Extended Kalman Filtering with Low-Rank Tensor Networks for MIMO Volterra System Identification

This article reformulates the multiple-input-multiple-output Volterra system identification problem as an extended Kalman filtering problem. This reformulation has two advantages. First, it results in a simplification of the solution compared to the Tensor Network Kalman filter as no tensor filtering equations are required anymore. The second...

Matrix Product Operator Restricted Boltzmann Machines

A restricted Boltzmann machine (RBM) learns a probability distribution over its input samples and has numerous uses like dimensionality reduction, classification and generative modeling. Conventional RBMs accept vectorized data that dismiss potentially important structural information in the original tensor (multi-way) input. Matrix-variate...

A Support Tensor Train Machine

There has been growing interest in extending traditional vector-based machine learning techniques to their tensor forms. Support tensor machine (STM) and support Tucker machine (STuM) are two typical tensor generalization of the conventional support vector machine (SVM). However, the expressive power of STM is restrictive due to its rank-one...

Fast and Accurate Tensor Completion with Total Variation Regularized Tensor Trains

We propose a new tensor completion method based on tensor trains. The to-be-completed tensor is modeled as a low-rank tensor train, where we use the known tensor entries and their coordinates to update the tensor train. A novel tensor train initialization procedure is proposed specifically for image and video completion, which is demonstrated...

Deep Model Compression and Inference Speedup of Sum-Product Networks on Tensor Trains

Sum-product networks (SPNs) constitute an emerging class of neural networks with clear probabilistic semantics and superior inference speed over other graphical models. This brief reveals an important connection between SPNs and tensor trains (TTs), leading to a new canonical form which we call tensor SPNs (tSPNs). Specifically, we...

MERACLE: Constructive Layer-Wise Conversion of a Tensor Train into a MERA

In this article, two new algorithms are presented that convert a given data tensor train into either a Tucker decomposition with orthogonal matrix factors or a multi-scale entanglement renormalization ansatz (MERA). The Tucker core tensor is never explicitly computed but stored as a tensor train instead, resulting in both computationally and...

Kernelized support tensor train machines

Tensor, a multi-dimensional data structure, has been exploited recently in the machine learning community. Traditional machine learning approaches are vector- or matrix-based, and cannot handle tensorial data directly. In this paper, we propose a tensor train (TT)-based kernel technique for the first time, and apply it to the conventional...