Related papers: Convolutional Maximum Mean Discrepancy for Inferen…

Understanding the role of turbulence in shaping the interstellar medium (ISM) is crucial for studying star formation, molecular cloud evolution, and cosmic ray propagation. Central to this is the measurement of the sonic Mach number…

In this paper, we consider a partial deconvolution kernel estimator for nonparametric regression when some covariates are measured with error while others are observed without error. We focus on a general and realistic setting in which the…

Efficient simulation of stochastic partial differential equations (SPDE) on general domains requires noise discretization. This paper employs piecewise linear interpolation of noise in a fully discrete finite element approximation of a…

Brain disorders are a major challenge to global health, causing millions of deaths each year. Accurate diagnosis of these diseases relies heavily on advanced medical imaging techniques such as Magnetic Resonance Imaging (MRI) and Computed…

Several researchers have proposed minimisation of maximum mean discrepancy (MMD) as a method to quantise probability measures, i.e., to approximate a target distribution by a representative point set. We consider sequential algorithms that…

We consider high-dimensional measurement errors with high-frequency data. Our objective is on recovering the high-dimensional cross-sectional covariance matrix of the random errors with optimality. In this problem, not all components of the…

Large-scale nonsmooth optimization problems arise in many real-world applications, but obtaining exact function and subgradient values for these problems may be computationally expensive or even infeasible. In many practical settings, only…

The ongoing technological revolution in measurement systems enables the acquisition of high-resolution samples in fields such as engineering, biology, and medicine. However, these observations are often subject to errors from measurement…

We propose Comprehensive Robust Dynamic Mode Decomposition (CR-DMD), a novel framework that robustifies the entire DMD process - from mode extraction to dimensional reduction - against mixed noise. Although standard DMD widely used for…

We introduce the concept of compressed convolution, a technique to convolve a given data set with a large number of non-orthogonal kernels. In typical applications our technique drastically reduces the effective number of computations. The…

We study inference on a low-dimensional functional $\beta$ in the presence of infinite-dimensional nuisance parameters. Classical inferential methods are typically based on Wald intervals, whose large-sample validity rests on asymptotic…

Noisy matrix completion aims at estimating a low-rank matrix given only partial and corrupted entries. Despite substantial progress in designing efficient estimation algorithms, it remains largely unclear how to assess the uncertainty of…

Bias evaluation is fundamental to trustworthy AI, both in terms of checking data quality and in terms of checking the outputs of AI systems. In testing data quality, for example, one may study the distance of a given dataset, viewed as a…

Despite the remarkable success, recent reconstruction-based anomaly detection (AD) methods via diffusion modeling still involve fine-grained noise-strength tuning and computationally expensive multi-step denoising, leading to a fundamental…

This work is focussed on the inversion task of inferring the distribution over parameters of interest leading to multiple sets of observations. The potential to solve such distributional inversion problems is driven by increasing…

Bearing fault diagnosis under varying working conditions faces challenges, including a lack of labeled data, distribution discrepancies, and resource constraints. To address these issues, we propose a progressive knowledge distillation…

We propose Sobolev-regularized Maximum Mean Discrepancy (SrMMD) gradient flow, a regularized variant of maximum mean discrepancy (MMD) gradient flow based on a gradient penalty on the witness function. The proposed regularization mitigates…

Noise Contrastive Estimation (NCE) has fueled major breakthroughs in representation learning and generative modeling. Yet a long-standing challenge remains: accurately estimating ratios between distributions that differ substantially, which…

Learning the true density in high-dimensional feature spaces is a well-known problem in machine learning. In this work, we consider generative autoencoders based on maximum-mean discrepancy (MMD) and provide theoretical insights. In…

Kernel mean embeddings are a popular tool that consists in representing probability measures by their infinite-dimensional mean embeddings in a reproducing kernel Hilbert space. When the kernel is characteristic, mean embeddings can be used…