arXiv research

CUR decomposition aids in clustering data from unknown subspaces.

When data is sampled from an unknown subspace, principal component analysis (PCA) provides an effective way to estimate the subspace and hence reduce the dimension of the data. At the heart of PCA is the Eckart-Young-Mirsky theorem, which characterizes the best rank k approximation of a matrix. In this paper, we prove …

Develops methods to construct confidence regions for singular subspaces in low-rank matrix regression.

Agents collaborate to reduce regret in a multi-agent linear bandit problem with side information.

We consider the problem of clustering noisy high-dimensional data points into a union of low-dimensional subspaces and a set of outliers. The number of subspaces, their dimensions, and their orientations are unknown. A probabilistic performance analysis of the thresholding-based subspace clustering (TSC) algorithm intr…

New research shows SSC fails when points on the same subspace are mislabeled.

We consider the problem of clustering a set of high-dimensional data points into sets of low-dimensional linear subspaces. The number of subspaces, their dimensions, and their orientations are unknown. We propose a simple and low-complexity clustering algorithm based on thresholding the correlations between the data po…

Subspace clustering refers to the problem of clustering high-dimensional data points into a union of low-dimensional linear subspaces, where the number of subspaces, their dimensions and orientations are all unknown. In this paper, we propose a variation of the recently introduced thresholding-based subspace clustering…

Proves subspace tracking with missing data and improves matrix completion.

Unified framework for structured principal subspace estimation with bounds and rates.

The paper finds non-Gaussian directions in high-dimensional data using Wasserstein distance.

Subspace clustering refers to the problem of clustering unlabeled high-dimensional data points into a union of low-dimensional linear subspaces, assumed unknown. In practice one may have access to dimensionality-reduced observations of the data only, resulting, e.g., from "undersampling" due to complexity and speed con…

BO method identifies sparse subspaces for efficient high-dimensional optimization.

The problem of clustering noisy and incompletely observed high-dimensional data points into a union of low-dimensional subspaces and a set of outliers is considered. The number of subspaces, their dimensions, and their orientations are assumed unknown. We propose a simple low-complexity subspace clustering algorithm, w…

Bayesian approach for online subspace learning from incomplete data.

A parameter-free method clusters data points from multiple subspaces.

Paper proposes clustering algorithms for data from Union of Polyhedral Cones model.

We briefly review recent progress in techniques for modeling and analyzing hyperspectral images and movies, in particular for detecting plumes of both known and unknown chemicals. For detecting chemicals of known spectrum, we extend the technique of using a single subspace for modeling the background to a "mixture of s…

Tyler's M-estimator's phase transition at DS-SNR = 1 is resolved.

Develops a method for causal inference with noisy confounders.

Subspace clustering refers to the problem of clustering unlabeled high-dimensional data points into a union of low-dimensional linear subspaces, whose number, orientations, and dimensions are all unknown. In practice one may have access to dimensionality-reduced observations of the data only, resulting, e.g., from unde…

Paper analyzes SSC for data with missing entries, improving performance.

New faster, space-saving methods for subspace embeddings in tensors.

New method estimates geodesic distances using spherelets.

New method identifies latent components in PNL mixtures without strong assumptions.

A new method splits surface flow discretizations into streamfunctions and harmonic fields.

We describe the Fast Greedy Sparse Subspace Clustering (FGSSC) algorithm providing an efficient method for clustering data belonging to a few low-dimensional linear or affine subspaces. The main difference of our algorithm from predecessors is its ability to work with noisy data having a high rate of erasures (missed e…

New algorithm catches moving subspaces in bandit problems.

Model improves covariance estimation from shared and distinct datasets.

Regularized M-estimators are used in diverse areas of science and engineering to fit high-dimensional models with some low-dimensional structure. Usually the low-dimensional structure is encoded by the presence of the (unknown) parameters in some low-dimensional model subspace. In such settings, it is desirable for est…

AGOP from KRR recovers central subspace in fewer samples than needed for prediction.

ProSub uses angles in feature space to classify data as in- or out-of-distribution.

Gradient flow solves multi-index regression for high-dimensional Gaussian data.

Efficient algorithms for low-rank bandits using subspace recovery.

Algorithm learns polynomials in Gaussian inputs with reduced sample complexity.

CobBO optimizes expensive functions in high dimensions by using a two-stage kernel approach.

This work quantifies the space of transferable adversarial examples.

The stable 4-genus of a knot K in 3-space is the limiting value of g_4(nK)/n, where g_4 denotes the 4-genus and n goes to infinity. This induces a seminorm on CQ, the concordance group tensored with the rational numbers. Basic properties of the stable genus are developed, as are examples focused on understanding the un…

This paper improves diffusion models for low-dimensional data.

New algorithm tackles bilinear bandit problem with low-rank structure.

Distributed learning tasks share a low-dimensional space.

EAGC boosts GCD by regulating gradient entanglement, improving known and novel category separability.

We consider the problem of joint estimation of structured inverse covariance matrices. We perform the estimation using groups of measurements with different covariances of the same unknown structure. Assuming the inverse covariances to span a low dimensional linear subspace in the space of symmetric matrices, our aim i…

The paper develops Kalman filters for unknown systems with sample complexity bounds.

Efficiently recovers data corrupted by adversarial noise in structured settings.

Study of symplectic Stiefel and Grassmann manifolds with geodesics and applications.

In many applications, such as economics, operations research and reinforcement learning, one often needs to estimate a multivariate regression function f subject to a convexity constraint. For example, in sequential decision processes the value of a state under optimal subsequent decisions may be known to be convex or …

A new method identifies key dimensions for function analysis.