The paper introduces a tensor-based formulation of the Viterbi algorithm for Hidden Semi-Markov Models (HSMMs), converting inner loops into tensor operations that align with SIMD and massively parallel architectures. It presents optimized implementations for single- and multi-core CPUs and, for the first time, GPUs. Experiments show speedups of up to 14× on a single core, over 200× with multi-core, and more than 570× on GPU compared to the sequential baseline, setting a new performance benchmark for large-scale HSMM decoding.
By Lorenzo Piarulli, Elia Belli, Daniele De Sensi
arXiv:2608. 13621v1 Announce Type: new Abstract: A hidden Markov model (HMM) combines three roles: inference of a hidden-state belief from observations, propagation through a Markov transition, and emission back to observation space.
By Yongchao Huang
arXiv:2606.08560v2 Announce Type: replace-cross
Abstract: We adopt the canonical polyadic (CP) decomposition to model high-dimensional tensor time series. Our primary goal is to identify and estimate...
By Jinyuan Chang, Guanglin Huang, Qiwei Yao, Long Yu
arXiv:2510. 25693v3 Announce Type: replace-cross Abstract: State-space models (SSMs) are a widely used tool in time series analysis.
By John-Joseph Brady, Benjamin Cox, Yunpeng Li, V\'ictor Elvira
arXiv:2606. 10085v1 Announce Type: new Abstract: Matrix-valued time series arise in a wide range of applications, such as spatio-temporal data from medical imaging and geophysics.
By Zhen Qin, Yang Chen
The paper introduces a Physics-informed Predictive Prior Tensor Autoencoder (PPPTAE) for anomaly detection in multi-dimensional time series. It combines reconstruction-based and prediction-based autoencoders by embedding a Bayesian fusion approach and a predictive prior that respects tensor correlations. The method incorporates physical laws via tensor low‑rank decomposition to prevent over‑generalization and is validated on real‑world datasets.
By Jianan Liu, Chunguang Li