Generalized Least Squares Kernelized Tensor Factorization

• URL: http://arxiv.org/abs/2412.07041v3
• Date: Tue, 11 Feb 2025 14:57:40 GMT
• Title: Generalized Least Squares Kernelized Tensor Factorization
• Authors: Mengying Lei, Lijun Sun,
• Abstract summary: Generalized Least Squares Kernelized Factorization (GL) framework for tensor completion is presented. GL integrates low-rank factorization with a locally correlated residual process. The proposed framework is evaluated on four real-world datasets across diverse spatial tasks.
• Score: 19.284198191705027
• License:
• Abstract: Completing multidimensional tensor-structured data with missing entries is a fundamental task for many real-world applications involving incomplete or corrupted datasets. For data with spatial or temporal side information, low-rank factorization models with smoothness constraints have demonstrated strong performance. Although effective at capturing global and long-range correlations, these models often struggle to capture short-scale, high-frequency variations in the data. To address this limitation, we propose the Generalized Least Squares Kernelized Tensor Factorization (GLSKF) framework for tensor completion. GLSKF integrates smoothness-constrained low-rank factorization with a locally correlated residual process; the resulting additive structure enables effective characterization of both global dependencies and local variations. Specifically, we define the covariance norm to enforce the smoothness of factor matrices in the global low-rank factorization, and use structured covariance/kernel functions to model the local processes. For model estimation, we develop an alternating least squares (ALS) procedure with closed-form solutions for each subproblem. GLSKF utilizes zero-padding and slicing operations based on projection matrices which preserve the Kronecker structure of covariances, facilitating efficient computations through the conjugate gradient (CG) method. The proposed framework is evaluated on four real-world datasets across diverse tasks. Experimental results demonstrate that GLSKF achieves superior performance and scalability, establishing it as a novel solution for multidimensional tensor completion.

Related papers

• Preventing Model Collapse in Gaussian Process Latent Variable Models [11.45681373843122]
  This paper theoretically examines the impact of projection variance on model collapse through the lens of a linear FourierVM. We tackle model collapse due to inadequate kernel flexibility by integrating the spectral mixture (SM) kernel and a differentiable random feature (RFF) kernel approximation. The proposedVM, named advisedRFLVM, is evaluated across diverse datasets and consistently outperforms various competing models.
  arXiv  Detail & Related papers  (2024-04-02T06:58:41Z)
• SIGMA: Scale-Invariant Global Sparse Shape Matching [50.385414715675076]
  We propose a novel mixed-integer programming (MIP) formulation for generating precise sparse correspondences for non-rigid shapes. We show state-of-the-art results for sparse non-rigid matching on several challenging 3D datasets.
  arXiv  Detail & Related papers  (2023-08-16T14:25:30Z)
• Probabilistic Shape Completion by Estimating Canonical Factors with Hierarchical VAE [48.03685702899071]
  We propose a novel method for 3D shape completion from a partial observation of a point cloud. Our method estimates the entire local feature field by a single feedforward network. A hierarchical variational autoencoder (VAE) with tiny canonicals is used to probabilistically estimate the canonical factors of the complete feature volume.
  arXiv  Detail & Related papers  (2022-12-06T23:41:31Z)
• Towards Understanding and Mitigating Dimensional Collapse in Heterogeneous Federated Learning [112.69497636932955]
  Federated learning aims to train models across different clients without the sharing of data for privacy considerations. We study how data heterogeneity affects the representations of the globally aggregated models. We propose sc FedDecorr, a novel method that can effectively mitigate dimensional collapse in federated learning.
  arXiv  Detail & Related papers  (2022-10-01T09:04:17Z)
• Bayesian Complementary Kernelized Learning for Multidimensional Spatiotemporal Data [11.763229353978321]
  We propose a new statistical framework -- Complementary Complementary Kernelized Learning (BCKL) BCKL offers superior performance in providing accurate posterior mean and high-quality uncertainty estimates.
  arXiv  Detail & Related papers  (2022-08-21T22:38:54Z)
• Tackling Data Heterogeneity: A New Unified Framework for Decentralized SGD with Sample-induced Topology [6.6682038218782065]
  We develop a general framework unifying several gradient-based optimization methods for empirical risk minimization problems. We provide a unified perspective for variance-reduction (VR) and gradient-tracking (GT) methods such as SAGA, Local-SVRG and GT-SAGA. The rate results reveal that VR and GT methods can effectively eliminate data within and across devices, respectively, enabling the exact convergence of the algorithm to the optimal solution.
  arXiv  Detail & Related papers  (2022-07-08T07:50:08Z)
• $\texttt{FedBC}$: Calibrating Global and Local Models via Federated Learning Beyond Consensus [66.62731854746856]
  In federated learning (FL), the objective of collaboratively learning a global model through aggregation of model updates across devices tends to oppose the goal of personalization via local information. In this work, we calibrate this tradeoff in a quantitative manner through a multi-criterion-based optimization. We demonstrate that $texttFedBC$ balances the global and local model test accuracy metrics across a suite datasets.
  arXiv  Detail & Related papers  (2022-06-22T02:42:04Z)
• Truncated tensor Schatten p-norm based approach for spatiotemporal traffic data imputation with complicated missing patterns [77.34726150561087]
  We introduce four complicated missing patterns, including missing and three fiber-like missing cases according to the mode-drivenn fibers. Despite nonity of the objective function in our model, we derive the optimal solutions by integrating alternating data-mputation method of multipliers.
  arXiv  Detail & Related papers  (2022-05-19T08:37:56Z)
• Scalable Spatiotemporally Varying Coefficient Modelling with Bayesian Kernelized Tensor Regression [17.158289775348063]
  Kernelized tensor Regression (BKTR) can be considered a new and scalable approach to modeling processes with low-rank cotemporal structure. We conduct extensive experiments on both synthetic and real-world data sets, and our results confirm the superior performance and efficiency of BKTR for model estimation and inference.
  arXiv  Detail & Related papers  (2021-08-31T19:22:23Z)
• Rank-R FNN: A Tensor-Based Learning Model for High-Order Data Classification [69.26747803963907]
  Rank-R Feedforward Neural Network (FNN) is a tensor-based nonlinear learning model that imposes Canonical/Polyadic decomposition on its parameters. First, it handles inputs as multilinear arrays, bypassing the need for vectorization, and can thus fully exploit the structural information along every data dimension. We establish the universal approximation and learnability properties of Rank-R FNN, and we validate its performance on real-world hyperspectral datasets.
  arXiv  Detail & Related papers  (2021-04-11T16:37:32Z)
• A Unified Framework for Coupled Tensor Completion [42.19293115131073]
  Coupled tensor decomposition reveals the joint data structure by incorporating priori knowledge that come from the latent coupled factors. The TR has powerful expression ability and achieves success in some multi-dimensional data processing applications. The proposed method is validated on numerical experiments on synthetic data, and experimental results on real-world data demonstrate its superiority over the state-of-the-art methods in terms of recovery accuracy.
  arXiv  Detail & Related papers  (2020-01-09T02:15:46Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.