New algorithm finds k-centers from noisy distance estimates.
problem Finding k-centers in unknown metric spaces with noisy distance queries.
method Active algorithms using UCB, Thompson Sampling, and Track-and-Stop.
result Approximation ratio of two with high probability.
New method recovers manifold distances from noisy data.
problem Reconstructing manifold geometry from noisy distance measurements.
method Develops new framework to estimate L2-norms of expectation-functions, uses geometric clusters to recover distances.
result Recovery of true distances up to an additive error of O(ε log ε⁻¹) under mild geometric assumptions.
DDPMs are robust to noisy score estimates and achieve optimal convergence rates in Wasserstein-2 distance.
problem Evaluating the quality of DDPMs in Wasserstein distance with noisy score estimates.
method Established finite-sample guarantees in Wasserstein-2 distance for DDPMs, considering noisy score estimates.
result Optimal convergence rates in Wasserstein-2 distance for DDPMs, matching Gaussian case.
The paper sets sample complexity bounds for learning high-dimensional simplices in noisy data.
problem Learning high-dimensional simplices from noisy data.
method Sample compression techniques and Fourier-based method for noisy observations.
result Established sample complexity bounds for simplex learning in noisy regimes.
New method beats volumetric barrier for manifold recovery.
problem Reconstructing latent geometry from noisy distances.
method Orthogonal Ring Distance Estimation Routine (ORDER).
result Achieves pointwise distance estimation of order n−2/(d+5). New ABC method improves Bézier simplex fitting for noisy data.
problem Overfitting in Bézier simplex fitting when sample points are not on the Pareto set.
method Extended Bézier simplex model to a probabilistic one and proposed a new learning algorithm based on approximate Bayesian computation (ABC) with Wasserstein distance.
result The new algorithm converges on a finite sample and outperforms deterministic methods on noisy instances.
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 problem the Riemannian manifold (M,g) is considered as an abstract metric space w…
We consider the problem of learning the nearest neighbor graph of a dataset of n items. The metric is unknown, but we can query an oracle to obtain a noisy estimate of the distance between any pair of items. This framework applies to problem domains where one wants to learn people's preferences from responses commonly …
Adaptive sampling theory has shown that, with proper assumptions on the signal class, algorithms exist to reconstruct a signal in Rd with an optimal number of samples. We generalize this problem to the case of spatial signals, where the sampling cost is a function of both the number of samples taken and t…
Method counters noisy labels by discounting distant samples.
problem Training models with noisy labels in medical and autonomous domains.
method Discounting distant samples from class centroids in latent space.
result Significant improvements in classification accuracy.
Paper finds sample complexity for learning high-dimensional simplices from noisy data.
problem Learning high-dimensional simplices from noisy samples.
method Combines sample compression, high-dimensional geometry, and Fourier analysis.
result Proves sample complexity bound for achieving a simplex within a certain distance from the true simplex.
A new robust metric compares distributions more accurately than existing methods.
problem Sensitivity to outliers and sampling discrepancy in Wasserstein distances.
method Introducing k-RPW, a partial p-Wasserstein distance.
result k-RPW converges faster to true distance and is more robust to outliers.
Classical multidimensional scaling is an important dimension reduction technique. Yet few theoretical results characterizing its statistical performance exist. This paper provides a theoretical framework for analyzing the quality of embedded samples produced by classical multidimensional scaling. This lays the foundati…
Proposes a method to compare noisy high-dimensional datasets with low-dimensional manifolds.
problem Comparing distributions on manifolds in noisy high-dimensional datasets.
method Linking low-rank structure to manifold geometry, developing a scale-invariant distance measure.
result Superior robustness and statistical power compared to existing methods.
Discretizations of Langevin diffusions provide a powerful method for sampling and Bayesian inference. However, such discretizations require evaluation of the gradient of the potential function. In several real-world scenarios, obtaining gradient evaluations might either be computationally expensive, or simply impossibl…
LARA forecasts financial asset trends by refining noisy labels and extracting profitable samples.
problem Low signal-to-noise ratio and stochastic nature of financial data lead to poor predictions.
method LARA combines LA-Attention and RA-Labeling to refine and extract profitable samples.
result LARA significantly outperforms existing methods on Qlib platform.
We study the problem of learning conditional generators from noisy labeled samples, where the labels are corrupted by random noise. A standard training of conditional GANs will not only produce samples with wrong labels, but also generate poor quality samples. We consider two scenarios, depending on whether the noise m…
The paper quantizes concatenated noisy vectors to a common cluster center, improving performance over naive methods.
problem Clustering concatenated noisy vectors from multiple sources.
method Asymptotic analysis of weighted sum of distances to a common cluster center.
result The clustering approach outperforms naive methods in terms of average distortion.
Understanding and developing a correlation measure that can detect general dependencies is not only imperative to statistics and machine learning, but also crucial to general scientific discovery in the big data age. In this paper, we establish a new framework that generalizes distance correlation --- a correlation mea…
We generalize Mallows model to learn distance metrics from data.
problem Learning optimal distance metrics from noisy ranking data.
method Propose Lα distances and develop FPTAS for sampling and MLE. result Strong consistency of estimators for various α and β. New metric compares noisy neural trajectories using optimal transport.
problem Existing metrics fail to capture differences in noisy, dynamic neural responses.
method Proposed an optimal transport distance metric for Gaussian processes.
result Metric effectively compares neural dynamics in different systems.
We find the minimax rate of convergence in Hausdorff distance for estimating a manifold M of dimension d embedded in R^D given a noisy sample from the manifold. We assume that the manifold satisfies a smoothness condition and that the noise distribution has compact support. We show that the optimal rate of convergence …
Unified meta algorithms estimate various distribution functionals in infinite-armed bandits.
problem Estimating various distribution functionals in infinite-armed bandits.
method Unified meta algorithms for offline and online settings, achieving optimal sample complexities.
result Online estimation offers significant advantage for certain distribution functionals.
Optimizes noisy IS with better proposal densities.
problem Improving IS estimators with noisy data.
method Derives optimal proposal densities considering noise variance.
result Optimal proposals enhance IS estimators by focusing on noisy regions.
Often noisy point clouds are given as an approximation of a particular compact set of interest. A finite point cloud is a compact set. This paper proves a reconstruction theorem which gives a sufficient condition, as a bound on the Hausdorff distance between two compact sets, for when certain offsets of these two sets …
We demonstrate an algorithm for learning a flexible color-magnitude diagram from noisy parallax and photometry measurements using a normalizing flow, a deep neural network capable of learning an arbitrary multi-dimensional probability distribution. We present a catalog of 640M photometric distance posteriors to nearby …
Noisy labels often occur in vision datasets, especially when they are obtained from crowdsourcing or Web scraping. We propose a new regularization method, which enables learning robust classifiers in presence of noisy data. To achieve this goal, we propose a new adversarial regularization scheme based on the Wasserstei…
DW-KNN improves KNN by integrating distance and neighbor reliability for better prediction accuracy.
problem Standard KNN assumes all neighbors are equally reliable, leading to unreliable predictions in heterogeneous feature spaces.
method DW-KNN integrates exponential distance with neighbor validity, providing instance-level interpretability and reducing hyperparameter sensitivity.
result DW-KNN achieves 0.8988 average accuracy, ranks 2nd among six methods, and has the lowest cross-validation variance.
Diffusion models tackle noisy inverse problems with posterior sampling.
problem Efficiently solving general noisy inverse problems.
method Approximation of posterior sampling for diffusion models.
result Diffusion models can handle various noise statistics and nonlinear problems.
Motivation: Public and private repositories of experimental data are growing to sizes that require dedicated methods for finding relevant data. To improve on the state of the art of keyword searches from annotations, methods for content-based retrieval have been proposed. In the context of gene expression experiments, …
Noisy labels are ubiquitous in real-world datasets, which poses a challenge for robustly training deep neural networks (DNNs) since DNNs can easily overfit to the noisy labels. Most recent efforts have been devoted to defending noisy labels by discarding noisy samples from the training set or assigning weights to train…
A new method selects clean samples to train DNNs with noisy labels.
problem Training deep neural networks with noisy labeled data.
method Adaptive k-set selection to choose clean samples at each epoch.
result The method guarantees performance with a theoretical bound on regret.
Study shows exponential gap in sample complexity between noisy and non-noisy recurrent neural networks.
problem Understanding the impact of noise on the sample complexity of recurrent neural networks.
method Analyzing noisy multi-layered sigmoid recurrent neural networks with independent noise and proving lower bounds.
result Exponential gap in sample complexity between noisy and non-noisy networks, even for small noise values.
New method improves sampling from noisy energy models.
problem Training and sampling challenges in Energy-Based Models.
method Pseudo-Gibbs sampling with moment matching.
result Effective sampling from clean model using noisy DSM-trained model.
Algorithm identifies nearest mode in noisy data.
problem Identifying the point with the minimum k-th nearest neighbor distance in unknown multivariate probability density.
method Sequential learning algorithm using noisy oracle queries to adaptively decide which points to query.
result Upper bounds on query complexity show significant improvement over baselines.
Improved reSGLD accelerates convergence in non-convex learning problems.
problem Inefficient swaps due to noisy energy estimators in reSGLD.
method Variance reduction for noisy energy estimators, theoretical analysis, and numerical experiments.
result Exponential acceleration in convergence for non-convex learning problems.
Estimates TV distance between autoregressive models under different access models.
problem Estimating the total variation distance between two autoregressive distributions.
method Three access models: sample access, logit access, and noisy logit access; provides query complexity for each.
result Improved query complexity for estimating TV distance in autoregressive models.
Smoothly recovers manifold from noisy data.
problem Recovering a manifold from noisy data points.
method Fits a Ck-smooth function to noisy samples. result Hausdorff distance between recovered manifold and original manifold is at most ε.
Learn ODEs from noisy data using RKHS and optimization.
problem Learning nonparametric ODEs from noisy data.
method Using RKHS theory, solve a constrained optimization problem iteratively with penalty methods and Euler approximations.
result Prove a generalization bound for L2 distance between true and estimated solutions.
The paper analyzes how noise affects distances in high-dimensional data and when they remain useful.
problem Noise corrupts distances in high-dimensional data, making them unreliable for identifying true nearest and farthest neighbors.
method The paper uses asymptotic probabilistic expressions to characterize noise effects and decomposes data into ground truth and noise components.
result Under certain conditions, empirical neighborhood relations remain truthful even when distance concentration occurs.
Paper tackles noisy comparison oracle for robust clustering algorithms.
problem Finding robust clustering algorithms under noisy comparison oracle.
method Develops algorithms for k-center clustering and agglomerative hierarchical clustering using noisy comparison oracle.
result Proves robust algorithms achieve good approximation guarantees with high probability.
This work incorporates topological features via persistence diagrams to classify point cloud data arising from materials science. Persistence diagrams are multisets summarizing the connectedness and holes of given data. A new distance on the space of persistence diagrams generates relevant input features for a classifi…
Clustering is one of the major roles in data mining that is widely application in pattern recognition and image segmentation. Fuzzy C-means (FCM) is the most used clustering algorithm that proven efficient, fast and easy to implement, however, FCM uses the Euclidean distance that often leads to clustering errors, espec…
Model learns metrics and preferences from user comparisons.
problem Simultaneous metric and preference learning from user comparisons.
method Jointly learns a metric and latent ideal points for each user.
result Model captures individual preferences and learns metrics efficiently.
Study efficient graph optimization with noisy data.
problem Optimizing functions on graphs with noisy observations.
method Best-arm identification and simulated annealing variants.
result Near-optimal solutions found with small query numbers.
SelectMix improves deep learning robustness against noisy labels.
problem Deep neural networks memorize noisy labels, degrading performance.
method Confidence-guided targeted sample mixing with soft labels.
result SelectMix consistently outperforms baseline methods on noisy label datasets.
Classical multidimensional scaling only works well when the noisy distances observed in a high dimensional space can be faithfully represented by Euclidean distances in a low dimensional space. Advanced models such as Maximum Variance Unfolding (MVU) and Minimum Volume Embedding (MVE) use Semi-Definite Programming (SDP…
Noise-corrected Langevin algorithm improves sampling from noisy data.
problem Sampling from noisy data with biased score function.
method Noise-corrected Langevin algorithm using noisy score function.
result Bias due to noisy data is removed, improving sampling accuracy.