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Modeling nonlinear systems with Volterra series is challenging because the number of kernel coefficients grows exponentially with the model order. This work introduces Bayesian Tensor Network Volterra kernel machines (BTN-V), extending the…

Recently, tensor data (or multidimensional array) have been generated in many modern applications, such as functional magnetic resonance imaging (fMRI) in neuroscience and videos in video analysis. Many efforts are made in recent years to…

We consider the problem of low-rank decomposition of incomplete multiway tensors. Since many real-world data lie on an intrinsically low dimensional subspace, tensor low-rank decomposition with missing entries has applications in many data…

Firms earning prediction plays a vital role in investment decisions, dividends expectation, and share price. It often involves multiple tensor-compatible datasets with non-linear multi-way relationships, spatiotemporal structures, and…

Tensor completion is the problem of estimating the missing values of high-order data from partially observed entries. Data corruption due to prevailing outliers poses major challenges to traditional tensor completion algorithms, which…

This paper explores the problem of multi-view spectral clustering (MVSC) based on tensor low-rank modeling. Unlike the existing methods that all adopt an off-the-shelf tensor low-rank norm without considering the special characteristics of…

A simple approach to obtaining uncertainty-aware neural networks for regression is to do Bayesian linear regression (BLR) on the representation from the last hidden layer. Recent work [Riquelme et al., 2018, Azizzadenesheli et al., 2018]…

Multi-relational learning has received lots of attention from researchers in various research communities. Most existing methods either suffer from superlinear per-iteration cost, or are sensitive to the given ranks. To address both issues,…

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…

In this paper we focus on the problem of completion of multidimensional arrays (also referred to as tensors) from limited sampling. Our approach is based on a recently proposed tensor-Singular Value Decomposition (t-SVD) [1]. Using this…

This paper presents a geometric analysis of the simultaneous blind deconvolution and phase retrieval (BDPR) problem via a structured low-rank tensor recovery framework. Due to the highly complicated structure of the associated sensing…

The low-tubal-rank tensor model has been recently proposed for real-world multidimensional data. In this paper, we study the low-tubal-rank tensor completion problem, i.e., to recover a third-order tensor by observing a subset of its…

Bayesian Additive Regression Trees (BART) is a tree-based machine learning method that has been successfully applied to regression and classification problems. BART assumes regularisation priors on a set of trees that work as weak learners…

Time series prediction has been a long-standing research topic and an essential application in many domains. Modern time series collected from sensor networks (e.g., energy consumption and traffic flow) are often large-scale and incomplete…

A novel low-rank completion algorithm based on the quaternion tensor is proposed in this paper. This approach uses the TQt-rank of quaternion tensor to maintain the structure of RGB channels throughout the entire process. In more detail,…

Streaming tensor factorization is a powerful tool for processing high-volume and multi-way temporal data in Internet networks, recommender systems and image/video data analysis. Existing streaming tensor factorization algorithms rely on…

This paper considers the completion problem for a tensor (also referred to as a multidimensional array) from limited sampling. Our greedy method is based on extending the low-rank approximation pursuit (LRAP) method for matrix completions…

Recurrent Neural Networks (RNNs) are powerful sequence modeling tools. However, when dealing with high dimensional inputs, the training of RNNs becomes computational expensive due to the large number of model parameters. This hinders RNNs…

Chinese Remainder Theorem (CRT) has been widely studied with its applications in frequency estimation, phase unwrapping, coding theory and distributed data storage. Since traditional CRT is greatly sensitive to the errors in residues due to…

Spatiotemporal traffic time series (e.g., traffic volume/speed) collected from sensing systems are often incomplete with considerable corruption and large amounts of missing values, preventing users from harnessing the full power of the…