Partition-Guided GANs

Despite the success of Generative Adversarial Networks (GANs), their training suffers from several well-known problems, including mode collapse and difficulties learning a disconnected set of manifolds. In this paper, we break down the challenging task of learning complex high dimensional distributions, supporting diverse data samples, to simpler sub-tasks. Our solution relies on designing a partitioner that breaks the space into smaller regions, each having a simpler distribution, and training a different generator for each partition. This is done in an unsupervised manner without requiring any labels. We formulate two desired criteria for the space partitioner that aid the training of our mixture of generators: 1) to produce connected partitions and 2) provide a proxy of distance between partitions and data samples, along with a direction for reducing that distance. These criteria are developed to avoid producing samples from places with non-existent data density, and also facilitate training by providing additional direction to the generators. We develop theoretical constraints for a space partitioner to satisfy the above criteria. Guided by our theoretical analysis, we design an effective neural architecture for the space partitioner that empirically assures these conditions. Experimental results on various standard benchmarks show that the proposed unsupervised model outperforms several recent methods.

Contextual Dropout: An Efficient Sample-Dependent Dropout Module

Dropout has been demonstrated as a simple and effective module to not only regularize the training process of deep neural networks, but also provide the uncertainty estimation for prediction. However, the quality of uncertainty estimation is highly dependent on the dropout probabilities. Most current models use the same dropout distributions across all data samples due to its simplicity. Despite the potential gains in the flexibility of modeling uncertainty, sample-dependent dropout, on the other hand, is less explored as it often encounters scalability issues or involves non-trivial model changes. In this paper, we propose contextual dropout with an efficient structural design as a simple and scalable sample-dependent dropout module, which can be applied to a wide range of models at the expense of only slightly increased memory and computational cost. We learn the dropout probabilities with a variational objective, compatible with both Bernoulli dropout and Gaussian dropout. We apply the contextual dropout module to various models with applications to image classification and visual question answering and demonstrate the scalability of the method with large-scale datasets, such as ImageNet and VQA 2.0. Our experimental results show that the proposed method outperforms baseline methods in terms of both accuracy and quality of uncertainty estimation.

Self-supervised Pre-training with Hard Examples Improves Visual Representations

Self-supervised pre-training (SSP) employs random image transformations to generate training data for visual representation learning. In this paper, we first present a modeling framework that unifies existing SSP methods as learning to predict pseudo-labels. Then, we propose new data augmentation methods of generating training examples whose pseudo-labels are harder to predict than those generated via random image transformations. Specifically, we use adversarial training and CutMix to create hard examples (HEXA) to be used as augmented views for MoCo-v2 and DeepCluster-v2, leading to two variants HEXA_{MoCo} and HEXA_{DCluster}, respectively. In our experiments, we pre-train models on ImageNet and evaluate them on multiple public benchmarks. Our evaluation shows that the two new algorithm variants outperform their original counterparts, and achieve new state-of-the-art on a wide range of tasks where limited task supervision is available for fine-tuning. These results verify that hard examples are instrumental in improving the generalization of the pre-trained models.

ACT: Asymptotic Conditional Transport

We propose conditional transport (CT) as a new divergence to measure the difference between two probability distributions. The CT divergence consists of the expected cost of a forward CT, which constructs a navigator to stochastically transport a data point of one distribution to the other distribution, and that of a backward CT which reverses the transport direction. To apply it to the distributions whose probability density functions are unknown but random samples are accessible, we further introduce asymptotic CT (ACT), whose estimation only requires access to mini-batch based discrete empirical distributions. Equipped with two navigators that amortize the computation of conditional transport plans, the ACT divergence comes with unbiased sample gradients that are straightforward to compute, making it amenable to mini-batch stochastic gradient descent based optimization. When applied to train a generative model, the ACT divergence is shown to strike a good balance between mode covering and seeking behaviors and strongly resist mode collapse. To model high-dimensional data, we show that it is sufficient to modify the adversarial game of an existing generative adversarial network (GAN) to a game played by a generator, a forward navigator, and a backward navigator, which try to minimize a distribution-to-distribution transport cost by optimizing both the distribution of the generator and conditional transport plans specified by the navigators, versus a critic that does the opposite by inflating the point-to-point transport cost. On a wide variety of benchmark datasets for generative modeling, substituting the default statistical distance of an existing GAN with the ACT divergence is shown to consistently improve the performance.

Hyperbolic Graph Embedding with Enhanced Semi-Implicit Variational Inference

Efficient modeling of relational data arising in physical, social, and information sciences is challenging due to complicated dependencies within the data. In this work we build off of semi-implicit graph variational auto-encoders to capture higher order statistics in a low-dimensional graph latent representation. We incorporate hyperbolic geometry in the latent space through a \poincare embedding to efficiently represent graphs exhibiting hierarchical structure. To address the naive posterior latent distribution assumptions in classical variational inference, we use semi-implicit hierarchical variational Bayes to implicitly capture posteriors of given graph data, which may exhibit heavy tails, multiple modes, skewness, and highly correlated latent structures. We show that the existing semi-implicit variational inference objective provably reduces information in the observed graph. Based on this observation, we estimate and add an additional mutual information term to the semi-implicit variational inference learning objective to capture rich correlations arising between the input and latent spaces. We show that the inclusion of this regularization term in conjunction with the \poincare embedding boosts the quality of learned high-level representations and enables more flexible and faithful graphical modeling. We experimentally demonstrate that our approach outperforms existing graph variational auto-encoders both in Euclidean and in hyperbolic spaces for edge link prediction and node classification.

Convex Polytope Trees

A decision tree is commonly restricted to use a single hyperplane to split the covariate space at each of its internal nodes. It often requires a large number of nodes to achieve high accuracy, hurting its interpretability. In this paper, we propose convex polytope trees (CPT) to expand the family of decision trees by an interpretable generalization of their decision boundary. The splitting function at each node of CPT is based on the logical disjunction of a community of differently weighted probabilistic linear decision-makers, which also geometrically corresponds to a convex polytope in the covariate space. We use a nonparametric Bayesian prior at each node to infer the community's size, encouraging simpler decision boundaries by shrinking the number of polytope facets. We develop a greedy method to efficiently construct CPT and scalable end-to-end training algorithms for the tree parameters when the tree structure is given. We empirically demonstrate the efficiency of CPT over existing state-of-the-art decision trees in several real-world classification and regression tasks from diverse domains.

Bayesian Attention Modules

Attention modules, as simple and effective tools, have not only enabled deep neural networks to achieve state-of-the-art results in many domains, but also enhanced their interpretability. Most current models use deterministic attention modules due to their simplicity and ease of optimization. Stochastic counterparts, on the other hand, are less popular despite their potential benefits. The main reason is that stochastic attention often introduces optimization issues or requires significant model changes. In this paper, we propose a scalable stochastic version of attention that is easy to implement and optimize. We construct simplex-constrained attention distributions by normalizing reparameterizable distributions, making the training process differentiable. We learn their parameters in a Bayesian framework where a data-dependent prior is introduced for regularization. We apply the proposed stochastic attention modules to various attention-based models, with applications to graph node classification, visual question answering, image captioning, machine translation, and language understanding. Our experiments show the proposed method brings consistent improvements over the corresponding baselines.

MCMC-Interactive Variational Inference

Leveraging well-established MCMC strategies, we propose MCMC-interactive variational inference (MIVI) to not only estimate the posterior in a time constrained manner, but also facilitate the design of MCMC transitions. Constructing a variational distribution followed by a short Markov chain that has parameters to learn, MIVI takes advantage of the complementary properties of variational inference and MCMC to encourage mutual improvement. On one hand, with the variational distribution locating high posterior density regions, the Markov chain is optimized within the variational inference framework to efficiently target the posterior despite a small number of transitions. On the other hand, the optimized Markov chain with considerable flexibility guides the variational distribution towards the posterior and alleviates its underestimation of uncertainty. Furthermore, we prove the optimized Markov chain in MIVI admits extrapolation, which means its marginal distribution gets closer to the true posterior as the chain grows. Therefore, the Markov chain can be used separately as an efficient MCMC scheme. Experiments show that MIVI not only accurately and efficiently approximates the posteriors but also facilitates designs of stochastic gradient MCMC and Gibbs sampling transitions.

Variational Temporal Deep Generative Model for Radar HRRP Target Recognition

We develop a recurrent gamma belief network (rGBN) for radar automatic target recognition (RATR) based on high-resolution range profile (HRRP), which characterizes the temporal dependence across the range cells of HRRP. The proposed rGBN adopts a hierarchy of gamma distributions to build its temporal deep generative model. For scalable training and fast out-of-sample prediction, we propose the hybrid of a stochastic-gradient Markov chain Monte Carlo (MCMC) and a recurrent variational inference model to perform posterior inference. To utilize the label information to extract more discriminative latent representations, we further propose supervised rGBN to jointly model the HRRP samples and their corresponding labels. Experimental results on synthetic and measured HRRP data show that the proposed models are efficient in computation, have good classification accuracy and generalization ability, and provide highly interpretable multi-stochastic-layer latent structure.