Amortized inference has led to efficient approximate inference for large datasets. The quality of posterior inference is largely determined by two factors: a) the ability of the variational distribution to model the true posterior and b) the capacity of the recognition network to generalize inference over all datapoints. We analyze approximate inference in variational autoencoders in terms of these factors. We find that suboptimal inference is often due to amortizing inference rather than the limited complexity of the approximating distribution. We show that this is due partly to the generator learning to accommodate the choice of approximation. Furthermore, we show that the parameters used to increase the expressiveness of the approximation play a role in generalizing inference rather than simply improving the complexity of the approximation.
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We reinterpreting the variational inference in a new perspective. Via this way, we can easily prove that EM algorithm, VAE, GAN, AAE, ALI(BiGAN) are all special cases of variational inference. The proof also reveals the loss of standard GAN is incomplete and it explains why we need to train GAN cautiously. From that, we find out a regularization term to improve stability of GAN training.
While Generative Adversarial Networks (GANs) have empirically produced impressive results on learning complex real-world distributions, recent work has shown that they suffer from lack of diversity or mode collapse. The theoretical work of Arora et al.~\cite{AroraGeLiMaZh17} suggests a dilemma about GANs' statistical properties: powerful discriminators cause overfitting, whereas weak discriminators cannot detect mode collapse. In contrast, we show in this paper that GANs can in principle learn distributions in Wasserstein distance (or KL-divergence in many cases) with polynomial sample complexity, if the discriminator class has strong distinguishing power against the particular generator class (instead of against all possible generators). For various generator classes such as mixture of Gaussians, exponential families, and invertible neural networks generators, we design corresponding discriminators (which are often neural nets of specific architectures) such that the Integral Probability Metric (IPM) induced by the discriminators can provably approximate the Wasserstein distance and/or KL-divergence. This implies that if the training is successful, then the learned distribution is close to the true distribution in Wasserstein distance or KL divergence, and thus cannot drop modes. Our preliminary experiments show that on synthetic datasets the test IPM is well correlated with KL divergence, indicating that the lack of diversity may be caused by the sub-optimality in optimization instead of statistical inefficiency.
Topic models have been widely explored as probabilistic generative models of documents. Traditional inference methods have sought closed-form derivations for updating the models, however as the expressiveness of these models grows, so does the difficulty of performing fast and accurate inference over their parameters. This paper presents alternative neural approaches to topic modelling by providing parameterisable distributions over topics which permit training by backpropagation in the framework of neural variational inference. In addition, with the help of a stick-breaking construction, we propose a recurrent network that is able to discover a notionally unbounded number of topics, analogous to Bayesian non-parametric topic models. Experimental results on the MXM Song Lyrics, 20NewsGroups and Reuters News datasets demonstrate the effectiveness and efficiency of these neural topic models.
The Pachinko Allocation Machine (PAM) is a deep topic model that allows representing rich correlation structures among topics by a directed acyclic graph over topics. Because of the flexibility of the model, however, approximate inference is very difficult. Perhaps for this reason, only a small number of potential PAM architectures have been explored in the literature. In this paper we present an efficient and flexible amortized variational inference method for PAM, using a deep inference network to parameterize the approximate posterior distribution in a manner similar to the variational autoencoder. Our inference method produces more coherent topics than state-of-art inference methods for PAM while being an order of magnitude faster, which allows exploration of a wider range of PAM architectures than have previously been studied.
Inferring missing links in knowledge graphs (KG) has attracted a lot of attention from the research community. In this paper, we tackle a practical query answering task involving predicting the relation of a given entity pair. We frame this prediction problem as an inference problem in a probabilistic graphical model and aim at resolving it from a variational inference perspective. In order to model the relation between the query entity pair, we assume that there exists an underlying latent variable (paths connecting two nodes) in the KG, which carries the equivalent semantics of their relations. However, due to the intractability of connections in large KGs, we propose to use variation inference to maximize the evidence lower bound. More specifically, our framework (\textsc{Diva}) is composed of three modules, i.e. a posterior approximator, a prior (path finder), and a likelihood (path reasoner). By using variational inference, we are able to incorporate them closely into a unified architecture and jointly optimize them to perform KG reasoning. With active interactions among these sub-modules, \textsc{Diva} is better at handling noise and coping with more complex reasoning scenarios. In order to evaluate our method, we conduct the experiment of the link prediction task on multiple datasets and achieve state-of-the-art performances on both datasets.
We propose a flipped-Adversarial AutoEncoder (FAAE) that simultaneously trains a generative model G that maps an arbitrary latent code distribution to a data distribution and an encoder E that embodies an "inverse mapping" that encodes a data sample into a latent code vector. Unlike previous hybrid approaches that leverage adversarial training criterion in constructing autoencoders, FAAE minimizes re-encoding errors in the latent space and exploits adversarial criterion in the data space. Experimental evaluations demonstrate that the proposed framework produces sharper reconstructed images while at the same time enabling inference that captures rich semantic representation of data.
We introduce an effective model to overcome the problem of mode collapse when training Generative Adversarial Networks (GAN). Firstly, we propose a new generator objective that finds it better to tackle mode collapse. And, we apply an independent Autoencoders (AE) to constrain the generator and consider its reconstructed samples as "real" samples to slow down the convergence of discriminator that enables to reduce the gradient vanishing problem and stabilize the model. Secondly, from mappings between latent and data spaces provided by AE, we further regularize AE by the relative distance between the latent and data samples to explicitly prevent the generator falling into mode collapse setting. This idea comes when we find a new way to visualize the mode collapse on MNIST dataset. To the best of our knowledge, our method is the first to propose and apply successfully the relative distance of latent and data samples for stabilizing GAN. Thirdly, our proposed model, namely Generative Adversarial Autoencoder Networks (GAAN), is stable and has suffered from neither gradient vanishing nor mode collapse issues, as empirically demonstrated on synthetic, MNIST, MNIST-1K, CelebA and CIFAR-10 datasets. Experimental results show that our method can approximate well multi-modal distribution and achieve better results than state-of-the-art methods on these benchmark datasets. Our model implementation is published here: //github.com/tntrung/gaan
Owing to the recent advances in "Big Data" modeling and prediction tasks, variational Bayesian estimation has gained popularity due to their ability to provide exact solutions to approximate posteriors. One key technique for approximate inference is stochastic variational inference (SVI). SVI poses variational inference as a stochastic optimization problem and solves it iteratively using noisy gradient estimates. It aims to handle massive data for predictive and classification tasks by applying complex Bayesian models that have observed as well as latent variables. This paper aims to decentralize it allowing parallel computation, secure learning and robustness benefits. We use Alternating Direction Method of Multipliers in a top-down setting to develop a distributed SVI algorithm such that independent learners running inference algorithms only require sharing the estimated model parameters instead of their private datasets. Our work extends the distributed SVI-ADMM algorithm that we first propose, to an ADMM-based networked SVI algorithm in which not only are the learners working distributively but they share information according to rules of a graph by which they form a network. This kind of work lies under the umbrella of `deep learning over networks' and we verify our algorithm for a topic-modeling problem for corpus of Wikipedia articles. We illustrate the results on latent Dirichlet allocation (LDA) topic model in large document classification, compare performance with the centralized algorithm, and use numerical experiments to corroborate the analytical results.
Partially inspired by successful applications of variational recurrent neural networks, we propose a novel variational recurrent neural machine translation (VRNMT) model in this paper. Different from the variational NMT, VRNMT introduces a series of latent random variables to model the translation procedure of a sentence in a generative way, instead of a single latent variable. Specifically, the latent random variables are included into the hidden states of the NMT decoder with elements from the variational autoencoder. In this way, these variables are recurrently generated, which enables them to further capture strong and complex dependencies among the output translations at different timesteps. In order to deal with the challenges in performing efficient posterior inference and large-scale training during the incorporation of latent variables, we build a neural posterior approximator, and equip it with a reparameterization technique to estimate the variational lower bound. Experiments on Chinese-English and English-German translation tasks demonstrate that the proposed model achieves significant improvements over both the conventional and variational NMT models.
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