechanical Engineering, Stanford University（机械工程系，斯坦福大学）；National Renewable Energy Laboratory（国家可再生能源实验室）；Ann and H.J. Smead Department of Aerospace Engineering Sciences, University of Colorado, Boulder（安与H.J.斯迈德航空航天工程科学系，科罗拉多大学，博尔德）
EURECOM（欧洲通信学院）；CSIRO’s Data61（澳大利亚联邦科学与工业研究组织Data61）；The University of Sydney（悉尼大学）
We develop a novel method for carrying out model selection for Bayesian autoencoders (BAEs) by means of prior hyper-parameter optimization. Inspired by the common practice of type-II maximum likelihood optimization and its equivalence to Kullback-Leibler divergence minimization, we propose to optimize the distributional sliced-Wasserstein distance (DSWD) between the output of the autoencoder and the empirical data distribution. The advantages of this formulation are that we can estimate the DSWD based on samples and handle high-dimensional problems. We carry out posterior estimation of the BAE…
University of Michigan（密歇根大学）；Technicolor（特艺集团）；Adobe（Adobe公司）
Unsupervised clustering is one of the most fundamental challenges in machine learning. A popular hypothesis is that data are generated from a union of low-dimensional nonlinear manifolds; thus an approach to clustering is identifying and separating these manifolds. In this paper, we present a novel approach to solve this problem by using a mixture of autoencoders. Our model consists of two parts: 1) a collection of autoencoders where each autoencoder learns the underlying manifold of a group of similar objects, and 2) a mixture assignment neural network, which takes the concatenated latent vec…
In this paper we propose a Deep Autoencoder MIxture Clustering (DAMIC) algorithm based on a mixture of deep autoencoders where each cluster is represented by an autoencoder. A clustering network transforms the data into another space and then selects one of the clusters. Next, the autoencoder associated with this cluster is used to reconstruct the data-point. The clustering algorithm jointly learns the nonlinear data representation and the set of autoencoders. The optimal clustering is found by minimizing the reconstruction loss of the mixture of autoencoder network. Unlike other deep clusteri…
In this paper we address the problem of enhancing speech signals in noisy mixtures using a source separation approach. We explore the use of neural networks as an alternative to a popular speech variance model based on supervised non-negative matrix factorization (NMF). More precisely, we use a variational autoencoder as a speaker-independent supervised generative speech model, highlighting the conceptual similarities that this approach shares with its NMF-based counterpart. In order to be free of generalization issues regarding the noisy recording environments, we follow the approach of havin…
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…
University of Oxford（牛津大学）；Alan Turing Institute（艾伦·图灵研究所）；University of Cambridge（剑桥大学）
Learning generative models that span multiple data modalities, such as vision and language, is often motivated by the desire to learn more useful, generalisable representations that faithfully capture common underlying factors between the modalities. In this work, we characterise successful learning of such models as the fulfillment of four criteria: i) implicit latent decomposition into shared and private subspaces, ii) coherent joint generation over all modalities, iii) coherent cross-generation across individual modalities, and iv) improved model learning for individual modalities through m…
University of Oxford（牛津大学）；Alan Turing Institute（艾伦·图灵研究所）
In clustering we normally output one cluster variable for each datapoint. However it is not necessarily the case that there is only one way to partition a given dataset into cluster components. For example, one could cluster objects by their colour, or by their type. Different attributes form a hierarchy, and we could wish to cluster in any of them. By disentangling the learnt latent representations of some dataset into different layers for different attributes we can then cluster in those latent spaces. We call this "disentangled clustering". Extending Variational Ladder Autoencoders (Zhao et…
ETH Zürich（苏黎世联邦理工学院）；Life Science Graduate School Zurich（苏黎世生命科学研究生院）；Swiss Institute of Bioinformatics（瑞士生物信息学研究所）；University of Tübingen（图宾根大学）
Clustering high-dimensional data, such as images or biological measurements, is a long-standingproblem and has been studied extensively. Recently, Deep Clustering has gained popularity due toits flexibility in fitting the specific peculiarities of complex data. Here we introduce the Mixture-of-Experts Similarity Variational Autoencoder (MoE-Sim-VAE), a novel generative clustering model.The model can learn multi-modal distributions of high-dimensional data and use these to generaterealistic data with high efficacy and efficiency. MoE-Sim-VAE is based on a Variational Autoencoder(VAE), where the…
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.
The dissimilarity mixture autoencoder (DMAE) is a neural network model for feature-based clustering that incorporates a flexible dissimilarity function and can be integrated into any kind of deep learning architecture. It internally represents a dissimilarity mixture model (DMM) that extends classical methods like K-Means, Gaussian mixture models, or Bregman clustering to any convex and differentiable dissimilarity function through the reinterpretation of probabilities as neural network representations. DMAE can be integrated with deep learning architectures into end-to-end models, allowing th…
This project aims to break down large pathology images into small tiles and then cluster those tiles into distinct groups without the knowledge of true labels, our analysis shows how difficult certain aspects of clustering tumorous and non-tumorous cells can be and also shows that comparing the results of different unsupervised approaches is not a trivial task. The project also provides a software package to be used by the digital pathology community, that uses some of the approaches developed to perform unsupervised unsupervised tile classification, which could then be easily manually labelle…
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…
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…
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…
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 …
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…
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…
Deep learning, even if it is very successful nowadays, traditionally needs very large amounts of labeled data to perform excellent on the classification task. In an attempt to solve this problem, the one-shot learning paradigm, which makes use of just one labeled sample per class and prior knowledge, becomes increasingly important. In this paper, we propose a new one-shot learning method, dubbed MoVAE (Mixture of Variational AutoEncoders), to perform classification. Complementary to prior studies, MoVAE represents a shift of paradigm in comparison with the usual one-shot learning methods, as i…
This work focuses on the problem of unraveling nonlinearly mixed latent components in an unsupervised manner. The latent components are assumed to reside in the probability simplex, and are transformed by an unknown post-nonlinear mixing system. This problem finds various applications in signal and data analytics, e.g., nonlinear hyperspectral unmixing, image embedding, and nonlinear clustering. Linear mixture learning problems are already ill-posed, as identifiability of the target latent components is hard to establish in general. With unknown nonlinearity involved, the problem is even more …
In this paper, we propose an end-to-end lifelong learning mixture of experts. Each expert is implemented by a Variational Autoencoder (VAE). The experts in the mixture system are jointly trained by maximizing a mixture of individual component evidence lower bounds (MELBO) on the log-likelihood of the given training samples. The mixing coefficients in the mixture, control the contributions of each expert in the goal representation. These are sampled from a Dirichlet distribution whose parameters are determined through non-parametric estimation during lifelong learning. The model can learn new t…
In this paper, we propose a source separation method that is trained by observing the mixtures and the class labels of the sources present in the mixture without any access to isolated sources. Since our method does not require source class labels for every time-frequency bin but only a single label for each source constituting the mixture signal, we call this scenario as weak class supervision. We associate a variational autoencoder (VAE) with each source class within a non-negative (compositional) model. Each VAE provides a prior model to identify the signal from its associated class in a so…
Recently, an audio-visual speech generative model based on variational autoencoder (VAE) has been proposed, which is combined with a nonnegative matrix factorization (NMF) model for noise variance to perform unsupervised speech enhancement. When visual data is clean, speech enhancement with audio-visual VAE shows a better performance than with audio-only VAE, which is trained on audio-only data. However, audio-visual VAE is not robust against noisy visual data, e.g., when for some video frames, speaker face is not frontal or lips region is occluded. In this paper, we propose a robust unsupervi…
Improving Normative Modeling for Multi-modal Neuroimaging Data using mixture-of-product-of-experts variational autoencoders
Department of Computer Science and Engineering, Washington University in St. Louis, USA（计算机科学与工程系，华盛顿大学圣路易斯分校）；Institute for Informatics, Data Science and Biostatistics, Washington University in St.Louis, USA（信息学、数据科学与生物统计研究所，华盛顿大学圣路易斯分校）；Department of Radiology, Washington University in St.Louis, USA（放射学系，华盛顿大学圣路易斯分校）
The University of Tokyo（东京大学）；National Institute of Technology, Kagawa College（国立高等专门学校机构 香川高等专门学校）；Yamaha Corporation（雅马哈公司）
A differentiable digital signal processing (DDSP) autoencoder is a musical sound synthesizer that combines a deep neural network (DNN) and spectral modeling synthesis. It allows us to flexibly edit sounds by changing the fundamental frequency, timbre feature, and loudness (synthesis parameters) extracted from an input sound. However, it is designed for a monophonic harmonic sound and cannot handle mixtures of harmonic sounds. In this paper, we propose a model (DDSP mixture model) that represents a mixture as the sum of the outputs of multiple pretrained DDSP autoencoders. By fitting the output…
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…
Recent developments in high throughput profiling of individual neurons have spurred data driven exploration of the idea that there exist natural groupings of neurons referred to as cell types. The promise of this idea is that the immense complexity of brain circuits can be reduced, and effectively studied by means of interactions between cell types. While clustering of neuron populations based on a particular data modality can be used to define cell types, such definitions are often inconsistent across different characterization modalities. We pose this issue of cross-modal alignment as an opt…
NTT Communication Science Laboratories, NTT Corporation（NTT 公司 NTT 通信科学实验室）；University of Tsukuba（筑波大学）
This paper proposes a multichannel source separation technique called the multichannel variational autoencoder (MVAE) method, which uses a conditional VAE (CVAE) to model and estimate the power spectrograms of the sources in a mixture. By training the CVAE using the spectrograms of training examples with source-class labels, we can use the trained decoder distribution as a universal generative model capable of generating spectrograms conditioned on a specified class label. By treating the latent space variables and the class label as the unknown parameters of this generative model, we can deve…
Training of discrete latent variable models remains challenging because passing gradient information through discrete units is difficult. We propose a new class of smoothing transformations based on a mixture of two overlapping distributions, and show that the proposed transformation can be used for training binary latent models with either directed or undirected priors. We derive a new variational bound to efficiently train with Boltzmann machine priors. Using this bound, we develop DVAE++, a generative model with a global discrete prior and a hierarchy of convolutional continuous variables. …
National Tsing Hua University（台湾清华大学）；National Taiwan Ocean University（台湾海洋大学）；Elan Microelectronics Corporation（义隆电子股份有限公司）；University of California, San Diego（加利福尼亚大学圣迭戈分校）
Electroencephalography (EEG) signals are often contaminated with artifacts. It is imperative to develop a practical and reliable artifact removal method to prevent misinterpretations of neural signals and underperformance of brain-computer interfaces. This study developed a new artifact removal method, IC-U-Net, which is based on the U-Net architecture for removing pervasive EEG artifacts and reconstructing brain sources. The IC-U-Net was trained using mixtures of brain and non-brain sources decomposed by independent component analysis and employed an ensemble of loss functions to model comple…
A Coupled Variational Autoencoder, which incorporates both a generalized loss function and latent layer distribution, shows improvement in the accuracy and robustness of generated replicas of MNIST numerals. The latent layer uses a Student's t-distribution to incorporate heavy-tail decay. The loss function uses a coupled logarithm, which increases the penalty on images with outlier likelihood. The generalized mean of the generated image's likelihood is used to measure the performance of the algorithm's decisiveness, accuracy, and robustness.
Princeton University（普林斯顿大学）；Institute for Advanced Study（高等研究院）
We present a new algorithm for Independent Component Analysis (ICA) which has provable performance guarantees. In particular, suppose we are given samples of the form $y = Ax + η$ where $A$ is an unknown $n \times n$ matrix and $x$ is a random variable whose components are independent and have a fourth moment strictly less than that of a standard Gaussian random variable and $η$ is an $n$-dimensional Gaussian random variable with unknown covariance $Σ$: We give an algorithm that provable recovers $A$ and $Σ$ up to an additive $ε$ and whose running time and sample complexity are polynomial in $…
One of the major shortcomings of variational autoencoders is the inability to produce generations from the individual modalities of data originating from mixture distributions. This is primarily due to the use of a simple isotropic Gaussian as the prior for the latent code in the ancestral sampling procedure for the data generations. We propose a novel formulation of variational autoencoders, conditional prior VAE (CP-VAE), which learns to differentiate between the individual mixture components and therefore allows for generations from the distributional data clusters. We assume a two-level ge…
Domain adaptation approaches aim to exploit useful information from the source domain where supervised learning examples are easier to obtain to address a learning problem in the target domain where there is no or limited availability of such examples. In classification problems, domain adaptation has been studied under varying supervised, unsupervised and semi-supervised conditions. However, a common situation when the labelled samples are available for a subset of target domain classes has been overlooked. In this paper, we formulate this particular domain adaptation problem within a general…
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…
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…
University College London（伦敦大学学院）；ASI Data Science（ASI数据科学）；Alan Turing Institute（艾伦·图灵研究所）
Generative models with both discrete and continuous latent variables are highly motivated by the structure of many real-world data sets. They present, however, subtleties in training often manifesting in the discrete latent being under leveraged. In this paper, we show that such models are more amenable to training when using the Optimal Transport framework of Wasserstein Autoencoders. We find our discrete latent variable to be fully leveraged by the model when trained, without any modifications to the objective function or significant fine tuning. Our model generates comparable samples to oth…
Indian Institute of Space Science and Technology（印度空间科学与技术学院）
Detecting stellar clusters have always been an important research problem in Astronomy. Although images do not convey very detailed information in detecting stellar density enhancements, we attempt to understand if new machine learning techniques can reveal patterns that would assist in drawing better inferences from the available image data. This paper describes an unsupervised approach in detecting star clusters using Deep Variational Autoencoder combined with a Gaussian Mixture Model. We show that our method works significantly well in comparison with state-of-the-art detection algorithm in…
