Related papers: Balancing Interpretability and Predictive Accuracy…

Tensor factorization has received increasing interest due to its intrinsic ability to capture latent factors in multi-dimensional data with many applications such as recommender systems and Electronic Health Records (EHR) mining. PARAFAC2…

For massive and heterogeneous modern datasets, it is of fundamental interest to provide guarantees on the accuracy of estimation when computational resources are limited. In the application of learning to rank, we provide a hierarchy of…

Tensor decompositions have proven to be effective in analyzing the structure of multidimensional data. However, most of these methods require a key parameter: the number of desired components. In the case of the CANDECOMP/PARAFAC…

Machine learning classification tasks often benefit from predicting a set of possible labels with confidence scores to capture uncertainty. However, existing methods struggle with the high-dimensional nature of the data and the lack of…

An increasing number of data science and machine learning problems rely on computation with tensors, which better capture the multi-way relationships and interactions of data than matrices. When tapping into this critical advantage, a key…

This paper conducts a rigorous analysis for provable estimation of multidimensional arrays, in particular third-order tensors, from a random subset of its corrupted entries. Our study rests heavily on a recently proposed tensor algebraic…

It has become routine to collect data that are structured as multiway arrays (tensors). There is an enormous literature on low rank and sparse matrix factorizations, but limited consideration of extensions to the tensor case in statistics.…

An important issue when using Machine Learning algorithms in recent research is the lack of interpretability. Although these algorithms provide accurate point predictions for various learning problems, uncertainty estimates connected with…

Most state of the art deep neural networks are overparameterized and exhibit a high computational cost. A straightforward approach to this problem is to replace convolutional kernels with its low-rank tensor approximations, whereas the…

Coupled tensor decomposition reveals the joint data structure by incorporating priori knowledge that come from the latent coupled factors. The tensor ring (TR) decomposition is invariant under the permutation of tensors with different mode…

Modeling variability in tensor decomposition methods is one of the challenges of source separation. One possible solution to account for variations from one data set to another, jointly analysed, is to resort to the PARAFAC2 model. However,…

We address the problem of tensor robust principal component analysis (TRPCA), which entails decomposing a given tensor into the sum of a low-rank tensor and a sparse tensor. By leveraging the tensor singular value decomposition (t-SVD), we…

Tensor decomposition is a mathematically supported technique for data compression. It consists of applying some kind of a Low Rank Decomposition technique on the tensors or matrices in order to reduce the redundancy of the data. However, it…

Tensor Robust Principal Component Analysis (TRPCA) holds a crucial position in machine learning and computer vision. It aims to recover underlying low-rank structures and to characterize the sparse structures of noise. Current approaches…

Tensor decomposition methods have proven effective in various applications, including compression and acceleration of neural networks. At the same time, the problem of determining optimal decomposition ranks, which present the crucial…

This chapter studies the problem of decomposing a tensor into a sum of constituent rank one tensors. While tensor decompositions are very useful in designing learning algorithms and data analysis, they are NP-hard in the worst-case. We will…

In biomedical research and other fields, it is now common to generate high content data that are both multi-source and multi-way. Multi-source data are collected from different high-throughput technologies while multi-way data are collected…

Over recent years it has become well accepted that user interest is not static or immutable. There are a variety of contextual factors, such as time of day, the weather or the user's mood, that influence the current interests of the user.…

First principles approaches have revolutionized our ability in using computers to predict, explore and design materials. A major advantage commonly associated with these approaches is that they are fully parameter free. However, numerically…

Neural document ranking models perform impressively well due to superior language understanding gained from pre-training tasks. However, due to their complexity and large number of parameters, these (typically transformer-based) models are…