Related papers: Sobolev GAN

For a function $f$ from the Sobolev space $W^{1,p}(C)$ ($C\subset\mathbb{R}^d$ is an open convex cone), a sharp inequality that estimates $\| f\|_{L_{\infty}}$ via the $L_{p}$-norm of its gradient and a seminorm of the function is obtained.…

Gradient-regularized value learning methods improve sample efficiency by leveraging learned models of transition dynamics and rewards to estimate return gradients. However, existing approaches, such as MAGE, struggle in stochastic or noisy…

The vanilla GAN (Goodfellow et al. 2014) suffers from mode collapse deeply, which usually manifests as that the images generated by generators tend to have a high similarity amongst them, even though their corresponding latent vectors have…

The learning of domain-invariant representations in the context of domain adaptation with neural networks is considered. We propose a new regularization method that minimizes the discrepancy between domain-specific latent feature…

We introduce the Mutual Information Machine (MIM), a novel formulation of representation learning, using a joint distribution over the observations and latent state in an encoder/decoder framework. Our key principles are symmetry and mutual…

We present an extension of the Kolmogorov-Smirnov (KS) two-sample test, which can be more sensitive to differences in the tails. Our test statistic is an integral probability metric (IPM) defined over a higher-order total variation ball,…

In this work, we explore the theoretical properties of conditional deep generative models under the statistical framework of distribution regression where the response variable lies in a high-dimensional ambient space but concentrates…

This paper studies the convergence of the estimation error process and the characterization of the corresponding invariant measure in distributed Kalman filtering for potentially unstable and large linear dynamic systems. A gossip network…

We construct a family of non-parametric (infinite-dimensional) manifolds of finite measures on $R^d$. The manifolds are modelled on a variety of weighted Sobolev spaces, including Hilbert-Sobolev spaces and mixed-norm spaces. Each supports…

Despite the frequent use of agent-based models (ABMs) for studying social phenomena, parameter estimation remains a challenge, often relying on costly simulation-based heuristics. This work uses variational inference to estimate the…

Let $\M$ be a smooth connected manifold endowed with a smooth measure $\mu$ and a smooth locally subelliptic diffusion operator $L$ which is symmetric with respect to $\mu$. We assume that $L$ satisfies a generalized curvature dimension…

Calibration refers to the statistical estimation of unknown model parameters in computer experiments, such that computer experiments can match underlying physical systems. This work develops a new calibration method for imperfect computer…

Identifying low-dimensional structure in high-dimensional probability measures is an essential pre-processing step for efficient sampling. We introduce a method for identifying and approximating a target measure $\pi$ as a perturbation of a…

This paper introduces a comprehensive framework for complex-valued probability measures and explores their novel applications in information theory and statistical analysis. We define a complex probability measure as a phase-modulated…

This article gives a new insight of kernel-based (approximation) methods to solve the high-dimensional stochastic partial differential equations. We will combine the techniques of meshfree approximation and kriging interpolation to extend…

Convex combinations of i.i.d. random variables without a finite mean can behave in a strikingly different way from the finite-mean case: as the weight vector becomes more balanced, the resulting combination may become stochastically larger,…

Current deep learning classifiers, carry out supervised learning and store class discriminatory information in a set of shared network weights. These weights cannot be easily altered to incrementally learn additional classes, since the…

Detection limits (DLs), where a variable is unable to be measured outside of a certain range, are common in research. Most approaches to handle DLs in the response variable implicitly make parametric assumptions on the distribution of data…

Generative Adversarial Networks (GANs) are modern methods to learn the underlying distribution of a data set. GANs have been widely used in sample synthesis, de-noising, domain transfer, etc. GANs, however, are designed in a model-free…

For general ferromagnetic Ising models whose coupling matrix has bounded spectral radius, we show that the log-Sobolev constant satisfies a simple bound expressed only in terms of the susceptibility of the model. This bound implies very…