Related papers: Noisy data clusters are hollow

We introduce a new approach for estimating the invariant density of a multidimensional diffusion when dealing with high-frequency observations blurred by independent noises. We consider the intermediate regime, where observations occur at…

Point cloud segmentation is a fundamental task in 3D. Despite recent progress on point cloud segmentation with the power of deep networks, current deep learning methods based on the clean label assumptions may fail with noisy labels. Yet,…

Dimensionless learning is a data-driven framework for discovering dimensionless numbers and scaling laws from experimental measurements. This tutorial introduces the method, explaining how it transforms experimental data into compact…

3D point clouds are often perturbed by noise due to the inherent limitation of acquisition equipments, which obstructs downstream tasks such as surface reconstruction, rendering and so on. Previous works mostly infer the displacement of…

Diffusion condensation is a dynamic process that yields a sequence of multiscale data representations that aim to encode meaningful abstractions. It has proven effective for manifold learning, denoising, clustering, and visualization of…

Analyzing large volumes of high-dimensional data is an issue of fundamental importance in data science, molecular simulations and beyond. Several approaches work on the assumption that the important content of a dataset belongs to a…

[Abridged] We present a novel technique, dubbed FiEstAS, to estimate the underlying density field from a discrete set of sample points in an arbitrary multidimensional space. FiEstAS assigns a volume to each point by means of a binary tree.…

Many measurement modalities which perform imaging by probing an object pixel-by-pixel, such as via Photoacoustic Microscopy, produce a multi-dimensional feature (typically a time-domain signal) at each pixel. In principle, the many degrees…

Typical properties of computing circuits composed of noisy logical gates are studied using the statistical physics methodology. A growth model that gives rise to typical random Boolean functions is mapped onto a layered Ising spin system,…

Neural volume rendering became increasingly popular recently due to its success in synthesizing novel views of a scene from a sparse set of input images. So far, the geometry learned by neural volume rendering techniques was modeled using a…

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…

A geometric form of information theory allows for reasonable, i.e. probabilistic, evidence-ranking based, and generalized noise-level dependent, classifications of the crystallographic and quasicrystallographic symmetries in noisy digital…

Noisy labels are ubiquitous in real-world datasets, which poses a challenge for robustly training deep neural networks (DNNs) as DNNs usually have the high capacity to memorize the noisy labels. In this paper, we find that the test accuracy…

Consider a target moving at a constant velocity on a unit-circumference circle, starting at an arbitrary location. To acquire the target, any region of the circle can be probed to obtain a noisy measurement of the target's presence, where…

Score-based diffusion models are a highly effective method for generating samples from a distribution of images. We consider scenarios where the training data comes from a noisy version of the target distribution, and present an efficiently…

Modern machine learning increasingly leverages the insight that high-dimensional data often lie near low-dimensional, non-linear manifolds, an idea known as the manifold hypothesis. By explicitly modeling the geometric structure of data…

The Boltzmann-Shannon Index (BSI) for clustered continuous data is introduced as a normalized measure that captures the relationship between geometry-based and frequency-based probability distributions defined over the clusters. In essence,…

Resolving a linear combination of point sources from their band-limited Fourier data is a fundamental problem in imaging and signal processing. With the incomplete Fourier data and the inevitable noise in the measurement, there is a…

The manifold hypothesis, which assumes that data lies on or close to an unknown manifold of low intrinsic dimension, is a staple of modern machine learning research. However, recent work has shown that real-world data exhibits distinct…

We investigate statistical properties of a likelihood approach to nonparametric estimation of a singular distribution using deep generative models. More specifically, a deep generative model is used to model high-dimensional data that are…