Related papers: Local Averaging Accurately Distills Manifold Struc…

We study nonparametric regression under covariate shift with structured data, where a small amount of labeled target data is supplemented by a large labeled source dataset. In many real-world settings, the covariates in the target domain…

Background noise in many fields such as medical imaging poses significant challenges for accurate diagnosis, prompting the development of denoising algorithms. Traditional methodologies, however, often struggle to address the complexities…

We consider reconstruction of a manifold, or, invariant manifold learning, where a smooth Riemannian manifold $M$ is determined from intrinsic distances (that is, geodesic distances) of points in a discrete subset of $M$. In the studied…

Manifold learning and dimensionality reduction techniques are ubiquitous in science and engineering, but can be computationally expensive procedures when applied to large data sets or when similarities are expensive to compute. To date,…

Unsupervised fault detection in multivariate time series plays a vital role in ensuring the stable operation of complex systems. Traditional methods often assume that normal data follow a single Gaussian distribution and identify anomalies…

This paper proposes a novel method for automatic MRI denoising that exploits last advances in deep learning feature regression and self-similarity properties of the MR images. The proposed method is a two-stage approach. In the first stage,…

The problem of network-constrained averaging is to compute the average of a set of values distributed throughout a graph G using an algorithm that can pass messages only along graph edges. We study this problem in the noisy setting, in…

Measurement correlations in quantum systems can exhibit non-local behavior, a fundamental aspect of quantum mechanics with applications such as device-independent quantum information processing. However, the explicit construction of local…

We consider minimizing a smooth and strongly convex objective function using a stochastic Newton method. At each iteration, the algorithm is given an oracle access to a stochastic estimate of the Hessian matrix. The oracle model includes…

Knowledge of the noise distribution in diffusion MRI is the centerpiece to quantify uncertainties arising from the acquisition process. Accurate estimation beyond textbook distributions often requires information about the acquisition…

Combining information both within and across trajectories, we propose a simple estimator for the local regularity of the trajectories of a stochastic process. Independent trajectories are measured with errors at randomly sampled time…

We introduce a method called multi-scale local shape analysis, or MLSA, for extracting features that describe the local structure of points within a dataset. The method uses both geometric and topological features at multiple levels of…

Accurate noise modelling is important for training of deep learning reconstruction algorithms. While noise models are well known for traditional imaging techniques, the noise distribution of a novel sensor may be difficult to determine a…

We present methods and results of shot-by-shot correlation of noisy measurements to extract entangled state and process tomography in a superconducting qubit architecture. We show that averaging continuous values, rather than counting…

We study the estimation of the reach, an ubiquitous regularity parameter in manifold estimation and geometric data analysis. Given an i.i.d. sample over an unknown $d$-dimensional $\mathcal{C}^k$-smooth submanifold of $\mathbb{R}^D$, we…

This paper presents a novel machine-learning framework for reconstructing low-order gust-encounter flow field and lift coefficients from sparse, noisy surface pressure measurements. Our study thoroughly investigates the time-varying…

We consider a problem of great practical interest: the repairing and recovery of a low-dimensional manifold embedded in high-dimensional space from noisy scattered data. Suppose that we observe a point cloud sampled from the low-dimensional…

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…

A generative modeling framework is proposed that combines diffusion models and manifold learning to efficiently sample data densities on manifolds. The approach utilizes Diffusion Maps to uncover possible low-dimensional underlying (latent)…

Complete characterization of a noisy multipartite quantum state in terms of entanglement requires full knowledge of how the entanglement content in the state is affected by the spatial distribution of noise in the state. Specifically, we…