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
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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 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 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. 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. 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. Algorithms for magnetic resonance (MR) image reconstruction from undersampled measurements exploit prior information to compensate for missing k-space data. Deep learning (DL) provides a powerful framework for extracting such information from existing image datasets, through learning, and then using it for reconstruction. Leveraging this, recent methods employed DL to learn mappings from undersampled to fully sampled images using paired datasets, including undersampled and corresponding fully sampled images, integrating prior knowledge implicitly. In this letter, we propose an alternative approach that learns the probability distribution of fully sampled MR images using unsupervised DL, specifically variational autoencoders (VAE), and use this as an explicit prior term in reconstruction, completely decoupling the encoding operation from the prior. The resulting reconstruction algorithm enjoys a powerful image prior to compensate for missing k-space data without requiring paired datasets for training nor being prone to associated sensitivities, such as deviations in undersampling patterns used in training and test time or coil settings. We evaluated the proposed method with T1 weighted images from a publicly available dataset, multi-coil complex images acquired from healthy volunteers ( @math ), and images with white matter lesions. The proposed algorithm, using the VAE prior, produced visually high quality reconstructions and achieved low RMSE values, outperforming most of the alternative methods on the same dataset. On multi-coil complex data, the algorithm yielded accurate magnitude and phase reconstruction results. In the experiments on images with white matter lesions, the method faithfully reconstructed the lesions. We study unsupervised generative modeling in terms of the optimal transport (OT) problem between true (but unknown) data distribution @math and the latent variable model distribution @math . We show that the OT problem can be equivalently written in terms of probabilistic encoders, which are constrained to match the posterior and prior distributions over the latent space. When relaxed, this constrained optimization problem leads to a penalized optimal transport (POT) objective, which can be efficiently minimized using stochastic gradient descent by sampling from @math and @math . We show that POT for the 2-Wasserstein distance coincides with the objective heuristically employed in adversarial auto-encoders (AAE) (, 2016), which provides the first theoretical justification for AAEs known to the authors. We also compare POT to other popular techniques like variational auto-encoders (VAE) (Kingma and Welling, 2014). Our theoretical results include (a) a better understanding of the commonly observed blurriness of images generated by VAEs, and (b) establishing duality between Wasserstein GAN (Arjovsky and Bottou, 2017) and POT for the 1-Wasserstein distance. Generative models such as Variational Auto Encoders (VAEs) and Generative Adversarial Networks (GANs) are typically trained for a fixed prior distribution in the latent space, such as uniform or Gaussian. After a trained model is obtained, one can sample the Generator in various forms for exploration and understanding, such as interpolating between two samples, sampling in the vicinity of a sample or exploring differences between a pair of samples applied to a third sample. In this paper, we show that the latent space operations used in the literature so far induce a distribution mismatch between the resulting outputs and the prior distribution the model was trained on. To address this, we propose to use distribution matching transport maps to ensure that such latent space operations preserve the prior distribution, while minimally modifying the original operation. Our experimental results validate that the proposed operations give higher quality samples compared to the original operations. In just three years, Variational Autoencoders (VAEs) have emerged as one of the most popular approaches to unsupervised learning of complicated distributions. VAEs are appealing because they are built on top of standard function approximators (neural networks), and can be trained with stochastic gradient descent. VAEs have already shown promise in generating many kinds of complicated data, including handwritten digits, faces, house numbers, CIFAR images, physical models of scenes, segmentation, and predicting the future from static images. This tutorial introduces the intuitions behind VAEs, explains the mathematics behind them, and describes some empirical behavior. No prior knowledge of variational Bayesian methods is assumed. This paper considers Bayesian data fusion of conventional robot sensor information with ambiguous human-generated categorical information about continuous world states of interest. First, it is shown that such soft information can be generally modeled via hybrid continuous-to-discrete likelihoods that are based on the softmax function. A new hybrid fusion procedure, called variational Bayesian importance sampling (VBIS), is then introduced to combine the strengths of variational Bayes approximations and fast Monte Carlo methods to produce reliable posterior estimates for Gaussian priors and softmax likelihoods. VBIS is then extended to more general fusion problems that involve complex Gaussian mixture (GM) priors and multimodal softmax likelihoods, leading to accurate GM approximations of highly non-Gaussian fusion posteriors for a wide range of robot sensor data and soft human data. Experiments for hardware-based multitarget search missions with a cooperative human-autonomous robot team show that humans can serve as highly informative sensors through proper data modeling and fusion, and that VBIS provides reliable and scalable Bayesian fusion estimates via GMs. Deep generative models have achieved impressive success in recent years. Generative Adversarial Networks (GANs) and Variational Autoencoders (VAEs), as emerging families for generative model learning, have largely been considered as two distinct paradigms and received extensive independent studies respectively. This paper aims to establish formal connections between GANs and VAEs through a new formulation of them. We interpret sample generation in GANs as performing posterior inference, and show that GANs and VAEs involve minimizing KL divergences of respective posterior and inference distributions with opposite directions, extending the two learning phases of classic wake-sleep algorithm, respectively. The unified view provides a powerful tool to analyze a diverse set of existing model variants, and enables to transfer techniques across research lines in a principled way. For example, we apply the importance weighting method in VAE literatures for improved GAN learning, and enhance VAEs with an adversarial mechanism that leverages generated samples. Experiments show generality and effectiveness of the transferred techniques. Patent prior art search is a type of search in the patent domain where documents are searched for that describe the work previously carried out related to a patent application. The goal of this search is to check whether the idea in the patent application is novel. Vocabulary mismatch is one of the main problems of patent retrieval which results in low retrievability of similar documents for a given patent application. In this paper we show how the term distribution of the cited documents in an initially retrieved ranked list can be used to address the vocabulary mismatch. We propose a method for query modeling estimation which utilizes the citation links in a pseudo relevance feedback set. We first build a topic dependent citation graph, starting from the initially retrieved set of feedback documents and utilizing citation links of feedback documents to expand the set. We identify the important documents in the topic dependent citation graph using a citation analysis measure. We then use the term distribution of the documents in the citation graph to estimate a query model by identifying the distinguishing terms and their respective weights. We then use these terms to expand our original query. We use CLEF-IP 2011 collection to evaluate the effectiveness of our query modeling approach for prior art search. We also study the influence of different parameters on the performance of the proposed method. The experimental results demonstrate that the proposed approach significantly improves the recall over a state-of-the-art baseline which uses the link-based structure of the citation graph but not the term distribution of the cited documents. Predicting future frames for a video sequence is a challenging generative modeling task. Promising approaches include probabilistic latent variable models such as the Variational Auto-Encoder. While VAEs can handle uncertainty and model multiple possible future outcomes, they have a tendency to produce blurry predictions. In this work we argue that this is a sign of underfitting. To address this issue, we propose to increase the expressiveness of the latent distributions and to use higher capacity likelihood models. Our approach relies on a hierarchy of latent variables, which defines a family of flexible prior and posterior distributions in order to better model the probability of future sequences. We validate our proposal through a series of ablation experiments and compare our approach to current state-of-the-art latent variable models. Our method performs favorably under several metrics in three different datasets. The old Asian legend about the blind men and the elephant comes to mind when looking at how different authors of scientific papers describe a piece of related prior work. It turns out that different citations to the same paper often focus on different aspects of that paper and that neither provides a full description of its full set of contributions. In this article, we will describe our investigation of this phenomenon. We studied citation summaries in the context of research papers in the biomedical domain. A citation summary is the set of citing sentences for a given article and can be used as a surrogate for the actual article in a variety of scenarios. It contains information that was deemed by peers to be important. Our study shows that citation summaries overlap to some extent with the abstracts of the papers and that they also differ from them in that they focus on different aspects of these papers than do the abstracts. In addition to this, co-cited articles (which are pairs of articles cited by another article) tend to be similar. We show results based on a lexical similarity metric called cohesion to justify our claims. © 2008 Wiley Periodicals, Inc. 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. Sum-Product Networks (SPNs) are probabilistic inference machines that admit exact inference in linear time in the size of the network. Existing parameter learning approaches for SPNs are largely based on the maximum likelihood principle and are subject to overfitting compared to more Bayesian approaches. Exact Bayesian posterior inference for SPNs is computationally intractable. Even approximation techniques such as standard variational inference and posterior sampling for SPNs are computationally infeasible even for networks of moderate size due to the large number of local latent variables per instance. In this work, we propose a novel deterministic collapsed variational inference algorithm for SPNs that is computationally efficient, easy to implement and at the same time allows us to incorporate prior information into the optimization formulation. Extensive experiments show a significant improvement in accuracy compared with a maximum likelihood based approach. In this paper we describe experiments conducted for CLEF- IP 2011 Prior Art Retrieval track. We examined the impact of 1) us- ing key phrase extraction to generate queries from input patent and 2) the use of citation network and (International Patent Classification) IPC class vector in ranking patents. Variations of a popular key phrase extrac- tion technique were explored for extracting and scoring terms of query patent. These terms are used as queries to retrieve similar patents. In the second approach, we use a two stage retrieval model to find similar patents. Each patent is represented as an IPC class vector. Citation net- work of patents is used to propagate these vectors from a node (patent) to its neighbors (cited patents). Similar patents are found by comparing query vector with vectors of patents in the corpus. Text based search is used to re-rank this solution set to improve precision. Two-stage sys- tem is used to retrieve and rank patents. Finally, we also extract and add citations present within the text of a query patent to the result set. Adding these citations (present in query patent text) to the results shows significant improvement in Mean Average Precision (MAP). The detection of anomalous executions is valuable for reducing potential hazards in assistive manipulation. Multimodal sensory signals can be helpful for detecting a wide range of anomalies. However, the fusion of high-dimensional and heterogeneous modalities is a challenging problem for model-based anomaly detection. We introduce a long short-term memory-based variational autoencoder (LSTM-VAE) that fuses signals and reconstructs their expected distribution by introducing a progress-based varying prior. Our LSTM-VAE-based detector reports an anomaly when a reconstruction-based anomaly score is higher than a state-based threshold. For evaluations with 1555 robot-assisted feeding executions, including 12 representative types of anomalies, our detector had a higher area under the receiver operating characteristic curve of 0.8710 than 5 other baseline detectors from the literature. We also show the variational autoencoding and state-based thresholding are effective in detecting anomalies from 17 raw sensory signals without significant feature engineering effort. 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. 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