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...

Enabling Large-Scale Probabilistic Seizure Detection with a Tensor-Network Kalman Filter for LS-SVM

Recent advancements in wearable EEG devices have highlighted the importance of accurate seizure detection algorithms, yet the ever-increasing size of the generated datasets poses a significant challenge to existing seizure detection methods based on kernel machines. Typically, this problem is mitigated by significantly undersampling the...

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...

Tensor network Kalman filter for LTI systems

An extension of the Tensor Network (TN) Kalman filter [2], [3] for large scale LTI systems is presented in this paper. The TN Kalman filter can handle exponentially large state vectors without constructing them explicitly. In order to have efficient algebraic operations, a low TN rank is required. We exploit the possibility to approximate the...