We introduce visual deprojection: the task of recovering an image or video that has been collapsed along a dimension. Projections arise in various contexts, such as long-exposure photography, where a dynamic scene is collapsed in time to produce a motion-blurred image, and corner cameras, where reflected light from a scene is collapsed along a spatial dimension because of an edge occluder to yield a 1D video. Deprojection is ill-posed-- often there are many plausible solutions for a given input. We first propose a probabilistic model capturing the ambiguity of the task. We then present a variational inference strategy using convolutional neural networks as functional approximators. Sampling from the inference network at test time yields plausible candidates from the distribution of original signals that are consistent with a given input projection. We evaluate the method on several datasets for both spatial and temporal deprojection tasks. We first demonstrate the method can recover human gait videos and face images from spatial projections, and then show that it can recover videos of moving digits from dramatically motion-blurred images obtained via temporal projection.
While Bayesian neural networks (BNNs) hold the promise of being flexible, well-calibrated statistical models, inference often requires approximations whose consequences are poorly understood. We study the quality of common variational methods in approximating the Bayesian predictive distribution. For single-hidden layer ReLU BNNs, we prove a fundamental limitation in function-space of two of the most commonly used distributions defined in weight-space: mean-field Gaussian and Monte Carlo dropout. We find there are simple cases where neither method can have substantially increased uncertainty in between well-separated regions of low uncertainty. We provide strong empirical evidence that exact inference does not have this pathology, hence it is due to the approximation and not the model. In contrast, for deep networks, we prove a universality result showing that there exist approximate posteriors in the above classes which provide flexible uncertainty estimates. However, we find empirically that pathologies of a similar form as in the single-hidden layer case can persist when performing variational inference in deeper networks. Our results motivate careful consideration of the implications of approximate inference methods in BNNs.
Blind image denoising is an important yet very challenging problem in computer vision due to the complicated acquisition process of real images. In this work we propose a new variational inference method, which integrates both noise estimation and image denoising into a unique Bayesian framework, for blind image denoising. Specifically, an approximate posterior, parameterized by deep neural networks, is presented by taking the intrinsic clean image and noise variances as latent variables conditioned on the input noisy image. This posterior provides explicit parametric forms for all its involved hyper-parameters, and thus can be easily implemented for blind image denoising with automatic noise estimation for the test noisy image. On one hand, as other data-driven deep learning methods, our method, namely variational denoising network (VDN), can perform denoising efficiently due to its explicit form of posterior expression. On the other hand, VDN inherits the advantages of traditional model-driven approaches, especially the good generalization capability of generative models. VDN has good interpretability and can be flexibly utilized to estimate and remove complicated non-i.i.d. noise collected in real scenarios. Comprehensive experiments are performed to substantiate the superiority of our method in blind image denoising.
The preprocessing pipelines in Natural Language Processing usually involve a step of removing sentences consisted of illegal characters. The definition of illegal characters and the specific removal strategy depend on the task, language, domain, etc, which often lead to tiresome and repetitive scripting of rules. In this paper, we introduce a simple statistical method, uniblock, to overcome this problem. For each sentence, uniblock generates a fixed-size feature vector using Unicode block information of the characters. A Gaussian mixture model is then estimated on some clean corpus using variational inference. The learned model can then be used to score sentences and filter corpus. We present experimental results on Sentiment Analysis, Language Modeling and Machine Translation, and show the simplicity and effectiveness of our method.
Representation learning over graph structured data has been mostly studied in static graph settings while efforts for modeling dynamic graphs are still scant. In this paper, we develop a novel hierarchical variational model that introduces additional latent random variables to jointly model the hidden states of a graph recurrent neural network (GRNN) to capture both topology and node attribute changes in dynamic graphs. We argue that the use of high-level latent random variables in this variational GRNN (VGRNN) can better capture potential variability observed in dynamic graphs as well as the uncertainty of node latent representation. With semi-implicit variational inference developed for this new VGRNN architecture (SI-VGRNN), we show that flexible non-Gaussian latent representations can further help dynamic graph analytic tasks. Our experiments with multiple real-world dynamic graph datasets demonstrate that SI-VGRNN and VGRNN consistently outperform the existing baseline and state-of-the-art methods by a significant margin in dynamic link prediction.
Aiming at a comprehensive and concise tutorial survey, recap of variational inference and reinforcement learning with Probabilistic Graphical Models are given with detailed derivations. Reviews and comparisons on recent advances in deep reinforcement learning are made from various aspects. We offer detailed derivations to a taxonomy of Probabilistic Graphical Model and Variational Inference methods in deep reinforcement learning, which serves as a complementary material on top of the original contributions.
The performance of multi-task learning in Convolutional Neural Networks (CNNs) hinges on the design of feature sharing between tasks within the architecture. The number of possible sharing patterns are combinatorial in the depth of the network and the number of tasks, and thus hand-crafting an architecture, purely based on the human intuitions of task relationships can be time-consuming and suboptimal. In this paper, we present a probabilistic approach to learning task-specific and shared representations in CNNs for multi-task learning. Specifically, we propose "stochastic filter groups'' (SFG), a mechanism to assign convolution kernels in each layer to "specialist'' or "generalist'' groups, which are specific to or shared across different tasks, respectively. The SFG modules determine the connectivity between layers and the structures of task-specific and shared representations in the network. We employ variational inference to learn the posterior distribution over the possible grouping of kernels and network parameters. Experiments demonstrate that the proposed method generalises across multiple tasks and shows improved performance over baseline methods.
Majority of the text modelling techniques yield only point-estimates of document embeddings and lack in capturing the uncertainty of the estimates. These uncertainties give a notion of how well the embeddings represent a document. We present Bayesian subspace multinomial model (Bayesian SMM), a generative log-linear model that learns to represent documents in the form of Gaussian distributions, thereby encoding the uncertainty in its co-variance. Additionally, in the proposed Bayesian SMM, we address a commonly encountered problem of intractability that appears during variational inference in mixed-logit models. We also present a generative Gaussian linear classifier for topic identification that exploits the uncertainty in document embeddings. Our intrinsic evaluation using perplexity measure shows that the proposed Bayesian SMM fits the data better as compared to the state-of-the-art neural variational document model on Fisher speech and 20Newsgroups text corpora. Our topic identification experiments show that the proposed systems are robust to over-fitting on unseen test data. The topic ID results show that the proposed model is outperforms state-of-the-art unsupervised topic models and achieve comparable results to the state-of-the-art fully supervised discriminative models.
Items in modern recommender systems are often organized in hierarchical structures. These hierarchical structures and the data within them provide valuable information for building personalized recommendation systems. In this paper, we propose a general hierarchical Bayesian learning framework, i.e., \emph{HBayes}, to learn both the structures and associated latent factors. Furthermore, we develop a variational inference algorithm that is able to learn model parameters with fast empirical convergence rate. The proposed HBayes is evaluated on two real-world datasets from different domains. The results demonstrate the benefits of our approach on item recommendation tasks, and show that it can outperform the state-of-the-art models in terms of precision, recall, and normalized discounted cumulative gain. To encourage the reproducible results, we make our code public on a git repo: \url{https://tinyurl.com/ycruhk4t}.
Semi-implicit graph variational auto-encoder (SIG-VAE) is proposed to expand the flexibility of variational graph auto-encoders (VGAE) to model graph data. SIG-VAE employs a hierarchical variational framework to enable neighboring node sharing for better generative modeling of graph dependency structure, together with a Bernoulli-Poisson link decoder. Not only does this hierarchical construction provide a more flexible generative graph model to better capture real-world graph properties, but also does SIG-VAE naturally lead to semi-implicit hierarchical variational inference that allows faithful modeling of implicit posteriors of given graph data, which may exhibit heavy tails, multiple modes, skewness, and rich dependency structures. Compared to VGAE, the derived graph latent representations by SIG-VAE are more interpretable, due to more expressive generative model and more faithful inference enabled by the flexible semi-implicit construction. Extensive experiments with a variety of graph data show that SIG-VAE significantly outperforms state-of-the-art methods on several different graph analytic tasks.
Variational inference is becoming more and more popular for approximating intractable posterior distributions in Bayesian statistics and machine learning. Meanwhile, a few recent works have provided theoretical justification and new insights on deep neural networks for estimating smooth functions in usual settings such as nonparametric regression. In this paper, we show that variational inference for sparse deep learning retains the same generalization properties than exact Bayesian inference. In particular, we highlight the connection between estimation and approximation theories via the classical bias-variance trade-off and show that it leads to near-minimax rates of convergence for H\"older smooth functions. Additionally, we show that the model selection framework over the neural network architecture via ELBO maximization does not overfit and adaptively achieves the optimal rate of convergence.
Monotonic neural networks have recently been proposed as a way to define invertible transformations. These transformations can be combined into powerful autoregressive flows that have been shown to be universal approximators of continuous probability distributions. Architectures that ensure monotonicity typically enforce constraints on weights and activation functions, which enables invertibility but leads to a cap on the expressiveness of the resulting transformations. In this work, we propose the Unconstrained Monotonic Neural Network (UMNN) architecture based on the insight that a function is monotonic as long as its derivative is strictly positive. In particular, this latter condition can be enforced with a free-form neural network whose only constraint is the positiveness of its output. We evaluate our new invertible building block within a new autoregressive flow (UMNN-MAF) and demonstrate its effectiveness on density estimation experiments. We also illustrate the ability of UMNNs to improve variational inference.
We consider an information theoretic approach to address the problem of identifying fake digital images. We propose an innovative method to formulate the issue of localizing manipulated regions in an image as a deep representation learning problem using the Information Bottleneck (IB), which has recently gained popularity as a framework for interpreting deep neural networks. Tampered images pose a serious predicament since digitized media is a ubiquitous part of our lives. These are facilitated by the easy availability of image editing software and aggravated by recent advances in deep generative models such as GANs. We propose InfoPrint, a computationally efficient solution to the IB formulation using approximate variational inference and compare it to a numerical solution that is computationally expensive. Testing on a number of standard datasets, we demonstrate that InfoPrint outperforms the state-of-the-art and the numerical solution. Additionally, it also has the ability to detect alterations made by inpainting GANs.
Recent advances in statistical inference have significantly expanded the toolbox of probabilistic modeling. Historically, probabilistic modeling has been constrained to (i) very restricted model classes where exact or approximate probabilistic inference were feasible, and (ii) small or medium-sized data sets which fit within the main memory of the computer. However, developments in variational inference, a general form of approximate probabilistic inference originated in statistical physics, are allowing probabilistic modeling to overcome these restrictions: (i) Approximate probabilistic inference is now possible over a broad class of probabilistic models containing a large number of parameters, and (ii) scalable inference methods based on stochastic gradient descent and distributed computation engines allow to apply probabilistic modeling over massive data sets. One important practical consequence of these advances is the possibility to include deep neural networks within a probabilistic model to capture complex non-linear stochastic relationships between random variables. These advances in conjunction with the release of novel probabilistic modeling toolboxes have greatly expanded the scope of application of probabilistic models, and allow these models to take advantage of the recent strides made by the deep learning community. In this paper we review the main concepts, methods and tools needed to use deep neural networks within a probabilistic modeling framework.
We introduce a new, rigorously-formulated Bayesian meta-learning algorithm that learns a probability distribution of model parameter prior for few-shot learning. The proposed algorithm employs a gradient-based variational inference to infer the posterior of model parameters to a new task. Our algorithm can be applied to any model architecture and can be implemented in various machine learning paradigms, including regression and classification. We show that the models trained with our proposed meta-learning algorithm are well calibrated and accurate, with state-of-the-art calibration and classification results on two few-shot classification benchmarks (Omniglot and Mini-ImageNet), and competitive results in a multi-modal task-distribution regression.
The importance weighted autoencoder (IWAE) (Burda et al., 2016) is a popular variational-inference method which achieves a tighter evidence bound (and hence a lower bias) than standard variational autoencoders by optimising a multi-sample objective, i.e. an objective that is expressible as an integral over $K > 1$ Monte Carlo samples. Unfortunately, IWAE crucially relies on the availability of reparametrisations and even if these exist, the multi-sample objective leads to inference-network gradients which break down as $K$ is increased (Rainforth et al., 2018). This breakdown can only be circumvented by removing high-variance score-function terms, either by heuristically ignoring them (which yields the 'sticking-the-landing' IWAE (IWAE-STL) gradient from Roeder et al. (2017)) or through an identity from Tucker et al. (2019) (which yields the 'doubly-reparametrised' IWAE (IWAE-DREG) gradient). In this work, we argue that directly optimising the proposal distribution in importance sampling as in the reweighted wake-sleep (RWS) algorithm from Bornschein & Bengio (2015) is preferable to optimising IWAE-type multi-sample objectives. To formalise this argument, we introduce an adaptive-importance sampling framework termed adaptive importance sampling for learning (AISLE) which slightly generalises the RWS algorithm. We then show that AISLE admits IWAE-STL and IWAE-DREG (i.e. the IWAE-gradients which avoid breakdown) as special cases.
In Bayesian machine learning, the posterior distribution is typically computationally intractable, hence variational inference is often required. In this approach, an evidence lower bound on the log likelihood of data is maximized during training. Variational Autoencoders (VAE) are one important example where variational inference is utilized. In this tutorial, we derive the variational lower bound loss function of the standard variational autoencoder. We do so in the instance of a gaussian latent prior and gaussian approximate posterior, under which assumptions the Kullback-Leibler term in the variational lower bound has a closed form solution. We derive essentially everything we use along the way; everything from Bayes' theorem to the Kullback-Leibler divergence.
Probabilistic programming is the idea of writing models from statistics and machine learning using program notations and reasoning about these models using generic inference engines. Recently its combination with deep learning has been explored intensely, leading to the development of deep probabilistic programming languages such as Pyro. At the core of this development lie inference engines based on stochastic variational inference algorithms. When asked to find information about the posterior distribution of a model written in such a language, these algorithms convert this posterior-inference query into an optimisation problem and solve it approximately by gradient ascent. In this paper, we analyse one of the most fundamental and versatile variational inference algorithms, called score estimator, using tools from denotational semantics and program analysis. We formally express what this algorithm does on models denoted by programs, and expose implicit assumptions made by the algorithm. The violation of these assumptions may lead to an undefined optimisation objective or the loss of convergence guarantee of the optimisation process. We then describe rules for proving these assumptions, which can be automated by static program analyses. Some of our rules use nontrivial facts from continuous mathematics, and let us replace requirements about integrals in the assumptions, by conditions involving differentiation or boundedness, which are much easier to prove automatically. Following our general methodology, we have developed a static program analysis for Pyro that aims at discharging the assumption about what we call model-guide support match. Applied to the eight representative model-guide pairs from the Pyro webpage, our analysis finds a bug in one of these cases, reveals a non-standard use of an inference engine in another, and shows the assumptions are met in the remaining cases.
Spatio-temporal (ST) data for urban applications, such as taxi demand, traffic flow, regional rainfall is inherently stochastic and unpredictable. Recently, deep learning based ST prediction models are proposed to learn the ST characteristics of data. However, it is still very challenging (1) to adequately learn the complex and non-linear ST relationships; (2) to model the high variations in the ST data volumes as it is inherently dynamic, changing over time (i.e., irregular) and highly influenced by many external factors, such as adverse weather, accidents, traffic control, PoI, etc.; and (3) as there can be many complicated external factors that can affect the accuracy and it is impossible to list them explicitly. To handle the aforementioned issues, in this paper, we propose a novel deep generative adversarial network based model (named, D-GAN) for more accurate ST prediction by implicitly learning ST feature representations in an unsupervised manner. D-GAN adopts a GAN-based structure and jointly learns generation and variational inference of data. More specifically, D-GAN consists of two major parts: (1) a deep ST feature learning network to model the ST correlations and semantic variations, and underlying factors of variations and irregularity in the data through the implicit distribution modelling; (2) a fusion module to incorporate external factors for reaching a better inference. To the best our knowledge, no prior work studies ST prediction problem via deep implicit generative model and in an unsupervised manner. Extensive experiments performed on two real-world datasets show that D-GAN achieves more accurate results than traditional as well as deep learning based ST prediction methods.
Bayesian inference was once a gold standard for learning with neural networks, providing accurate full predictive distributions and well calibrated uncertainty. However, scaling Bayesian inference techniques to deep neural networks is challenging due to the high dimensionality of the parameter space. In this paper, we construct low-dimensional subspaces of parameter space, such as the first principal components of the stochastic gradient descent (SGD) trajectory, which contain diverse sets of high performing models. In these subspaces, we are able to apply elliptical slice sampling and variational inference, which struggle in the full parameter space. We show that Bayesian model averaging over the induced posterior in these subspaces produces accurate predictions and well calibrated predictive uncertainty for both regression and image classification.