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Through-wall radars are researched and developed for the detection, localization, and tracking of human activities in indoor environments. Electromagnetic wave propagation through walls introduces refraction, attenuation, multipath, and…

Conditional estimation given specific covariate values (i.e., local conditional estimation or functional estimation) is ubiquitously useful with applications in engineering, social and natural sciences. Existing data-driven non-parametric…

This paper addresses the mode collapse for generative adversarial networks (GANs). We view modes as a geometric structure of data distribution in a metric space. Under this geometric lens, we embed subsamples of the dataset from an…

Generative adversarial networks (GANs) have been shown to provide an effective way to model complex distributions and have obtained impressive results on various challenging tasks. However, typical GANs require fully-observed data during…

Generative adversarial networks (GANs) are a family of generative models that do not minimize a single training criterion. Unlike other generative models, the data distribution is learned via a game between a generator (the generative…

We show that training of generative adversarial network (GAN) may not have good generalization properties; e.g., training may appear successful but the trained distribution may be far from target distribution in standard metrics. However,…

The Bayesian inference approach is widely used to tackle inverse problems due to its versatile and natural ability to handle ill-posedness. However, it often faces challenges when dealing with situations involving continuous fields or…

We present a deep learning model for data-driven simulations of random dynamical systems without a distributional assumption. The deep learning model consists of a recurrent neural network, which aims to learn the time marching structure,…

In recent years, Generative Adversarial Networks (GANs) have drawn a lot of attentions for learning the underlying distribution of data in various applications. Despite their wide applicability, training GANs is notoriously difficult. This…

This work presents the first statistical performance guarantees for group-invariant generative models. Many real data, such as images and molecules, are invariant to certain group symmetries, which can be taken advantage of to learn more…

One of the biggest challenges in the research of generative adversarial networks (GANs) is assessing the quality of generated samples and detecting various levels of mode collapse. In this work, we construct a novel measure of performance…

Generative adversarial networks (GANs) have given us a great tool to fit implicit generative models to data. Implicit distributions are ones we can sample from easily, and take derivatives of samples with respect to model parameters. These…

Nonparametric detection of existence of an anomalous structure over a network is investigated. Nodes corresponding to the anomalous structure (if one exists) receive samples generated by a distribution q, which is different from a…

We study the efficacy and efficiency of deep generative networks for approximating probability distributions. We prove that neural networks can transform a low-dimensional source distribution to a distribution that is arbitrarily close to a…

Distribution matching can be used to learn invariant representations with applications in fairness and robustness. Most prior works resort to adversarial matching methods but the resulting minimax problems are unstable and challenging to…

We propose a higher-level associative memory for learning adversarial networks. Generative adversarial network (GAN) framework has a discriminator and a generator network. The generator (G) maps white noise (z) to data samples while the…

Generative adversarial network (GAN) is a minimax game between a generator mimicking the true model and a discriminator distinguishing the samples produced by the generator from the real training samples. Given an unconstrained…

Generative Adversarial Networks (GANs), as a framework for estimating generative models via an adversarial process, have attracted huge attention and have proven to be powerful in a variety of tasks. However, training GANs is well known for…

For the sparse vector model, we consider estimation of the target vector, of its L2-norm and of the noise variance. We construct adaptive estimators and establish the optimal rates of adaptive estimation when adaptation is considered with…

Although current data augmentation methods are successful to alleviate the data insufficiency, conventional augmentation are primarily intra-domain while advanced generative adversarial networks (GANs) generate images remaining uncertain,…