Related papers: Noisy data clusters are hollow
Deep neural networks (DNNs) are powerful tools in computer vision tasks. However, in many realistic scenarios label noise is prevalent in the training images, and overfitting to these noisy labels can significantly harm the generalization…
Information-theoretic definitions for the noise associated with a quantum measurement and the corresponding disturbance to the state of the system have recently been introduced [F. Buscemi et al., Phys. Rev. Lett. 112, 050401 (2014)]. These…
This paper begins with a description of methods for estimating image probability density functions that reflects the observation that such data is usually constrained to lie in restricted regions of the high-dimensional image space-not…
Gravitational lensing is potentially able to observe mass-selected halos, and to measure the projected cluster mass function. An optimal mass-selection requires a quantitative understanding of the noise behavior in mass maps. This paper is…
Deep neural networks have incredible capacity and expressibility, and can seemingly memorize any training set. This introduces a problem when training in the presence of noisy labels, as the noisy examples cannot be distinguished from clean…
Quantum noise in a model of singly resonant frequency doubling including phase mismatch and driving in the harmonic mode is analyzed. The general formulae about the fixed points and their stability as well as the squeezing spectra…
In an idealistic setting, quantum metrology protocols allow to sense physical parameters with mean squared error that scales as $1/N^2$ with the number of particles involved---substantially surpassing the $1/N$-scaling characteristic to…
Randomized experiments are the gold standard for evaluating the effects of changes to real-world systems. Data in these tests may be difficult to collect and outcomes may have high variance, resulting in potentially large measurement error.…
Given the significance of physical measures in understanding the complexity of dynamical systems as well as the noisy nature of real-world systems, investigating the stability of physical measures under noise perturbations is undoubtedly a…
A novel elastic time distance for sparse multivariate functional data is proposed and used to develop a robust distance-based two-layer partition clustering method. With this proposed distance, the new approach not only can detect correct…
In this paper, we extend our research concerning the standard and linearized monotonicity methods for the inverse problem of the time harmonic elastic wave equation and introduce the modification of these methods for noisy data. In more…
Often, high dimensional data lie close to a low-dimensional submanifold and it is of interest to understand the geometry of these submanifolds. The homology groups of a manifold are important topological invariants that provide an algebraic…
While classical data analysis has addressed observations that are real numbers or elements of a real vector space, at present many statistical problems of high interest in the sciences address the analysis of data that consist of more…
This paper studies distributed estimation and support recovery for high-dimensional linear regression model with heavy-tailed noise. To deal with heavy-tailed noise whose variance can be infinite, we adopt the quantile regression loss…
In point clouds, noise directly perturbs point coordinates that encode both spatial location and geometry, making one-to-one correspondence construction more challenging than in images. Existing methods impose statistical mappings across…
In this paper, we consider a novel machine learning problem, that is, learning a classifier from noisy label distributions. In this problem, each instance with a feature vector belongs to at least one group. Then, instead of the true label…
We adapt previous research on category theory and topological unsupervised learning to develop a functorial perspective on manifold learning, also known as nonlinear dimensionality reduction. We first characterize manifold learning…
We study the recovery of geometric structure from data generated by convolving the uniform measure on a smooth compact submanifold $M\subset\mathbb{R}^D$ with ambient Gaussian noise. Our main result is that several fundamental Riemannian…
We study the problem of aggregation noisy labels. Usually, it is solved by proposing a stochastic model for the process of generating noisy labels and then estimating the model parameters using the observed noisy labels. A traditional…
We consider a high-dimensional mixture of two Gaussians in the noisy regime where even an oracle knowing the centers of the clusters misclassifies a small but finite fraction of the points. We provide a rigorous analysis of the…