Many different methods to train deep generative models have been introduced in the past. In this paper, we propose to extend the variational auto-encoder (VAE) framework with a new type of prior which we call "Variational Mixture of Posteriors" prior, or VampPrior for short. The VampPrior consists of a mixture distribution (e.g., a mixture of Gaussians) with components given by variational posteriors conditioned on learnable pseudo-inputs. We further extend this prior to a two layer hierarchical model and show that this architecture with a coupled prior and posterior, learns significantly better models. The model also avoids the usual local optima issues related to useless latent dimensions that plague VAEs. We provide empirical studies on six datasets, namely, static and binary MNIST, OMNIGLOT, Caltech 101 Silhouettes, Frey Faces and Histopathology patches, and show that applying the hierarchical VampPrior delivers state-of-the-art results on all datasets in the unsupervised permutation invariant setting and the best results or comparable to SOTA methods for the approach with convolutional networks.
Concurrently to our work, in @cite_31 a variational VAE with a memory was proposed. This approach shares similarities with the VampPrior in terms of a learnable memory (pseudo-inputs in our case) and a multimodal prior. Nevertheless, there are two main differences. First, our prior is an explicit mixture while they sample components. Second, we showed that the optimal prior requires to be coupled with the variational posterior. In the experiments we showed that the VampPrior improves the generative capabilities of the VAE but in @cite_31 it was noticed that the generative performance is comparable to the standard normal prior. We claim that the success of the VampPrior follows from the utilization of the variational posterior in the prior, a part that is missing in @cite_31 .
@cite_31
2617620476 2556467266 2952584433 2083712543 2792210438 2922338294 1779483307 2963275229 2913002991 2558122535 2951789542 2951575317 2915002151 2963799213 2462462929 2752796333 2963085847 2604777655 2594538354 2952006246
Many different methods to train deep generative models have been introduced in the past. In this paper, we propose to extend the variational auto-encoder (VAE) framework with a new type of prior which we call "Variational Mixture of Posteriors" prior, or VampPrior for short. The VampPrior consists of a mixture distribution (e.g., a mixture of Gaussians) with components given by variational posteriors conditioned on learnable pseudo-inputs. We further extend this prior to a two layer hierarchical model and show that this architecture with a coupled prior and posterior, learns significantly better models. The model also avoids the usual local optima issues related to useless latent dimensions that plague VAEs. We provide empirical studies on six datasets, namely, static and binary MNIST, OMNIGLOT, Caltech 101 Silhouettes, Frey Faces and Histopathology patches, and show that applying the hierarchical VampPrior delivers state-of-the-art results on all datasets in the unsupervised permutation invariant setting and the best results or comparable to SOTA methods for the approach with convolutional networks. 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 this heuristic and provide an intuition of the various processes with the help of visualizations. Finally, we demonstrate the performance of our model on synthetic data, MNIST and SVHN, showing that the obtained clusters are distinct, interpretable and result in achieving competitive performance on unsupervised clustering to the state-of-the-art results. The recently developed variational autoencoders (VAEs) have proved to be an effective confluence of the rich representational power of neural networks with Bayesian methods. However, most work on VAEs use a rather simple prior over the latent variables such as standard normal distribution, thereby restricting its applications to relatively simple phenomena. In this work, we propose hierarchical nonparametric variational autoencoders, which combines tree-structured Bayesian nonparametric priors with VAEs, to enable infinite flexibility of the latent representation space. Both the neural parameters and Bayesian priors are learned jointly using tailored variational inference. The resulting model induces a hierarchical structure of latent semantic concepts underlying the data corpus, and infers accurate representations of data instances. We apply our model in video representation learning. Our method is able to discover highly interpretable activity hierarchies, and obtain improved clustering accuracy and generalization capacity based on the learned rich representations. Three Bayesian related approaches, namely, variational Bayesian (VB), minimum message length (MML) and Bayesian Ying-Yang (BYY) harmony learning, have been applied to automatically determining an appropriate number of components during learning Gaussian mixture model (GMM). This paper aims to provide a comparative investigation on these approaches with not only a Jeffreys prior but also a conjugate Dirichlet-Normal-Wishart (DNW) prior on GMM. In addition to adopting the existing algorithms either directly or with some modifications, the algorithm for VB with Jeffreys prior and the algorithm for BYY with DNW prior are developed in this paper to fill the missing gap. The performances of automatic model selection are evaluated through extensive experiments, with several empirical findings: 1) Considering priors merely on the mixing weights, each of three approaches makes biased mistakes, while considering priors on all the parameters of GMM makes each approach reduce its bias and also improve its performance. 2) As Jeffreys prior is replaced by the DNW prior, all the three approaches improve their performances. Moreover, Jeffreys prior makes MML slightly better than VB, while the DNW prior makes VB better than MML. 3) As the hyperparameters of DNW prior are further optimized by each of its own learning principle, BYY improves its performances while VB and MML deteriorate their performances when there are too many free hyper-parameters. Actually, VB and MML lack a good guide for optimizing the hyper-parameters of DNW prior. 4) BYY considerably outperforms both VB and MML for any type of priors and whether hyper-parameters are optimized. Being different from VB and MML that rely on appropriate priors to perform model selection, BYY does not highly depend on the type of priors. It has model selection ability even without priors and performs already very well with Jeffreys prior, and incrementally improves as Jeffreys prior is replaced by the DNW prior. Finally, all algorithms are applied on the Berkeley segmentation database of real world images. Again, BYY considerably outperforms both VB and MML, especially in detecting the objects of interest from a confusing background. The Variational Autoencoder (VAE) has proven to be an effective model for producing semantically meaningful latent representations for natural data. However, it has thus far seen limited application to sequential data, and, as we demonstrate, existing recurrent VAE models have difficulty modeling sequences with long-term structure. To address this issue, we propose the use of a hierarchical decoder, which first outputs embeddings for subsequences of the input and then uses these embeddings to generate each subsequence independently. This structure encourages the model to utilize its latent code, thereby avoiding the "posterior collapse" problem which remains an issue for recurrent VAEs. We apply this architecture to modeling sequences of musical notes and find that it exhibits dramatically better sampling, interpolation, and reconstruction performance than a "flat" baseline model. An implementation of our "MusicVAE" is available online at this http URL We propose a topic-guided variational autoencoder (TGVAE) model for text generation. Distinct from existing variational autoencoder (VAE) based approaches, which assume a simple Gaussian prior for the latent code, our model specifies the prior as a Gaussian mixture model (GMM) parametrized by a neural topic module. Each mixture component corresponds to a latent topic, which provides guidance to generate sentences under the topic. The neural topic module and the VAE-based neural sequence module in our model are learned jointly. In particular, a sequence of invertible Householder transformations is applied to endow the approximate posterior of the latent code with high flexibility during model inference. Experimental results show that our TGVAE outperforms alternative approaches on both unconditional and conditional text generation, which can generate semantically-meaningful sentences with various topics. The variational autoencoder (VAE; Kingma, Welling (2014)) is a recently proposed generative model pairing a top-down generative network with a bottom-up recognition network which approximates posterior inference. It typically makes strong assumptions about posterior inference, for instance that the posterior distribution is approximately factorial, and that its parameters can be approximated with nonlinear regression from the observations. As we show empirically, the VAE objective can lead to overly simplified representations which fail to use the network's entire modeling capacity. We present the importance weighted autoencoder (IWAE), a generative model with the same architecture as the VAE, but which uses a strictly tighter log-likelihood lower bound derived from importance weighting. In the IWAE, the recognition network uses multiple samples to approximate the posterior, giving it increased flexibility to model complex posteriors which do not fit the VAE modeling assumptions. We show empirically that IWAEs learn richer latent space representations than VAEs, leading to improved test log-likelihood on density estimation benchmarks. Abstract: The variational autoencoder (VAE; Kingma, Welling (2014)) is a recently proposed generative model pairing a top-down generative network with a bottom-up recognition network which approximates posterior inference. It typically makes strong assumptions about posterior inference, for instance that the posterior distribution is approximately factorial, and that its parameters can be approximated with nonlinear regression from the observations. As we show empirically, the VAE objective can lead to overly simplified representations which fail to use the network's entire modeling capacity. We present the importance weighted autoencoder (IWAE), a generative model with the same architecture as the VAE, but which uses a strictly tighter log-likelihood lower bound derived from importance weighting. In the IWAE, the recognition network uses multiple samples to approximate the posterior, giving it increased flexibility to model complex posteriors which do not fit the VAE modeling assumptions. We show empirically that IWAEs learn richer latent space representations than VAEs, leading to improved test log-likelihood on density estimation benchmarks. With the introduction of the variational autoencoder (VAE), probabilistic latent variable models have received renewed attention as powerful generative models. However, their performance in terms of test likelihood and quality of generated samples has been surpassed by autoregressive models without stochastic units. Furthermore, flow-based models have recently been shown to be an attractive alternative that scales well to high-dimensional data. In this paper we close the performance gap by constructing VAE models that can effectively utilize a deep hierarchy of stochastic variables and model complex covariance structures. We introduce the Bidirectional-Inference Variational Autoencoder (BIVA), characterized by a skip-connected generative model and an inference network formed by a bidirectional stochastic inference path. We show that BIVA reaches state-of-the-art test likelihoods, generates sharp and coherent natural images, and uses the hierarchy of latent variables to capture different aspects of the data distribution. We observe that BIVA, in contrast to recent results, can be used for anomaly detection. We attribute this to the hierarchy of latent variables which is able to extract high-level semantic features. Finally, we extend BIVA to semi-supervised classification tasks and show that it performs comparably to state-of-the-art results by generative adversarial networks. Deep convolutional neural networks (CNNs) have proven highly effective for visual recognition, where learning a universal representation from activations of convolutional layer plays a fundamental problem. In this paper, we present Fisher Vector encoding with Variational Auto-Encoder (FV-VAE), a novel deep architecture that quantizes the local activations of convolutional layer in a deep generative model, by training them in an end-to-end manner. To incorporate FV encoding strategy into deep generative models, we introduce Variational Auto-Encoder model, which steers a variational inference and learning in a neural network which can be straightforwardly optimized using standard stochastic gradient method. Different from the FV characterized by conventional generative models (e.g., Gaussian Mixture Model) which parsimoniously fit a discrete mixture model to data distribution, the proposed FV-VAE is more flexible to represent the natural property of data for better generalization. Extensive experiments are conducted on three public datasets, i.e., UCF101, ActivityNet, and CUB-200-2011 in the context of video action recognition and fine-grained image classification, respectively. Superior results are reported when compared to state-of-the-art representations. Most remarkably, our proposed FV-VAE achieves to-date the best published accuracy of 94.2 on UCF101. Deep convolutional neural networks (CNNs) have proven highly effective for visual recognition, where learning a universal representation from activations of convolutional layer plays a fundamental problem. In this paper, we present Fisher Vector encoding with Variational Auto-Encoder (FV-VAE), a novel deep architecture that quantizes the local activations of convolutional layer in a deep generative model, by training them in an end-to-end manner. To incorporate FV encoding strategy into deep generative models, we introduce Variational Auto-Encoder model, which steers a variational inference and learning in a neural network which can be straightforwardly optimized using standard stochastic gradient method. Different from the FV characterized by conventional generative models (e.g., Gaussian Mixture Model) which parsimoniously fit a discrete mixture model to data distribution, the proposed FV-VAE is more flexible to represent the natural property of data for better generalization. Extensive experiments are conducted on three public datasets, i.e., UCF101, ActivityNet, and CUB-200-2011 in the context of video action recognition and fine-grained image classification, respectively. Superior results are reported when compared to state-of-the-art representations. Most remarkably, our proposed FV-VAE achieves to-date the best published accuracy of 94.2 on UCF101. In this paper we explore the effect of architectural choices on learning a Variational Autoencoder (VAE) for text generation. In contrast to the previously introduced VAE model for text where both the encoder and decoder are RNNs, we propose a novel hybrid architecture that blends fully feed-forward convolutional and deconvolutional components with a recurrent language model. Our architecture exhibits several attractive properties such as faster run time and convergence, ability to better handle long sequences and, more importantly, it helps to avoid some of the major difficulties posed by training VAE models on textual data. Variational autoencoders (VAEs) have received much attention recently as an end-to-end architecture for text generation with latent variables. In this paper, we investigate several multi-level structures to learn a VAE model to generate long, and coherent text. In particular, we use a hierarchy of stochastic layers between the encoder and decoder networks to generate more informative latent codes. We also investigate a multi-level decoder structure to learn a coherent long-term structure by generating intermediate sentence representations as high-level plan vectors. Empirical results demonstrate that a multi-level VAE model produces more coherent and less repetitive long text compared to the standard VAE models and can further mitigate the posterior-collapse issue. Learning useful representations without supervision remains a key challenge in machine learning. In this paper, we propose a simple yet powerful generative model that learns such discrete representations. Our model, the Vector Quantised-Variational AutoEncoder (VQ-VAE), differs from VAEs in two key ways: the encoder network outputs discrete, rather than continuous, codes; and the prior is learnt rather than static. In order to learn a discrete latent representation, we incorporate ideas from vector quantisation (VQ). Using the VQ method allows the model to circumvent issues of posterior collapse'' -— where the latents are ignored when they are paired with a powerful autoregressive decoder -— typically observed in the VAE framework. Pairing these representations with an autoregressive prior, the model can generate high quality images, videos, and speech as well as doing high quality speaker conversion and unsupervised learning of phonemes, providing further evidence of the utility of the learnt representations. In this paper, we propose a non-local structured prior for volumetric multi-view 3D reconstruction. Towards this goal, we present a novel Markov random field model based on ray potentials in which assumptions about large 3D surface patches such as planarity or Manhattan world constraints can be efficiently encoded as probabilistic priors. We further derive an inference algorithm that reasons jointly about voxels, pixels and image segments, and estimates marginal distributions of appearance, occupancy, depth, normals and planarity. Key to tractable inference is a novel hybrid representation that spans both voxel and pixel space and that integrates non-local information from 2D image segmentations in a principled way. We compare our non-local prior to commonly employed local smoothness assumptions and a variety of state-of-the-art volumetric reconstruction baselines on challenging outdoor scenes with textureless and reflective surfaces. Our experiments indicate that regularizing over larger distances has the potential to resolve ambiguities where local regularizers fail. Learning useful representations without supervision remains a key challenge in machine learning. In this paper, we propose a simple yet powerful generative model that learns such discrete representations. Our model, the Vector Quantised-Variational AutoEncoder (VQ-VAE), differs from VAEs in two key ways: the encoder network outputs discrete, rather than continuous, codes; and the prior is learnt rather than static. In order to learn a discrete latent representation, we incorporate ideas from vector quantisation (VQ). Using the VQ method allows the model to circumvent issues of "posterior collapse" -- where the latents are ignored when they are paired with a powerful autoregressive decoder -- typically observed in the VAE framework. Pairing these representations with an autoregressive prior, the model can generate high quality images, videos, and speech as well as doing high quality speaker conversion and unsupervised learning of phonemes, providing further evidence of the utility of the learnt representations. We extend variational autoencoders (VAEs) to collaborative filtering for implicit feedback. This non-linear probabilistic model enables us to go beyond the limited modeling capacity of linear factor models which still largely dominate collaborative filtering research. We introduce a generative model with multinomial likelihood and use Bayesian inference to learn this powerful generative model. Despite widespread use in language modeling and economics, the multinomial likelihood receives less attention in the recommender systems literature. We introduce a different regularization parameter for the learning objective, which proves to be crucial for achieving competitive performance. Remarkably, there is an efficient way to tune the parameter using annealing. The resulting model and learning algorithm has information-theoretic connections to maximum entropy discrimination and the information bottleneck principle. Empirically, we show that the proposed approach significantly outperforms several state-of-the-art baselines, including two recently-proposed neural network approaches, on several real-world datasets. We also provide extended experiments comparing the multinomial likelihood with other commonly used likelihood functions in the latent factor collaborative filtering literature and show favorable results. Finally, we identify the pros and cons of employing a principled Bayesian inference approach and characterize settings where it provides the most significant improvements. We propose a new unsupervised sentence salience framework for Multi-Document Summarization (MDS), which can be divided into two components: latent semantic modeling and salience estimation. For latent semantic modeling, a neural generative model called Variational Auto-Encoders (VAEs) is employed to describe the observed sentences and the corresponding latent semantic representations. Neural variational inference is used for the posterior inference of the latent variables. For salience estimation, we propose an unsupervised data reconstruction framework, which jointly considers the reconstruction for latent semantic space and observed term vector space. Therefore, we can capture the salience of sentences from these two different and complementary vector spaces. Thereafter, the VAEs-based latent semantic model is integrated into the sentence salience estimation component in a unified fashion, and the whole framework can be trained jointly by back-propagation via multi-task learning. Experimental results on the benchmark datasets DUC and TAC show that our framework achieves better performance than the state-of-the-art models. Recent work on generative modeling of text has found that variational auto-encoders (VAE) incorporating LSTM decoders perform worse than simpler LSTM language models (, 2015). This negative result is so far poorly understood, but has been attributed to the propensity of LSTM decoders to ignore conditioning information from the encoder. In this paper, we experiment with a new type of decoder for VAE: a dilated CNN. By changing the decoder's dilation architecture, we control the effective context from previously generated words. In experiments, we find that there is a trade off between the contextual capacity of the decoder and the amount of encoding information used. We show that with the right decoder, VAE can outperform LSTM language models. We demonstrate perplexity gains on two datasets, representing the first positive experimental result on the use VAE for generative modeling of text. Further, we conduct an in-depth investigation of the use of VAE (with our new decoding architecture) for semi-supervised and unsupervised labeling tasks, demonstrating gains over several strong baselines. Clustering is among the most fundamental tasks in computer vision and machine learning. In this paper, we propose Variational Deep Embedding (VaDE), a novel unsupervised generative clustering approach within the framework of Variational Auto-Encoder (VAE). Specifically, VaDE models the data generative procedure with a Gaussian Mixture Model (GMM) and a deep neural network (DNN): 1) the GMM picks a cluster; 2) from which a latent embedding is generated; 3) then the DNN decodes the latent embedding into observables. Inference in VaDE is done in a variational way: a different DNN is used to encode observables to latent embeddings, so that the evidence lower bound (ELBO) can be optimized using Stochastic Gradient Variational Bayes (SGVB) estimator and the reparameterization trick. Quantitative comparisons with strong baselines are included in this paper, and experimental results show that VaDE significantly outperforms the state-of-the-art clustering methods on 4 benchmarks from various modalities. Moreover, by VaDE's generative nature, we show its capability of generating highly realistic samples for any specified cluster, without using supervised information during training. Lastly, VaDE is a flexible and extensible framework for unsupervised generative clustering, more general mixture models than GMM can be easily plugged in.