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Tensors in the form of multilinear arrays are ubiquitous in data science applications. Captured real-world data, including video, hyperspectral images, and discretized physical systems, naturally occur as tensors and often come with…

Higher-order tensors arise frequently in applications such as neuroimaging, recommendation system, social network analysis, and psychological studies. We consider the problem of low-rank tensor estimation from possibly incomplete,…

The tensor train (TT) rank has received increasing attention in tensor completion due to its ability to capture the global correlation of high-order tensors ($\textrm{order} >3$). For third order visual data, direct TT rank minimization has…

Recent efforts to unravel the mystery of implicit regularization in deep learning have led to a theoretical focus on matrix factorization -- matrix completion via linear neural network. As a step further towards practical deep learning, we…

To efficiently express tensor data using the Tucker format, a critical task is to minimize the multilinear rank such that the model would not be over-flexible and lead to overfitting. Due to the lack of rank minimization tools in tensor,…

Tensor decomposition methods allow us to learn the parameters of latent variable models through decomposition of low-order moments of data. A significant limitation of these algorithms is that there exists no general method to regularize…

Real-world spatio-temporal data is often incomplete or inaccurate due to various data loading delays. For example, a location-disease-time tensor of case counts can have multiple delayed updates of recent temporal slices for some locations…

Low rank tensor representation underpins much of recent progress in tensor completion. In real applications, however, this approach is confronted with two challenging problems, namely (1) tensor rank determination; (2) handling real tensor…

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…

In this paper, we study the problem of low-rank tensor learning, where only a few of training samples are observed and the underlying tensor has a low-rank structure. The existing methods are based on the sum of nuclear norms of unfolding…

One of the key factors of enabling machine learning models to comprehend and solve real-world tasks is to leverage multimodal data. Unfortunately, annotation of multimodal data is challenging and expensive. Recently, self-supervised…

The detection and normalization of temporal expressions is an important task and preprocessing step for many applications. However, prior work on normalization is rule-based, which severely limits the applicability in real-world…

In recent years, multimodal AI has seen an upward trend as researchers are integrating data of different types such as text, images, speech into modelling to get the best results. This project leverages multimodal AI and matrix…

Modeling of multidimensional signal using tensor is more convincing than representing it as a collection of matrices. The tensor based approaches can explore the abundant spatial and temporal structures of the mutlidimensional signal. The…

This paper proposes a novel method for learning highly nonlinear, multivariate functions from examples. Our method takes advantage of the property that continuous functions can be approximated by polynomials, which in turn are representable…

Recent studies highlight the potential of textual modalities in conditioning the speech separation model's inference process. However, regularization-based methods remain underexplored despite their advantages of not requiring auxiliary…

In this article, we develop methods for estimating a low rank tensor from noisy observations on a subset of its entries to achieve both statistical and computational efficiencies. There have been a lot of recent interests in this problem of…

Recently, the \textit{Tensor Nuclear Norm~(TNN)} regularization based on t-SVD has been widely used in various low tubal-rank tensor recovery tasks. However, these models usually require smooth change of data along the third dimension to…

We study low rank matrix and tensor completion and propose novel algorithms that employ adaptive sampling schemes to obtain strong performance guarantees. Our algorithms exploit adaptivity to identify entries that are highly informative for…

Tensor train (TT) factorization and corresponding TT rank, which can well express the low-rankness and mode correlations of higher-order tensors, have attracted much attention in recent years. However, TT factorization based methods are…