Recent work used importance sampling ideas for better variational bounds on likelihoods. We clarify the applicability of these ideas to pure probabilistic inference, by showing the resulting Importance Weighted Variational Inference (IWVI) technique is an instance of augmented variational inference, thus identifying the looseness in previous work. Experiments confirm IWVI's practicality for probabilistic inference. As a second contribution, we investigate inference with elliptical distributions, which improves accuracy in low dimensions, and convergence in high dimensions.
The growing need to analyze large collections of documents has led to great developments in topic modeling. Since documents are frequently associated with other related variables, such as labels or ratings, much interest has been placed on supervised topic models. However, the nature of most annotation tasks, prone to ambiguity and noise, often with high volumes of documents, deem learning under a single-annotator assumption unrealistic or unpractical for most real-world applications. In this article, we propose two supervised topic models, one for classification and another for regression problems, which account for the heterogeneity and biases among different annotators that are encountered in practice when learning from crowds. We develop an efficient stochastic variational inference algorithm that is able to scale to very large datasets, and we empirically demonstrate the advantages of the proposed model over state-of-the-art approaches.
Generalising well in supervised learning tasks relies on correctly extrapolating the training data to a large region of the input space. One way to achieve this is to constrain the predictions to be invariant to transformations on the input that are known to be irrelevant (e.g. translation). Commonly, this is done through data augmentation, where the training set is enlarged by applying hand-crafted transformations to the inputs. We argue that invariances should instead be incorporated in the model structure, and learned using the marginal likelihood, which correctly rewards the reduced complexity of invariant models. We demonstrate this for Gaussian process models, due to the ease with which their marginal likelihood can be estimated. Our main contribution is a variational inference scheme for Gaussian processes containing invariances described by a sampling procedure. We learn the sampling procedure by back-propagating through it to maximise the marginal likelihood.
Modeling spillover effects from observational data is an important problem in economics, business, and other fields of research. % It helps us infer the causality between two seemingly unrelated set of events. For example, if consumer spending in the United States declines, it has spillover effects on economies that depend on the U.S. as their largest export market. In this paper, we aim to infer the causation that results in spillover effects between pairs of entities (or units), we call this effect as \textit{paired spillover}. To achieve this, we leverage the recent developments in variational inference and deep learning techniques to propose a generative model called Linked Causal Variational Autoencoder (LCVA). Similar to variational autoencoders (VAE), LCVA incorporates an encoder neural network to learn the latent attributes and a decoder network to reconstruct the inputs. However, unlike VAE, LCVA treats the \textit{latent attributes as confounders that are assumed to affect both the treatment and the outcome of units}. Specifically, given a pair of units $u$ and $\bar{u}$, their individual treatment and outcomes, the encoder network of LCVA samples the confounders by conditioning on the observed covariates of $u$, the treatments of both $u$ and $\bar{u}$ and the outcome of $u$. Once inferred, the latent attributes (or confounders) of $u$ captures the spillover effect of $\bar{u}$ on $u$. Using a network of users from job training dataset (LaLonde (1986)) and co-purchase dataset from Amazon e-commerce domain, we show that LCVA is significantly more robust than existing methods in capturing spillover effects.
We develop unbiased implicit variational inference (UIVI), a method that expands the applicability of variational inference by defining an expressive variational family. UIVI considers an implicit variational distribution obtained in a hierarchical manner using a simple reparameterizable distribution whose variational parameters are defined by arbitrarily flexible deep neural networks. Unlike previous works, UIVI directly optimizes the evidence lower bound (ELBO) rather than an approximation to the ELBO. We demonstrate UIVI on several models, including Bayesian multinomial logistic regression and variational autoencoders, and show that UIVI achieves both tighter ELBO and better predictive performance than existing approaches at a similar computational cost.
Generating versatile and appropriate synthetic speech requires control over the output expression separate from the spoken text. Important non-textual speech variation is seldom annotated, in which case output control must be learned in an unsupervised fashion. In this paper, we perform an in-depth study of methods for unsupervised learning of control in statistical speech synthesis. For example, we show that popular unsupervised training heuristics can be interpreted as variational inference in certain autoencoder models. We additionally connect these models to VQ-VAEs, another, recently-proposed class of deep variational autoencoders, which we show can be derived from a very similar mathematical argument. The implications of these new probabilistic interpretations are discussed. We illustrate the utility of the various approaches with an application to acoustic modelling for emotional speech synthesis, where the unsupervised methods for learning expression control (without access to emotional labels) are found to give results that in many aspects match or surpass the previous best supervised approach.
To backpropagate the gradients through stochastic binary layers, we propose the augment-REINFORCE-merge (ARM) estimator that is unbiased, exhibits low variance, and has low computational complexity. Exploiting variable augmentation, REINFORCE, and reparameterization, the ARM estimator achieves adaptive variance reduction for Monte Carlo integration by merging two expectations via common random numbers. The variance-reduction mechanism of the ARM estimator can also be attributed to either antithetic sampling in an augmented space, or the use of an optimal anti-symmetric "self-control" baseline function together with the REINFORCE estimator in that augmented space. Experimental results show the ARM estimator provides state-of-the-art performance in auto-encoding variational inference and maximum likelihood estimation, for discrete latent variable models with one or multiple stochastic binary layers. Python code for reproducible research is publicly available.
In this work, we develop a novel Bayesian estimation method for the Dirichlet process (DP) mixture of the inverted Dirichlet distributions, which has been shown to be very flexible for modeling vectors with positive elements. The recently proposed extended variational inference (EVI) framework is adopted to derive an analytically tractable solution. The convergency of the proposed algorithm is theoretically guaranteed by introducing single lower bound approximation to the original objective function in the VI framework. In principle, the proposed model can be viewed as an infinite inverted Dirichelt mixture model (InIDMM) that allows the automatic determination of the number of mixture components from data. Therefore, the problem of pre-determining the optimal number of mixing components has been overcome. Moreover, the problems of over-fitting and under-fitting are avoided by the Bayesian estimation approach. Comparing with several recently proposed DP-related methods, the good performance and effectiveness of the proposed method have been demonstrated with both synthesized data and real data evaluations.
We present a deep generative model of bilingual sentence pairs for machine translation. The model generates source and target sentences jointly from a shared latent representation and is parameterised by neural networks. We perform efficient training using amortised variational inference and reparameterised gradients. Additionally, we discuss the statistical implications of joint modelling and propose an efficient approximation to maximum a posteriori decoding for fast test-time predictions. We demonstrate the effectiveness of our model in three machine translation scenarios: in-domain training, mixed-domain training, and learning from a mix of gold-standard and synthetic data. Our experiments show consistently that our joint formulation outperforms conditional modelling (i.e. standard neural machine translation) in all such scenarios.
We explore methods for option discovery based on variational inference and make two algorithmic contributions. First: we highlight a tight connection between variational option discovery methods and variational autoencoders, and introduce Variational Autoencoding Learning of Options by Reinforcement (VALOR), a new method derived from the connection. In VALOR, the policy encodes contexts from a noise distribution into trajectories, and the decoder recovers the contexts from the complete trajectories. Second: we propose a curriculum learning approach where the number of contexts seen by the agent increases whenever the agent's performance is strong enough (as measured by the decoder) on the current set of contexts. We show that this simple trick stabilizes training for VALOR and prior variational option discovery methods, allowing a single agent to learn many more modes of behavior than it could with a fixed context distribution. Finally, we investigate other topics related to variational option discovery, including fundamental limitations of the general approach and the applicability of learned options to downstream tasks.
Inference models are a key component in scaling variational inference to deep latent variable models, most notably as encoder networks in variational auto-encoders (VAEs). By replacing conventional optimization-based inference with a learned model, inference is amortized over data examples and therefore more computationally efficient. However, standard inference models are restricted to direct mappings from data to approximate posterior estimates. The failure of these models to reach fully optimized approximate posterior estimates results in an amortization gap. We aim toward closing this gap by proposing iterative inference models, which learn to perform inference optimization through repeatedly encoding gradients. Our approach generalizes standard inference models in VAEs and provides insight into several empirical findings, including top-down inference techniques. We demonstrate the inference optimization capabilities of iterative inference models and show that they outperform standard inference models on several benchmark data sets of images and text.
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.
Bayesian inference plays an important role in advancing machine learning, but faces computational challenges when applied to complex models such as deep neural networks. Variational inference circumvents these challenges by formulating Bayesian inference as an optimization problem and solving it using gradient-based optimization. In this paper, we argue in favor of natural-gradient approaches which, unlike their gradient-based counterparts, can improve convergence by exploiting the information geometry of the solutions. We show how to derive fast yet simple natural-gradient updates by using a duality associated with exponential-family distributions. An attractive feature of these methods is that, by using natural-gradients, they are able to extract accurate local approximations for individual model components. We summarize recent results for Bayesian deep learning showing the superiority of natural-gradient approaches over their gradient counterparts.
In recent years, research on image generation methods has been developing fast. The auto-encoding variational Bayes method (VAEs) was proposed in 2013, which uses variational inference to learn a latent space from the image database and then generates images using the decoder. The generative adversarial networks (GANs) came out as a promising framework, which uses adversarial training to improve the generative ability of the generator. However, the generated pictures by GANs are generally blurry. The deep convolutional generative adversarial networks (DCGANs) were then proposed to leverage the quality of generated images. Since the input noise vectors are randomly sampled from a Gaussian distribution, the generator has to map from a whole normal distribution to the images. This makes DCGANs unable to reflect the inherent structure of the training data. In this paper, we propose a novel deep model, called generative adversarial networks with decoder-encoder output noise (DE-GANs), which takes advantage of both the adversarial training and the variational Bayesain inference to improve the performance of image generation. DE-GANs use a pre-trained decoder-encoder architecture to map the random Gaussian noise vectors to informative ones and pass them to the generator of the adversarial networks. Since the decoder-encoder architecture is trained by the same images as the generators, the output vectors could carry the intrinsic distribution information of the original images. Moreover, the loss function of DE-GANs is different from GANs and DCGANs. A hidden-space loss function is added to the adversarial loss function to enhance the robustness of the model. Extensive empirical results show that DE-GANs can accelerate the convergence of the adversarial training process and improve the quality of the generated images.
The problem of distributed representation learning is one in which multiple sources of information $X_1,\ldots,X_K$ are processed separately so as to learn as much information as possible about some ground truth $Y$. We investigate this problem from information-theoretic grounds, through a generalization of Tishby's centralized Information Bottleneck (IB) method to the distributed setting. Specifically, $K$ encoders, $K \geq 2$, compress their observations $X_1,\ldots,X_K$ separately in a manner such that, collectively, the produced representations preserve as much information as possible about $Y$. We study both discrete memoryless (DM) and memoryless vector Gaussian data models. For the discrete model, we establish a single-letter characterization of the optimal tradeoff between complexity (or rate) and relevance (or information) for a class of memoryless sources (the observations $X_1,\ldots,X_K$ being conditionally independent given $Y$). For the vector Gaussian model, we provide an explicit characterization of the optimal complexity-relevance tradeoff. Furthermore, we develop a variational bound on the complexity-relevance tradeoff which generalizes the evidence lower bound (ELBO) to the distributed setting. We also provide two algorithms that allow to compute this bound: i) a Blahut-Arimoto type iterative algorithm which enables to compute optimal complexity-relevance encoding mappings by iterating over a set of self-consistent equations, and ii) a variational inference type algorithm in which the encoding mappings are parametrized by neural networks and the bound approximated by Markov sampling and optimized with stochastic gradient descent. Numerical results on synthetic and real datasets are provided to support the efficiency of the approaches and algorithms developed in this paper.
Neural attention has become central to many state-of-the-art models in natural language processing and related domains. Attention networks are an easy-to-train and effective method for softly simulating alignment; however, the approach does not marginalize over latent alignments in a probabilistic sense. This property makes it difficult to compare attention to other alignment approaches, to compose it with probabilistic models, and to perform posterior inference conditioned on observed data. A related latent approach, hard attention, fixes these issues, but is generally harder to train and less accurate. This work considers variational attention networks, alternatives to soft and hard attention for learning latent variable alignment models, with tighter approximation bounds based on amortized variational inference. We further propose methods for reducing the variance of gradients to make these approaches computationally feasible. Experiments show that for machine translation and visual question answering, inefficient exact latent variable models outperform standard neural attention, but these gains go away when using hard attention based training. On the other hand, variational attention retains most of the performance gain but with training speed comparable to neural attention.
We present a representation learning algorithm that learns a low-dimensional latent dynamical system from high-dimensional \textit{sequential} raw data, e.g., video. The framework builds upon recent advances in amortized inference methods that use both an inference network and a refinement procedure to output samples from a variational distribution given an observation sequence, and takes advantage of the duality between control and inference to approximately solve the intractable inference problem using the path integral control approach. The learned dynamical model can be used to predict and plan the future states; we also present the efficient planning method that exploits the learned low-dimensional latent dynamics. Numerical experiments show that the proposed path-integral control based variational inference method leads to tighter lower bounds in statistical model learning of sequential data. The supplementary video: https://youtu.be/xCp35crUoLQ
We propose a Variational Time Series Feature Extractor (VTSFE), inspired by the VAE-DMP model of Chen et al., to be used for action recognition and prediction. Our method is based on variational autoencoders. It improves VAE-DMP in that it has a better noise inference model, a simpler transition model constraining the acceleration in the trajectories of the latent space, and a tighter lower bound for the variational inference. We apply the method for classification and prediction of whole-body movements on a dataset with 7 tasks and 10 demonstrations per task, recorded with a wearable motion capture suit. The comparison with VAE and VAE-DMP suggests the better performance of our method for feature extraction. An open-source software implementation of each method with TensorFlow is also provided. In addition, a more detailed version of this work can be found in the indicated code repository. Although it was meant to, the VTSFE hasn't been tested for action prediction, due to a lack of time in the context of Maxime Chaveroche's Master thesis at INRIA.
In this paper we propose two novel bounds for the log-likelihood based on Kullback-Leibler and the R\'{e}nyi divergences, which can be used for variational inference and in particular for the training of Variational AutoEncoders. Our proposal is motivated by the difficulties encountered in training VAEs on continuous datasets with high contrast images, such as those with handwritten digits and characters, where numerical issues often appear unless noise is added, either to the dataset during training or to the generative model given by the decoder. The new bounds we propose, which are obtained from the maximization of the likelihood of an interval for the observations, allow numerically stable training procedures without the necessity of adding any extra source of noise to the data.
Particle-based variational inference methods (ParVIs) have gained attention in the Bayesian inference literature, for their capacity to yield flexible and accurate approximations. We explore ParVIs from the perspective of Wasserstein gradient flows, and make both theoretical and practical contributions. We unify various finite-particle approximations that existing ParVIs use, and recognize that the approximation is essentially a compulsory smoothing treatment, in either of two equivalent forms. This novel understanding reveals the assumptions and relations of existing ParVIs, and also inspires new ParVIs. We propose an acceleration framework and a principled bandwidth-selection method for general ParVIs; these are based on the developed theory and leverage the geometry of the Wasserstein space. Experimental results show the improved convergence by the acceleration framework and enhanced sample accuracy by the bandwidth-selection method.