Related papers: Coupled tensor models for probability mass functio…

We introduce the tensor numerical method for solution of the $d$-dimensional optimal control problems with fractional Laplacian type operators in constraints discretized on large $n^{\otimes d}$ tensor-product Cartesian grids. The approach…

Recovery of low-rank matrices from a small number of linear measurements is now well-known to be possible under various model assumptions on the measurements. Such results demonstrate robustness and are backed with provable theoretical…

As tensors become widespread in modern data analysis, Tucker low-rank Principal Component Analysis (PCA) has become essential for dimensionality reduction and structural discovery in tensor datasets. Motivated by the common scenario where…

Multi-modal populations of networks arise in many scenarios including in large-scale multi-modal neuroimaging studies that capture both functional and structural neuroimaging data for thousands of subjects. A major research question in such…

A new algorithm of the canonical polyadic decomposition (CPD) presented here. It features lower computational complexity and memory usage than the available state of the art implementations. We begin with some examples of CPD applications…

Mixtures of linear dynamical systems (MoLDS) provide a path to model time-series data that exhibit diverse temporal dynamics across trajectories. However, its application remains challenging in complex and noisy settings, limiting its…

Tensor networks are a powerful modeling framework developed for computational many-body physics, which have only recently been applied within machine learning. In this work we utilize a uniform matrix product state (u-MPS) model for…

Assume that f is a strict convex function with a unique minimum in R^n. We divide the vector of n-variables to d groups of vector subvariables with d at least two. We assume that we can find the partial minimum of f with respect to each…

This work is concerned with the propagation of uncertainty across coupled domain problems with high-dimensional random inputs. A stochastic model reduction approach based on low-rank separated representations is proposed for the partitioned…

Point cloud (PCD) anomaly detection steadily emerges as a promising research area. This study aims to improve PCD anomaly detection performance by combining handcrafted PCD descriptions with powerful pre-trained 2D neural networks. To this…

Recently, a tensor factorization based method for a low tubal rank tensor completion problem of a third order tensor was proposed, which performed better than some existing methods. Tubal rank is only defined on one mode of third order…

High-dimensional tensor-valued predictors arise in modern applications, increasingly as learned representations from neural networks. Existing tensor classification methods rely on sparsity or Tucker structures and often lack theoretical…

Mixed-precision training is a crucial technique for scaling deep learning models, but successful mixedprecision training requires identifying and applying the right combination of training methods. This paper presents our preliminary study…

We propose a novel fast and robust 3D point clouds segmentation framework via coupled feature selection, named 3DCFS, that jointly performs semantic and instance segmentation. Inspired by the human scene perception process, we design a…

The collinear factorization theorem, combined with finite-order calculations in perturbative QCD, provides a powerful framework to obtain predictions for many collider observables. However, for observables which involve multiple energy…

The representation theory of tensor functions is a powerful mathematical tool for constitutive modeling of anisotropic materials. A major limitation of the traditional theory is that many point groups require fourth- or sixth-order…

1) We introduce random discrete Morse theory as a computational scheme to measure the complicatedness of a triangulation. The idea is to try to quantify the frequence of discrete Morse matchings with a certain number of critical cells. Our…

Tensor factorizations (TF) are powerful tools for the efficient representation and analysis of multidimensional data. However, classic TF methods based on maximum likelihood estimation underperform when applied to zero-inflated count data,…

Efficient probability density estimation is a core challenge in statistical machine learning. Tensor-based probabilistic graph methods address interpretability and stability concerns encountered in neural network approaches. However, a…

Discovering components that are shared in multiple datasets, next to dataset-specific features, has great potential for studying the relationships between different subjects or tasks in functional Magnetic Resonance Imaging (fMRI) data.…