arXiv research

GLIMPS tackles abundant outlier detection in matched subspace detection.

Subspace match fails to accurately assess neural network representations.

Detects missing tensor signals in a KS subspace with high probability.

Flow Matching models help generative models stay within the subspace of real data.

New theory shows neural networks learn similar representations under certain conditions.

Improved SSC clustering with reduced computation time and accuracy.

Subspace clustering methods based on $\ell_1$, $\ell_2$ or nuclear norm regularization have become very popular due to their simplicity, theoretical guarantees and empirical success. However, the choice of the regularizer can greatly impact both theory and practice. For instance, $\ell_1$ regularization is guaranteed t…

Extends subspace detour method to Gromov-Wasserstein problem.

Paper proves noise-tolerant SSC using greedy methods under coherence conditions.

A new method for generative modeling of discrete data using geometric latent subspaces.

Detect anomalies in complex networks using topological subspace detectors.

Sparsity-based subspace clustering algorithms have attracted significant attention thanks to their excellent performance in practical applications. A prominent example is the sparse subspace clustering (SSC) algorithm by Elhamifar and Vidal, which performs spectral clustering based on an adjacency matrix obtained by sp…

Sparse Subspace Clustering (SSC) is a state-of-the-art method for clustering high-dimensional data points lying in a union of low-dimensional subspaces. However, while $\ell_1$ optimization-based SSC algorithms suffer from high computational complexity, other variants of SSC, such as Orthogonal Matching Pursuit-based S…

We study sparse principal components analysis in high dimensions, where $p$ (the number of variables) can be much larger than $n$ (the number of observations), and analyze the problem of estimating the subspace spanned by the principal eigenvectors of the population covariance matrix. We introduce two complementary not…

State-of-the-art algorithms for sparse subspace clustering perform spectral clustering on a similarity matrix typically obtained by representing each data point as a sparse combination of other points using either basis pursuit (BP) or orthogonal matching pursuit (OMP). BP-based methods are often prohibitive in practic…

Unions of subspaces provide a powerful generalization to linear subspace models for collections of high-dimensional data. To learn a union of subspaces from a collection of data, sets of signals in the collection that belong to the same subspace must be identified in order to obtain accurate estimates of the subspace s…

LOL method simplifies forming linear combinations of latent variables.

LOFT separates subspace rotation and transformation for orthogonal fine-tuning.

Optimal subspace embedding with near-optimal sparsity for high-dimensional data.

Detects domain shifts in datasets using interpretable feature subspaces.

With increasing concerns about security, the need for highly secure physical biometrics-based authentication systems utilizing \emph{cancelable biometric} technologies is on the rise. Because the problem of cancelable template generation deals with the trade-off between template security and matching performance, many …

This paper improves OMP-based sparse subspace clustering with data-adaptive capability.

Bayesian optimization guided by experimenter intuition and beliefs.

Given an overcomplete dictionary $A$ and a signal $b$ that is a linear combination of a few linearly independent columns of $A$, classical sparse recovery theory deals with the problem of recovering the unique sparse representation $x$ such that $b = A x$. It is known that under certain conditions on $A$, $x$ can be re…

SMAVE optimizes SDR by projecting onto a low-dimensional subspace on a Riemannian manifold.

The paper tackles subspace-preserving recovery of sparse signals from overcomplete dictionaries.

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…

Develops a method for causal inference with noisy confounders.

New SQ lower bounds for NGCA without requiring chi-squared condition.

New algorithm catches moving subspaces in bandit problems.

Proposes a robust variant of Wasserstein distance using subspace projections.

Estimates shared linear subspace from noisy data with multiple users.

Low-degree method fails to predict robust subspace recovery problem.

Matching Pursuit LASSIn Part I \cite{TanPMLPart1}, a Matching Pursuit LASSO ({MPL}) algorithm has been presented for solving large-scale sparse recovery (SR) problems. In this paper, we present a subspace search to further improve the performance of MPL, and then continue to address another major challenge of SR -- bat…

SkMM selects data for finetuning by balancing bias and variance.

We introduce a method to construct $G_2$-instantons over compact $G_2$-manifolds arising as the twisted connected sum of a matching pair of building blocks [Kov03,KL11,CHNP12]. Our construction is based on gluing $G_2$-instantons obtained from holomorphic bundles over the building blocks via the first named author's wo…

Unified analysis of multilabel Fisher discriminants with improved dimensionality and robustness.

EpiMer merges models by solving Fréchet mean on a Riemannian manifold.

Improved spectral method recovers sparse vectors in random subspaces.

The paper develops methods to reduce deployment risk under dynamic covariate shifts.

A new framework for PPLS combines noise estimation, optimization, and calibration.

Test-time training adapts a pretrained model to each prompt via parameter updates, improving accuracy under pretraining-to-test distribution shifts.

Convex iso-Delaunay regions found in flat surface strata.

Framework uses low-dimensional maps to solve high-dimensional Bayesian inference problems.

Novel tensor perturbation bounds for orthogonal iteration methods.

Paper tackles subspace estimation from noisy, partial data matrices.

New method aligns diffusion models for inference-time properties without retraining.

Paper uses random projection to preserve subspace structure for efficient data analysis.