Related papers: Functional Bayesian Tucker Decomposition for Conti…

Tensor ring (TR) decomposition has recently received increased attention due to its superior expressive performance for high-order tensors. However, the applicability of traditional TR decomposition algorithms to real-world applications is…

A tensor is a multi-way array that can represent, in addition to a data set, the expression of a joint law or a multivariate function. As such it contains the description of the interactions between the variables corresponding to each of…

In this paper, we propose a new algorithm for point cloud denoising based on the tensor Tucker decomposition. We first represent the local surface patches of a noisy point cloud to be matrices by their distances to a reference point, and…

Attempts of studying implicit regularization associated to gradient descent (GD) have identified matrix completion as a suitable test-bed. Late findings suggest that this phenomenon cannot be phrased as a minimization-norm problem, implying…

We propose tensor time series imputation when the missing pattern in the tensor data can be general, as long as any two data positions along a tensor fibre are both observed for enough time points. The method is based on a tensor time…

Bayesian inference in high-dimensional discrete-input additive noise models is a fundamental challenge in communication systems, as the support of the required joint a posteriori probability (APP) mass function grows exponentially with the…

Multivariate functional data present theoretical and practical complications which are not found in univariate functional data. One of these is a situation where the component functions of multivariate functional data are positive and are…

Tucker decomposition is proposed to reduce the memory requirement of the far-fields in the fast multipole method (FMM)-accelerated surface integral equation simulators. It is particularly used to compress the far-fields of FMM groups, which…

Recurrent Neural Networks (RNNs) have been widely used in sequence analysis and modeling. However, when processing high-dimensional data, RNNs typically require very large model sizes, thereby bringing a series of deployment challenges.…

In the realm of tensor optimization, the low-rank Tucker decomposition is crucial for reducing the number of parameters and for saving storage. We explore the geometry of Tucker tensor varieties -- the set of tensors with bounded Tucker…

Most machine learning models for structured data encode the structural knowledge of a node by leveraging simple aggregation functions (in neural models, typically a weighted sum) of the information in the node's neighbourhood. Nevertheless,…

Motivated by the challenges of analyzing high-dimensional ($p \gg n$) sequencing data from longitudinal microbiome studies, where samples are collected at multiple time points from each subject, we propose supervised functional tensor…

Tensor decompositions are invaluable tools in analyzing multimodal datasets. In many real-world scenarios, such datasets are far from being static, to the contrary they tend to grow over time. For instance, in an online social network…

Reducing parameter redundancies in neural network architectures is crucial for achieving feasible computational and memory requirements during training and inference phases. Given its easy implementation and flexibility, one promising…

The problem of incomplete data is common in signal processing and machine learning. Tensor completion algorithms aim to recover the incomplete data from its partially observed entries. In this paper, taking advantages of high…

Given a time-evolving tensor with missing entries, how can we effectively factorize it for precisely predicting the missing entries? Tensor factorization has been extensively utilized for analyzing various multi-dimensional real-world data.…

Part 2 of this monograph builds on the introduction to tensor networks and their operations presented in Part 1. It focuses on tensor network models for super-compressed higher-order representation of data/parameters and related cost…

Functional data analysis, which models data as realizations of random functions over a continuum, has emerged as a useful tool for time series data. Often, the goal is to infer the dynamic connections (or time-varying conditional…

A key challenge in spatial statistics is the analysis for massive spatially-referenced data sets. Such analyses often proceed from Gaussian process specifications that can produce rich and robust inference, but involve dense covariance…

While nonparametric density estimators often perform well on low dimensional data, their performance can suffer when applied to higher dimensional data, owing presumably to the curse of dimensionality. One technique for avoiding this is to…