Related papers: Local Averaging Accurately Distills Manifold Struc…

Analyzing large volumes of high-dimensional data requires dimensionality reduction: finding meaningful low-dimensional structures hidden in their high-dimensional observations. Such practice is needed in atomistic simulations of complex…

Quantum metrology promises precision beyond classical limits, yet environmental noise typically degrades the quantum resources required for such enhancement. In this work, we investigate frequency estimation in noisy continuous-variable…

Neuronal activity is found to lie on low-dimensional manifolds embedded within the high-dimensional neuron space. Variants of principal component analysis are frequently employed to assess these manifolds. These methods are, however,…

This paper develops a new mathematical framework for denoising in blind two-dimensional (2D) super-resolution upon using the atomic norm. The framework denoises a signal that consists of a weighted sum of an unknown number of time-delayed…

This paper establishes a nearly optimal algorithm for estimating the frequencies and amplitudes of a mixture of sinusoids from noisy equispaced samples. We derive our algorithm by viewing line spectral estimation as a sparse recovery…

Spatially localized deformation components are very useful for shape analysis and synthesis in 3D geometry processing. Several methods have recently been developed, with an aim to extract intuitive and interpretable deformation components.…

In the field of medical image analysis, deep learning models have demonstrated remarkable success in enhancing diagnostic accuracy and efficiency. However, the reliability of these models is heavily dependent on the quality of training…

Most existing image denoising algorithms can only deal with a single type of noise, which violates the fact that the noisy observed images in practice are often suffered from more than one type of noise during the process of acquisition and…

Noise is a part of data whether the data is from measurement, experiment or ... A few techniques are suggested for noise reduction to improve the data quality in recent years some of which are based on wavelet, orthogonalization and neural…

We present and analyze an algorithm for estimating the size, under a Gaussian or uniform measure, of a localized neighborhood in neural network parameter space with behavior similar to an ``anchor'' point. We refer to this as the "local…

We study the problem of learning general (i.e., not necessarily homogeneous) halfspaces with Random Classification Noise under the Gaussian distribution. We establish nearly-matching algorithmic and Statistical Query (SQ) lower bound…

Many applications have benefited remarkably from low-dimensional models in the recent decade. The fact that many signals, though high dimensional, are intrinsically low dimensional has given the possibility to recover them stably from a…

This paper studies the classical problem of detecting the locations of signal occurrences in a one-dimensional noisy measurement. Assuming the signal occurrences do not overlap, we formulate the detection task as a constrained likelihood…

In this paper, we find a sample complexity bound for learning a simplex from noisy samples. Assume a dataset of size $n$ is given which includes i.i.d. samples drawn from a uniform distribution over an unknown simplex in $\mathbb{R}^K$,…

We present a framework for learning probability distributions on topologically non-trivial manifolds, utilizing normalizing flows. Current methods focus on manifolds that are homeomorphic to Euclidean space, enforce strong structural priors…

We investigate the inference of varifold structures in a statistical framework: assuming that we have access to i.i.d. samples in $\mathbb{R}^n$ obtained from an underlying $d$--dimensional shape $S$ endowed with a possibly non uniform…

Compressive Sensing (CS) exploits the surprising fact that the information contained in a sparse signal can be preserved in a small number of compressive, often random linear measurements of that signal. Strong theoretical guarantees have…

While it is common practice in applied network analysis to report various standard network summary statistics, these numbers are rarely accompanied by uncertainty quantification. Yet any error inherent in the measurements underlying the…

Timely detection of abrupt anomalies is crucial for real-time monitoring and security of modern systems producing high-dimensional data. With this goal, we propose effective and scalable algorithms. Proposed algorithms are nonparametric as…

Recently, Hyperspectral Image (HSI) classification has attracted increasing attention in remote sensing. However, HSI data are inherently high-dimensional but low-rank, with discriminative information concentrated on a low-dimensional…