Related papers: Noisy data clusters are hollow
3D dynamic point clouds provide a natural discrete representation of real-world objects or scenes in motion, with a wide range of applications in immersive telepresence, autonomous driving, surveillance, \etc. Nevertheless, dynamic point…
Reliability analysis aims at estimating the failure probability of an engineering system. It often requires multiple runs of a limit-state function, which usually relies on computationally intensive simulations. Traditionally, these…
High-dimensional data are ubiquitous, with examples ranging from natural images to scientific datasets, and often reside near low-dimensional manifolds. Leveraging this geometric structure is vital for downstream tasks, including signal…
In our experience of working with domain experts who are using today's AutoML systems, a common problem we encountered is what we call "unrealistic expectations" -- when users are facing a very challenging task with a noisy data acquisition…
Multidimensional scaling is an important dimension reduction tool in statistics and machine learning. Yet few theoretical results characterizing its statistical performance exist, not to mention any in high dimensions. By considering a…
A noise-based non-parametric technique for detecting nebulous objects, for example, irregular or clumpy galaxies, and their structure in noise is introduced. "Noise-based" and "non-parametric" imply that this technique imposes negligible…
We consider a situation where the distribution of a random variable is being estimated by the empirical distribution of noisy measurements of that variable. This is common practice in, for example, teacher value-added models and other…
Learning signed distance functions (SDFs) from 3D point clouds is an important task in 3D computer vision. However, without ground truth signed distances, point normals or clean point clouds, current methods still struggle from learning…
The Gaussian kernel and its traditional normalizations (e.g., row-stochastic) are popular approaches for assessing similarities between data points. Yet, they can be inaccurate under high-dimensional noise, especially if the noise magnitude…
Existing dimensionality reduction methods are adept at revealing hidden underlying manifolds arising from high-dimensional data and thereby producing a low-dimensional representation. However, the smoothness of the manifolds produced by…
This paper addresses the observability analysis and the optimal design of observation parameters in the presence of noisy measurements and parametric uncertainties. The main underlying frameworks are the nonlinear constrained moving horizon…
Distant and weak supervision allow to obtain large amounts of labeled training data quickly and cheaply, but these automatic annotations tend to contain a high amount of errors. A popular technique to overcome the negative effects of these…
The denoising process of diffusion models can be interpreted as an approximate projection of noisy samples onto the data manifold. Moreover, the noise level in these samples approximates their distance to the underlying manifold. Building…
We first exhibit a multimodal image registration task, for which a neural network trained on a dataset with noisy labels reaches almost perfect accuracy, far beyond noise variance. This surprising auto-denoising phenomenon can be explained…
Learning signed distance functions (SDFs) from point clouds is an important task in 3D computer vision. However, without ground truth signed distances, point normals or clean point clouds, current methods still struggle from learning SDFs…
It has been known for almost 30 years that quantum circuits with interspersed depolarizing noise converge to the uniform distribution at $\omega(\log n)$ depth, where $n$ is the number of qubits, making them classically simulable. We show…
Locating a target is key in many applications, namely in high-stakes real-world scenarios, like detecting humans or obstacles in vehicular networks. In scenarios where precise statistics of the measurement noise are unavailable,…
Understanding generalization in deep neural networks is an active area of research. A promising avenue of exploration has been that of margin measurements: the shortest distance to the decision boundary for a given sample or that sample's…
Reconstructing accurate implicit surface representations from point clouds remains a challenging task, particularly when data is captured using low-quality scanning devices. These point clouds often contain substantial noise, leading to…
Filaments are ubiquitous in astronomical data sets. Be it in particle simulations or observations, filaments are always tracers of a perturbation in the equilibrium of the studied system and hold essential information on its history and…