Related papers: SVD Provably Denoises Nearest Neighbor Data

Fixed-radius near neighbor search is a fundamental data operation that retrieves all data points within a user-specified distance to a query point. There are efficient algorithms that can provide fast approximate query responses, but they…

The $k$-Nearest Neighbor Search ($k$-NNS) is the backbone of several cloud-based services such as recommender systems, face recognition, and database search on text and images. In these services, the client sends the query to the cloud…

Clustering-based Approximate Nearest Neighbor Search (ANNS) organizes a set of points into partitions, and searches only a few of them to find the nearest neighbors of a query. Despite its popularity, there are virtually no analytical tools…

Significant progress has been made in self-supervised image denoising (SSID) in the recent few years. However, most methods focus on dealing with spatially independent noise, and they have little practicality on real-world sRGB images with…

We consider stochastic approximation for the least squares regression problem in the non-strongly convex setting. We present the first practical algorithm that achieves the optimal prediction error rates in terms of dependence on the noise…

This paper considers the problem of recovering the permutation of an n-dimensional random vector X observed in Gaussian noise. First, a general expression for the probability of error is derived when a linear decoder (i.e., linear estimator…

Consider a dataset of n(d) points generated independently from R^d according to a common p.d.f. f_d with support(f_d) = [0,1]^d and sup{f_d([0,1]^d)} growing sub-exponentially in d. We prove that: (i) if n(d) grows sub-exponentially in d,…

In the last few years, with the rapid development of deep learning technologies, supervised methods based on convolutional neural networks have greatly enhanced the performance of medical image denoising. However, these methods require…

We study the problem of training a two-layer neural network (NN) of arbitrary width using stochastic gradient descent (SGD) where the input $\boldsymbol{x}\in \mathbb{R}^d$ is Gaussian and the target $y \in \mathbb{R}$ follows a…

We investigate the problem of finding reverse nearest neighbors efficiently. Although provably good solutions exist for this problem in low or fixed dimensions, to this date the methods proposed in high dimensions are mostly heuristic. We…

In real-world applications, anomaly detection (AD) often operates without access to anomalous data, necessitating semi-supervised methods that rely solely on normal data. Among these methods, deep k-nearest neighbor (deep kNN) AD stands out…

Nearest neighbor search (NNS) aims to locate the points in high-dimensional space that is closest to the query point. The brute-force approach for finding the nearest neighbor becomes computationally infeasible when the number of points is…

This paper investigates the recovery of a spectrally sparse signal from its partially revealed noisy entries within the framework of spectral compressive sensing. Nonconvex optimization approaches have recently been proposed based on…

Nearest neighbor search (NNS) has a wide range of applications in information retrieval, computer vision, machine learning, databases, and other areas. Existing state-of-the-art algorithm for nearest neighbor search, Hierarchical Navigable…

We consider the problem of clustering noisy finite-length observations of stationary ergodic random processes according to their generative models without prior knowledge of the model statistics and the number of generative models. Two…

We develop a data-driven approach for signal denoising that utilizes variational mode decomposition (VMD) algorithm and Cramer Von Misses (CVM) statistic. In comparison with the classical empirical mode decomposition (EMD), VMD enjoys…

We develop an efficient and robust high-dimensional sparse Fourier algorithm for noisy samples. Earlier in the paper ``Multi-dimensional sublinear sparse Fourier algorithm" (2016), an efficient sparse Fourier algorithm with $\Theta(ds \log…

Deep neural networks (DNNs) have achieved remarkable success in a variety of computer vision tasks, where massive labeled images are routinely required for model optimization. Yet, the data collected from the open world are unavoidably…

The ultimate aim of image restoration like denoising is to find an exact correlation between the noisy and clear image domains. But the optimization of end-to-end denoising learning like pixel-wise losses is performed in a sample-to-sample…

Semi-supervised classification, where unlabeled data are massive but labeled data are limited, often arises in machine learning applications. We address this challenge under high-dimensional data by leveraging the manifold and cluster…