A new clustering method improves recovery guarantees by re-embedding data.
problem Improving recovery guarantees in clustering algorithms.
method Chaining four techniques: leapfrog distances, multidimensional scaling, spectral methods, and sum-of-norms clustering.
result Re-embedding data improves recovery guarantees of clustering.
Method recovers particle orientations from cryo-EM projections.
problem Unknown orientations in cryo-EM images.
method Two-step process: estimating distances and recovering orientations.
result Accurate orientation recovery from noisy projections.
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). The paper tracks patient recovery using graphs of joint movement data.
problem Tracking individual patient recovery trajectories in physical therapy.
method Bayesian learning of Random Geometric Graphs from joint movement data.
result Optimal exercise routines can be recommended based on patient recovery data.
For a certain class of distributions, we prove that the linear programming relaxation of k-medoids clustering---a variant of k-means clustering where means are replaced by exemplars from within the dataset---distinguishes points drawn from nonoverlapping balls with high probability once the number of points drawn a…
Posterior sampling estimator achieves near-optimal recovery guarantees for signals from any prior distribution.
problem Characterizing measurement complexity for signals from any prior distribution, including the entire space.
method Characterization of measurement complexity using posterior sampling estimator for Gaussian measurements and any prior distribution.
result Posterior sampling estimator achieves near-optimal recovery guarantees for signals from any prior distribution, robust to model mismatch.
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.
The paper tackles subspace-preserving recovery of sparse signals from overcomplete dictionaries.
problem Recovering sparse signals from overcomplete dictionaries when the signal lies in a subspace of the dictionary.
method Geometric conditions and covering radius/angular distance to ensure subspace-preserving recovery.
result Theoretical analysis shows that subspace-preserving recovery is possible without requiring incoherence or restricted isometry of the dictionary.
The paper analyzes conditions for solving low-rank matrix recovery problems with noisy measurements.
problem Low-rank matrix recovery with corrupted measurements.
method Analysis of the restricted isometry property (RIP) and local search methods.
result Sharp bounds on the maximum distance between local minimizers and the ground truth.
APGD algorithm reconstructs point set from partial distance measurements.
problem Reconstructing point set configuration from partial Euclidean distance measurements.
method Asymmetric Projected Gradient Descent (APGD) for EDMC problem.
result Global convergence and exact recovery with O(μ2r3κ2nlogn) observations. We study the problem of corrupted sensing, a generalization of compressed sensing in which one aims to recover a signal from a collection of corrupted or unreliable measurements. While an arbitrary signal cannot be recovered in the face of arbitrary corruption, tractable recovery is possible when both signal and corrup…
Paper tackles robust Euclidean distance estimation with sparse outliers.
problem Estimating point positions from corrupted distance measurements.
method Proposes a novel algorithm using Nyström method and robust PCA.
result Achieves accurate recovery with minimal anchors and sparse outliers.
Algorithm finds a subspace minimizing distances to inliers with outliers.
problem Finding a k-dimensional subspace minimizing distances to inliers with outliers. method Extends dimension reduction techniques and bi-criteria approximations based on sampling.
result Efficient algorithm for multiplicative (1+ε)-approximation of optimal solution. The paper reduces normal curvature and enhances homology recovery via embedded submanifolds.
problem Recovering the homology of submanifolds with narrow cycles.
method Embedding submanifolds into scaled oriented Grassmannian bundles to reduce normal curvature and stabilize Čech persistent homology.
result The Čech persistent homology is stable with respect to the interleaving distance and provides lower bounds on scales for homology recovery.
Paper proposes a method to recover point configurations from noisy distance data.
problem Recovering point configurations from noisy distance data.
method Robust Euclidean Distance Geometry via Dual Basis (RoDEoDB) algorithm.
result Exact recovery guarantees for point configuration and Gram matrix under mild conditions.
Reinforcement learning mimics expert behavior.
problem Learning from expert demonstrations in reinforcement learning.
method Reduction to reinforcement learning with a stationary reward.
result Expert reward can be recovered and imitation learning is bounded.
We propose a neural network for unsupervised anomaly detection with a novel robust subspace recovery layer (RSR layer). This layer seeks to extract the underlying subspace from a latent representation of the given data and removes outliers that lie away from this subspace. It is used within an autoencoder. The encoder …
A fundamental question in data analysis, machine learning and signal processing is how to compare between data points. The choice of the distance metric is specifically challenging for high-dimensional data sets, where the problem of meaningfulness is more prominent (e.g. the Euclidean distance between images). In this…
New bounds for private matrix approximation using Gaussian noise and Dyson Brownian Motion.
problem Private approximation of symmetric matrices with Gaussian noise.
method Viewing Gaussian noise as Dyson Brownian Motion to track eigenvalue and eigenvector evolution.
result Improved bounds on Frobenius-distance utility for private matrix approximation.
This work improves distribution recovery from sparse data using Random Forest implicit regularization.
problem Distribution recovery from limited statistics.
method Closed-form estimator for scaled beta distributions, using composite quantile and moment matching.
result Improved classification accuracy through closed-form distribution recovery and implicit regularization.
We assume i.i.d. data sampled from a mixture distribution with K components along fixed d-dimensional linear subspaces and an additional outlier component. For p>0, we study the simultaneous recovery of the K fixed subspaces by minimizing the l_p-averaged distances of the sampled data points from any K subspaces. Under…
We assume data independently sampled from a mixture distribution on the unit ball of the D-dimensional Euclidean space with K+1 components: the first component is a uniform distribution on that ball representing outliers and the other K components are uniform distributions along K d-dimensional linear subspaces restric…
Iterative reweighted algorithms, as a class of algorithms for sparse signal recovery, have been found to have better performance than their non-reweighted counterparts. However, for solving the problem of multiple measurement vectors (MMVs), all the existing reweighted algorithms do not account for temporal correlation…
Revisits Isomap, showing it constructs Euclidean representations of geodesic structure.
problem Nonlinear dimension reduction of manifold data.
method Revisits Isomap's rationale, clarifying its approach to constructing Euclidean representations of geodesic structure.
result Convexity is not required for shortest path distances to converge to Riemannian distances.
Recover simple irreversible Finsler geometry from travel time data
problem Stable recovery of a simple irreversible Finsler geometry
method Use a Gromov-Hausdorff distance adapted to irreversible metric spaces
result Unique and Lipschitz-stable recovery
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…
Feature interactions can contribute to a large proportion of variation in many prediction models. In the era of big data, the coexistence of high dimensionality in both responses and covariates poses unprecedented challenges in identifying important interactions. In this paper, we suggest a two-stage interaction identi…
We study exact recovery conditions for convex relaxations of point cloud clustering problems, focusing on two of the most common optimization problems for unsupervised clustering: k-means and k-median clustering. Motivations for focusing on convex relaxations are: (a) they come with a certificate of optimality, and…
New clustering method recovers hidden tree structure from data.
problem Recovering hidden hierarchical structure in data.
method Maximum average dot product for merging clusters in hierarchical clustering.
result The algorithm produces a tree that accurately represents the underlying generative hierarchical structure.
Study uses data to analyze COPD patients' impact on hospital systems.
problem Understanding and quantifying resource requirements for COPD patients.
method Combines segmentation, queuing theory, and data recovery techniques.
result Finding useful operational results from incomplete administrative data.
For a compact Riemannian manifold with boundary, we want to find the metric structure from knowledge of distances between boundary points. This is called the "boundary rigidity problem". If the boundary is not concave, which means locally not all shortest paths lie entirely in the boundary, then we are able to find the…
Optimal algorithms learn Gaussian trees and polytrees from data.
problem Learning undirected Gaussian trees and polytrees from data.
method Two approaches: Chow-Liu algorithm for tree structure and modified PC algorithm for polytree structure.
result Explicit finite-sample guarantees and matching lower bounds for both approaches.
We introduce the {\it diffusion K-means} clustering method on Riemannian submanifolds, which maximizes the within-cluster connectedness based on the diffusion distance. The diffusion K-means constructs a random walk on the similarity graph with vertices as data points randomly sampled on the manifolds and edges as …
Holographic Invariant Storage uses vector architectures to ensure LLM safety at design time.
problem Mitigating context drift in large language models (LLMs) during deployment.
method Introduces Holographic Invariant Storage (HIS) protocol that combines known properties of bipolar Vector Symbolic Architectures into a design-time safety contract.
result Closed-form guarantees for single-signal recovery fidelity, continuous-noise robustness, and multi-signal capacity degradation are provided and validated.
This work presents a fast and non-convex algorithm for robust subspace recovery. The data sets considered include inliers drawn around a low-dimensional subspace of a higher dimensional ambient space, and a possibly large portion of outliers that do not lie nearby this subspace. The proposed algorithm, which we refer t…
Convex clustering is a recent stable alternative to hierarchical clustering. It formulates the recovery of progressively coalescing clusters as a regularized convex problem. While convex clustering was originally designed for handling Euclidean distances between data points, in a growing number of applications, the dat…
Algorithm learns affine transformations robustly from corrupted samples.
problem Learning affine transformations from corrupted samples.
method New geometric certificate and iterative improvement method.
result Total variation distance of O(ε) between learned and original distributions. Polynomial-time algorithm for estimating covariance in corrupted Gaussian data.
problem Estimating covariance in data with up to 1-α fraction of adversarial corruptions.
method Uses low-degree sum-of-squares certificates for anti-concentration and hypercontractivity.
result Outputs a list of candidate parameters with high probability containing a nearly correct covariance.
Hyperbolic embeddings offer excellent quality with few dimensions when embedding hierarchical data structures like synonym or type hierarchies. Given a tree, we give a combinatorial construction that embeds the tree in hyperbolic space with arbitrarily low distortion without using optimization. On WordNet, our combinat…
Enhances community detection in correlated networks with node attributes.
problem Community detection in multiple networks with correlated node attributes and edges.
method Introduced the correlated Contextual Stochastic Block Model (CSBM), developed a two-step matching procedure.
result Algorithm recovers exact node correspondence, enabling enhanced community detection.
A new Wasserstein K-means method for clustering probability distributions.
problem Clustering probability distributions using the Wasserstein metric.
method Distance-based K-means with SDP relaxation for Wasserstein barycenters. result Distance-based K-means outperforms centroid-based K-means for clustering probability distributions. We derive an arbitrage free relationship between recovery swap rates, digital default swap spreads and conventional CDS spreads, and argue that the fair forward recovery rate used in recovery swaps must contain a convexity premium over the expected recovery value.
Efficiently simulates and calibrates the rough Bergomi model using Wasserstein distance.
problem High computational complexity in pricing and calibration of the rough Bergomi model.
method Developed a modified-sum-of-exponentials Monte Carlo scheme and a calibration approach based on Wasserstein-1 distance.
result The method achieves high pricing accuracy and improved parameter recovery, optimization stability, and out-of-sample performance.
The goal of ordinal embedding is to represent items as points in a low-dimensional Euclidean space given a set of constraints in the form of distance comparisons like "item i is closer to item j than item k". Ordinal constraints like this often come from human judgments. To account for errors and variation in jud…
Method uses Seq2Seq learning to automatically generate recovery commands for ICT systems.
problem Manual decision-making for recovery commands is time-consuming and error-prone.
method Seq2Seq neural network model trained on past logs and commands.
result The model can estimate accurate recovery commands from new failures.
A new model explains U- and Swoosh-shaped stock price recovery during the COVID-19.
problem Modeling stock price recovery during the COVID-19 with V- and L-shaped recovery.
method Introducing a sentiment variable θ to quantify investor sentiment and simulate U- and Swoosh-shaped recovery. result The model explains U- and Swoosh-shaped recovery of sectoral indices with positive sentiment.
This paper improves support recovery in universal one-bit compressed sensing.
problem Support recovery in one-bit compressed sensing for sparse signals.
method Proposes approximate support recovery and superset recovery algorithms with polynomial-time complexity.
result Achieves improved support recovery with fewer measurements compared to existing methods.
This work provides a guaranteed tensor recovery method by combining low-rankness and smoothness priors.
problem Guaranteed tensor recovery with theoretical guarantees for low-rank and smoothness priors.
method Developed a new regularization term that combines low-rankness and smoothness priors, proving exact recovery guarantees.
result Rigorously proved exact recovery guarantees for tensor completion and tensor robust principal component analysis.