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Generative models, such as Generative Adversarial Networks (GANs), have been used for unsupervised anomaly detection. While performance keeps improving, several limitations exist particularly attributed to difficulties at capturing multimodal supports and to the ability to approximate the underlying distribution closer to the tails, i.e. the boundary of the distribution's support. This paper proposes an approach that attempts to alleviate such shortcomings. We propose an invertible-residual-network-based model, the Boundary of Distribution Support Generator (BDSG). GANs generally do not guarantee the existence of a probability distribution and here, we use the recently developed Invertible Residual Network (IResNet) and Residual Flow (ResFlow), for density estimation. These models have not yet been used for anomaly detection. We leverage IResNet and ResFlow for Out-of-Distribution (OoD) sample detection and for sample generation on the boundary using a compound loss function that forces the samples to lie on the boundary. The BDSG addresses non-convex support, disjoint components, and multimodal distributions. Results on synthetic data and data from multimodal distributions, such as MNIST and CIFAR-10, demonstrate competitive performance compared to methods from the literature.

An important property for deep neural networks is the ability to perform robust out-of-distribution detection on previously unseen data. This property is essential for safety purposes when deploying models for real world applications. Recent studies show that probabilistic generative models can perform poorly on this task, which is surprising given that they seek to estimate the likelihood of training data. To alleviate this issue, we propose the exponentially tilted Gaussian prior distribution for the Variational Autoencoder (VAE) which pulls points onto the surface of a hyper-sphere in latent space. This achieves state-of-the art results on the area under the curve-receiver operator characteristics metric using just the negative log-likelihood that the VAE naturally assigns. Because this prior is a simple modification of the traditional VAE prior, it is faster and easier to implement than competitive methods.

Conventional deconvolution methods utilize hand-crafted image priors to constrain the optimization. While deep-learning-based methods have simplified the optimization by end-to-end training, they fail to generalize well to blurs unseen in the training dataset. Thus, training image-specific models is important for higher generalization. Deep image prior (DIP) provides an approach to optimize the weights of a randomly initialized network with a single degraded image by maximum a posteriori (MAP), which shows that the architecture of a network can serve as the hand-crafted image prior. Different from the conventional hand-crafted image priors that are statistically obtained, it is hard to find a proper network architecture because the relationship between images and their corresponding network architectures is unclear. As a result, the network architecture cannot provide enough constraint for the latent sharp image. This paper proposes a new variational deep image prior (VDIP) for blind image deconvolution, which exploits additive hand-crafted image priors on latent sharp images and approximates a distribution for each pixel to avoid suboptimal solutions. Our mathematical analysis shows that the proposed method can better constrain the optimization. The experimental results further demonstrate that the generated images have better quality than that of the original DIP on benchmark datasets. The source code of our VDIP is available at //github.com/Dong-Huo/VDIP-Deconvolution.

Markov Chain Monte Carlo (MCMC) methods form one of the algorithmic foundations of high-dimensional Bayesian inverse problems. The recent development of likelihood-informed subspace (LIS) methods offer a viable route to designing efficient MCMC methods for exploring high-dimensional posterior distributions via exploiting the intrinsic low-dimensional structure of the underlying inverse problem. However, existing LIS methods and the associated performance analysis often assume that the prior distribution is Gaussian. This assumption is limited for inverse problems aiming to promote sparsity in the parameter estimation, as heavy-tailed priors, e.g., Laplace distribution or the elastic net commonly used in Bayesian LASSO, are often needed in this case. To overcome this limitation, we consider a prior normalization technique that transforms any non-Gaussian (e.g. heavy-tailed) priors into standard Gaussian distributions, which make it possible to implement LIS methods to accelerate MCMC sampling via such transformations. We also rigorously investigate the integration of such transformations with several MCMC methods for high-dimensional problems. Finally, we demonstrate various aspects of our theoretical claims on two nonlinear inverse problems.

The posterior over Bayesian neural network (BNN) parameters is extremely high-dimensional and non-convex. For computational reasons, researchers approximate this posterior using inexpensive mini-batch methods such as mean-field variational inference or stochastic-gradient Markov chain Monte Carlo (SGMCMC). To investigate foundational questions in Bayesian deep learning, we instead use full-batch Hamiltonian Monte Carlo (HMC) on modern architectures. We show that (1) BNNs can achieve significant performance gains over standard training and deep ensembles; (2) a single long HMC chain can provide a comparable representation of the posterior to multiple shorter chains; (3) in contrast to recent studies, we find posterior tempering is not needed for near-optimal performance, with little evidence for a "cold posterior" effect, which we show is largely an artifact of data augmentation; (4) BMA performance is robust to the choice of prior scale, and relatively similar for diagonal Gaussian, mixture of Gaussian, and logistic priors; (5) Bayesian neural networks show surprisingly poor generalization under domain shift; (6) while cheaper alternatives such as deep ensembles and SGMCMC methods can provide good generalization, they provide distinct predictive distributions from HMC. Notably, deep ensemble predictive distributions are similarly close to HMC as standard SGLD, and closer than standard variational inference.

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.

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

Zero shot learning in Image Classification refers to the setting where images from some novel classes are absent in the training data but other information such as natural language descriptions or attribute vectors of the classes are available. This setting is important in the real world since one may not be able to obtain images of all the possible classes at training. While previous approaches have tried to model the relationship between the class attribute space and the image space via some kind of a transfer function in order to model the image space correspondingly to an unseen class, we take a different approach and try to generate the samples from the given attributes, using a conditional variational autoencoder, and use the generated samples for classification of the unseen classes. By extensive testing on four benchmark datasets, we show that our model outperforms the state of the art, particularly in the more realistic generalized setting, where the training classes can also appear at the test time along with the novel classes.

We investigate deep generative models that can exchange multiple modalities bi-directionally, e.g., generating images from corresponding texts and vice versa. A major approach to achieve this objective is to train a model that integrates all the information of different modalities into a joint representation and then to generate one modality from the corresponding other modality via this joint representation. We simply applied this approach to variational autoencoders (VAEs), which we call a joint multimodal variational autoencoder (JMVAE). However, we found that when this model attempts to generate a large dimensional modality missing at the input, the joint representation collapses and this modality cannot be generated successfully. Furthermore, we confirmed that this difficulty cannot be resolved even using a known solution. Therefore, in this study, we propose two models to prevent this difficulty: JMVAE-kl and JMVAE-h. Results of our experiments demonstrate that these methods can prevent the difficulty above and that they generate modalities bi-directionally with equal or higher likelihood than conventional VAE methods, which generate in only one direction. Moreover, we confirm that these methods can obtain the joint representation appropriately, so that they can generate various variations of modality by moving over the joint representation or changing the value of another modality.

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.