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arXiv research

A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.

168,742 papers · 148 categories

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336598130 · May 202619922001200920172026
48 results for shared subspace

Study optimizes shared singular subspace estimation from noisy matrices.

problem Estimating shared singular subspaces across multiple noisy matrices.
method Low-rank matrix denoising framework with Stack-SVD and novel estimators.
result Stack-SVD achieves minimax rate-optimality for identical shared subspaces, and novel estimators for partial sharing.

Model improves covariance estimation from shared and distinct datasets.

problem Limited sample sizes and shared covariance structure across related datasets.
method Spiked covariance model with shared subspace, closed-form pooling weight, and asymptotic guarantees.
result Improves estimation of high-dimensional covariance matrices from related datasets.

The paper proposes methods to find a shared active subspace for multivariate vector-valued functions.

problem Minimizing the deviation between function evaluations in the original and reconstructed spaces.
method Manipulating gradients or SPD matrices to identify a shared structure.
result Summing SPD matrices often identifies the best shared active subspace.

This paper analyzes AJIVE for estimating shared subspace across multiple datasets, revealing its strengths and limitations.

problem Estimating shared subspace across multiple datasets with varying degrees of misalignment.
method Angle-based Joint and Individual Variation Explained (AJIVE) method, a two-stage spectral approach.
result AJIVE's performance in high signal-to-noise ratio (SNR) regimes and its non-diminishing error in low-SNR settings.

Paper proposes CLAIR for efficient LLM fine-tuning across clients.

problem Fine-tuning large language models (LLMs) efficiently and collaboratively.
method Federated LoRA fine-tuning with Collaborative Low-rank Alignment and Identifiable Recovery (CLAIR).
result CLAIR achieves better performance and contamination detection compared to local fine-tuning.

We study the problem of distributed multi-task learning with shared representation, where each machine aims to learn a separate, but related, task in an unknown shared low-dimensional subspaces, i.e. when the predictor matrix has low rank. We consider a setting where each task is handled by a different machine, with sa…

2016-03-07abs ↗pdf ↗

The paper proposes a method to balance fairness and prediction accuracy by adjusting data representations.

problem Machine learning models can inherit and amplify historical biases, leading to unfair outcomes.
method The paper uses subspace decomposition and influence analysis to control the fairness-utility trade-off.
result The method effectively improves fairness while preserving predictive performance.

Study on reliability of latent reuse in diffusion models under distribution shift.

problem When can latent spaces from a source dataset be reused for a target dataset with different distributions?
method Considered a source-target setting with approximately low-dimensional datasets near different subspaces. Analyzed the target-domain score error due to principal-angle misalignment and target ambient noise.
result Latent reuse is reliable only if the source and target subspaces are close and the target ambient noise is not too amplified.

Most existing approaches address multi-view subspace clustering problem by constructing the affinity matrix on each view separately and afterwards propose how to extend spectral clustering algorithm to handle multi-view data. This paper presents an approach to multi-view subspace clustering that learns a joint subspace…

2017-08-29abs ↗pdf ↗

A method for identifying joint and individual subspaces from multi-view data.

problem Unclear conditions for reliably identifying joint and individual subspaces from noisy, high-dimensional measurements.
method Rigorously quantifies conditions based on signal rank, principal angles, and noise levels. Characterizes spectrum perturbations of product of projection matrices.
result Estimates joint and individual subspaces more accurately than existing approaches in simulations and real-world applications.

Estimates shared linear subspace from noisy data with multiple users.

problem Recovering shared linear subspace from noisy data with non-isotropic noise.
method Estimates shared subspace using at least two data points per user, avoiding restrictive assumptions.
result Upper and lower bounds for estimation error match, showing no additional error due to noise irregularity.

Method captures shared information across many views robustly.

problem Modeling hundreds of views per event and learning robust embeddings without view knowledge.
method View bootstrapping using multi-view correlation and matrix concentration theory.
result View bootstrapping captures shared information across many views robustly.

Dockless bike sharing systems need effective bike flow prediction models.

problem Imbalanced and dynamic use of bikes leads to mandatory rebalancing operations.
method Divide urban area into regions, model spatio-temporal bike flows, extract traffic patterns, and predict bike flows.
result Interpretable bike flow prediction model provides valuable insights into bike flow analysis.

Multi-task learning (MTL) allows deep neural networks to learn from related tasks by sharing parameters with other networks. In practice, however, MTL involves searching an enormous space of possible parameter sharing architectures to find (a) the layers or subspaces that benefit from sharing, (b) the appropriate amoun…

2017-05-23abs ↗pdf ↗

In this work we propose a method for reducing the dimensionality of tensor objects in a binary classification framework. The proposed Common Mode Patterns method takes into consideration the labels' information, and ensures that tensor objects that belong to different classes do not share common features after the redu…

2019-02-06abs ↗pdf ↗

GAME improves matrix completion by considering subgroup-specific latent structures.

problem Heterogeneous data with overlapping categories, smoothing away subgroup-specific variation.
method Group-Aware Matrix Estimation (GAME) with overlapping nuclear-norm penalties.
result GAME outperforms global low-rank estimators in structured missingness regimes.

In the paradigm of multi-task learning, mul- tiple related prediction tasks are learned jointly, sharing information across the tasks. We propose a framework for multi-task learn- ing that enables one to selectively share the information across the tasks. We assume that each task parameter vector is a linear combi- nat…

2012-06-27abs ↗pdf ↗

This paper presents a new multitask learning framework that learns a shared representation among the tasks, incorporating both task and feature clusters. The jointly-induced clusters yield a shared latent subspace where task relationships are learned more effectively and more generally than in state-of-the-art multitas…

2017-03-03abs ↗pdf ↗

Multi-view clustering is an important and fundamental problem. Many multi-view subspace clustering methods have been proposed, and most of them assume that all views share a same coefficient matrix. However, the underlying information of multi-view data are not fully exploited under this assumption, since the coefficie…

2019-06-19abs ↗pdf ↗

Quaternion self-attention reduces computational cost and improves performance.

problem Existing quaternion self-attention increases computational cost and diverges attention distributions.
method Proposes a shared-score quaternion self-attention mechanism.
result Reduces score-computation multiplications by 75% and softmax operations from four to one.

Adversarial examples are maliciously perturbed inputs designed to mislead machine learning (ML) models at test-time. They often transfer: the same adversarial example fools more than one model. In this work, we propose novel methods for estimating the previously unknown dimensionality of the space of adversarial inputs…

2017-04-11abs ↗pdf ↗

CoreFlow models matrix-valued distributions efficiently, preserving shared low-rank structure.

problem Learning matrix-valued distributions from high-dimensional and incomplete data.
method Low-rank flow model that learns shared row/column subspaces and trains a normalizing flow on the core.
result CoreFlow improves generation quality in few-sample regimes and remains competitive in data-rich settings.

The hyperbolic manifold is a smooth manifold of negative constant curvature. While the hyperbolic manifold is well-studied in the literature, it has gained interest in the machine learning and natural language processing communities lately due to its usefulness in modeling continuous hierarchies. Tasks with hierarchica…

2019-03-18abs ↗pdf ↗

New bounds on learning shared representations improve model performance and efficiency.

problem Improving model performance and efficiency through shared representations across clients.
method Established new upper and lower bounds on statistical error, designed a spectral estimator for non-convex least-squares solutions.
result Optimal statistical rate achieved when shared representation is well covered across clients.

The paper analyzes PLS-SVD in high-dimensional data integration, revealing its strengths and limitations.

problem Understanding the behavior of PLS-SVD in high-dimensional data integration.
method Analysis using random matrix theory and singular value decomposition.
result PLS-SVD exhibits counter-intuitive or limiting behavior in certain regimes and outperforms PCA when detecting common latent subspace.

We will develop simple relations between the arc-lengths of a pair of geodesics that share common end-points. The two geodesics differ only by the requirement that one is constrained to lie in a subspace of the parent manifold. We will present two applications of our results. In the first example we explore the converg…

2015-12-10abs ↗pdf ↗

LASER compresses recursive model activations by exploiting their low-dimensional structure.

problem Understanding and optimizing the geometric structure of recursive reasoning trajectories.
method Dynamic low-rank basis tracking via matrix-free subspace tracking with a fidelity-triggered reset mechanism.
result Recursive activations occupy a linear, low-dimensional subspace that can be compressed efficiently.

Improved neural network training in low-dimensional random bases.

problem Inefficient optimization in large-scale neural networks.
method Re-draw random subspace at each training step, apply independent projections to different network parts.
result Significantly better optimization performance and efficiency.

Enhancing spectral embedding for low-dimensional embeddings in rare disease cohorts

problem Representing clinical concepts and patients in electronic health records
method Spectral-based unsupervised learning with flexible knowledge transfer
result Outperforms competing approaches in challenging scenarios

Proposes HeteroJIVE for joint subspace estimation in multi-view data with statistical and structural heterogeneity.

problem Joint subspace estimation in multi-view data with varying statistical and structural heterogeneity.
method HeteroJIVE: A weighted two-stage spectral algorithm addressing statistical and structural heterogeneity.
result HeteroJIVE achieves the O(K1/2)O(K^{-1/2}) rate without iterative refinement, validating the oracle-optimal weighting scheme.

Multi-view clustering is an important approach to analyze multi-view data in an unsupervised way. Among various methods, the multi-view subspace clustering approach has gained increasing attention due to its encouraging performance. Basically, it integrates multi-view information into graphs, which are then fed into sp…

2019-12-03abs ↗pdf ↗

Proposes joint LCA for multiview data to identify shared and view-specific components.

problem Extracting shared components sequentially from multiview data.
method Formulates a matrix decomposition model with joint and individual structures, proposes a penalty term objective function, and employs a refitting procedure.
result Achieves simultaneous estimation and rank selection for cross covariance.

Proposes a method for multi-view clustering that integrates consistent and complementary graph regularizers.

problem Multi-view clustering where views have both consistent and complementary information.
method Consistent and complementary graph-regularized multi-view subspace clustering (GRMSC).
result The proposed method outperforms state-of-the-art methods on benchmark datasets.