A block-sparse Tensor Train Format for sample-efficient high-dimensional Polynomial Regression
Low-rank tensors are an established framework for high-dimensional least-squares problems. We propose to extend this framework by including the concept of block-sparsity. In the context of polynomial regression each sparsity pattern corresponds to some subspace of homogeneous multivariate polynomials. This allows us to adapt the ansatz space to align better with known sample complexity results. The resulting method is tested in numerical experiments and demonstrates improved computational resource utilization and sample efficiency.
Code (1)
Tasks
regressionSimilar Papers 제목 키워드 기반
Consistent spectral clustering in sparse tensor block models
High-order clustering aims to classify objects in multiway datasets that are prevalent in various fields such as bioinformatics, social network analysis, and recommendation systems. These tasks often involve data that is…
ClusteringRecommendation SystemsTensor vs Matrix Methods: Robust Tensor Decomposition under Block Sparse Perturbations
Robust tensor CP decomposition involves decomposing a tensor into low rank and sparse components. We propose a novel non-convex iterative algorithm with guaranteed recovery. It alternates between low-rank CP decompositio…
Action DetectionActivity DetectionTensor DecompositionSparse Nonnegative CANDECOMP/PARAFAC Decomposition in Block Coordinate Descent Framework: A Comparison Study
Nonnegative CANDECOMP/PARAFAC (NCP) decomposition is an important tool to process nonnegative tensor. Sometimes, additional sparse regularization is needed to extract meaningful nonnegative and sparse components. Thus, a…
Tensor DecompositionFused3S: Fast Sparse Attention on Tensor Cores
Sparse attention is a core building block in many leading neural network models, from graph-structured learning to sparse sequence modeling. It can be decomposed into a sequence of three sparse matrix operations (3S): sa…
GPUVariable Binding for Sparse Distributed Representations: Theory and Applications
Symbolic reasoning and neural networks are often considered incompatible approaches. Connectionist models known as Vector Symbolic Architectures (VSAs) can potentially bridge this gap. However, classical VSAs and neural …
compressed sensing