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Tag: rank

  • Enforcing Calibration in Multi-Output Probabilistic Regression with Pre-rank Regularization

    Enforcing Calibration in Multi-Output Probabilistic Regression with Pre-rank Regularization arXiv:2510.21273v1 Announce Type: new Abstract: Probabilistic models must be well calibrated to support reliable decision-making. While calibration in single-output regression is well studied, defining and achieving multivariate calibration in multi-output regression remains considerably more challenging. The existing literature on multivariate calibration primarily focuses on diagnostic tools…

  • A Probabilistic Basis for Low-Rank Matrix Learning

    A Probabilistic Basis for Low-Rank Matrix Learning arXiv:2510.05447v1 Announce Type: new Abstract: Low rank inference on matrices is widely conducted by optimizing a cost function augmented with a penalty proportional to the nuclear norm $Vert cdot Vert_*$. However, despite the assortment of computational methods for such problems, there is a surprising lack of understanding of…

  • Transformed $ell_1$ Regularizations for Robust Principal Component Analysis: Toward a Fine-Grained Understanding

    Transformed $ell_1$ Regularizations for Robust Principal Component Analysis: Toward a Fine-Grained Understanding arXiv:2510.03624v1 Announce Type: new Abstract: Robust Principal Component Analysis (RPCA) aims to recover a low-rank structure from noisy, partially observed data that is also corrupted by sparse, potentially large-magnitude outliers. Traditional RPCA models rely on convex relaxations, such as nuclear norm and $ell_1$…

  • Low-Rank Adaptation of Evolutionary Deep Neural Networks for Efficient Learning of Time-Dependent PDEs

    Low-Rank Adaptation of Evolutionary Deep Neural Networks for Efficient Learning of Time-Dependent PDEs arXiv:2509.16395v1 Announce Type: new Abstract: We study the Evolutionary Deep Neural Network (EDNN) framework for accelerating numerical solvers of time-dependent partial differential equations (PDEs). We introduce a Low-Rank Evolutionary Deep Neural Network (LR-EDNN), which constrains parameter evolution to a low-rank subspace, thereby…

  • Asynchronous Gossip Algorithms for Rank-Based Statistical Methods

    Asynchronous Gossip Algorithms for Rank-Based Statistical Methods arXiv:2509.07543v1 Announce Type: new Abstract: As decentralized AI and edge intelligence become increasingly prevalent, ensuring robustness and trustworthiness in such distributed settings has become a critical issue-especially in the presence of corrupted or adversarial data. Traditional decentralized algorithms are vulnerable to data contamination as they typically rely on…

  • The Nondecreasing Rank

    The Nondecreasing Rank arXiv:2509.00265v1 Announce Type: new Abstract: In this article the notion of the nondecreasing (ND) rank of a matrix or tensor is introduced. A tensor has an ND rank of r if it can be represented as a sum of r outer products of vectors, with each vector satisfying a monotonicity constraint. It…

  • A Smoothing Newton Method for Rank-one Matrix Recovery

    A Smoothing Newton Method for Rank-one Matrix Recovery arXiv:2507.23017v1 Announce Type: new Abstract: We consider the phase retrieval problem, which involves recovering a rank-one positive semidefinite matrix from rank-one measurements. A recently proposed algorithm based on Bures-Wasserstein gradient descent (BWGD) exhibits superlinear convergence, but it is unstable, and existing theory can only prove local linear…

  • Performance of Rank-One Tensor Approximation on Incomplete Data

    Performance of Rank-One Tensor Approximation on Incomplete Data arXiv:2504.07818v1 Announce Type: new Abstract: We are interested in the estimation of a rank-one tensor signal when only a portion $varepsilon$ of its noisy observation is available. We show that the study of this problem can be reduced to that of a random matrix model whose spectral…

  • Decentralized Inference for Distributed Geospatial Data Using Low-Rank Models

    Decentralized Inference for Distributed Geospatial Data Using Low-Rank Models arXiv:2502.00309v1 Announce Type: new Abstract: Advancements in information technology have enabled the creation of massive spatial datasets, driving the need for scalable and efficient computational methodologies. While offering viable solutions, centralized frameworks are limited by vulnerabilities such as single-point failures and communication bottlenecks. This paper presents…

  • Guaranteed Nonconvex Low-Rank Tensor Estimation via Scaled Gradient Descent

    Guaranteed Nonconvex Low-Rank Tensor Estimation via Scaled Gradient Descent arXiv:2501.01696v1 Announce Type: new Abstract: Tensors, which give a faithful and effective representation to deliver the intrinsic structure of multi-dimensional data, play a crucial role in an increasing number of signal processing and machine learning problems. However, tensor data are often accompanied by arbitrary signal corruptions,…

  • Low-Rank Correction for Quantized LLMs

    Low-Rank Correction for Quantized LLMs arXiv:2412.07902v1 Announce Type: new Abstract: We consider the problem of model compression for Large Language Models (LLMs) at post-training time, where the task is to compress a well-trained model using only a small set of calibration input data. In this work, we introduce a new low-rank approach to correct for…

  • Training-Free Bayesianization for Low-Rank Adapters of Large Language Models

    Training-Free Bayesianization for Low-Rank Adapters of Large Language Models arXiv:2412.05723v1 Announce Type: new Abstract: Estimating the uncertainty of responses of Large Language Models~(LLMs) remains a critical challenge. While recent Bayesian methods have demonstrated effectiveness in quantifying uncertainty through low-rank weight updates, they typically require complex fine-tuning or post-training procedures. In this paper, we propose Training-Free…