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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2511.13514 |
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| _version_ | 1866914161396547584 |
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| author | Vipulananthan, Pragatheeswaran Premaratne, Kamal Sarkar, Dilip Murthi, Manohar N. |
| author_facet | Vipulananthan, Pragatheeswaran Premaratne, Kamal Sarkar, Dilip Murthi, Manohar N. |
| contents | Accurate uncertainty quantification is a critical challenge in machine learning. While neural networks are highly versatile and capable of learning complex patterns, they often lack interpretability due to their ``black box'' nature. On the other hand, probabilistic ``white box'' models, though interpretable, often suffer from a significant performance gap when compared to neural networks. To address this, we propose a novel quantum physics-based ``white box'' method that offers both accurate uncertainty quantification and enhanced interpretability. By mapping the kernel mean embedding (KME) of a time series data vector to a reproducing kernel Hilbert space (RKHS), we construct a tensor network-inspired 1D spin chain Hamiltonian, with the KME as one of its eigen-functions or eigen-modes. We then solve the associated Schr{ö}dinger equation and apply perturbation theory to quantify uncertainty, thereby improving the interpretability of tasks performed with the quantum tensor network-based model. We demonstrate the effectiveness of this methodology, compared to state-of-the-art ``white box" models, in change point detection and time series clustering, providing insights into the uncertainties associated with decision-making throughout the process. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_13514 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Quantum Tensor Network-Based Viewpoint for Modeling and Analysis of Time Series Data Vipulananthan, Pragatheeswaran Premaratne, Kamal Sarkar, Dilip Murthi, Manohar N. Machine Learning Information Theory Accurate uncertainty quantification is a critical challenge in machine learning. While neural networks are highly versatile and capable of learning complex patterns, they often lack interpretability due to their ``black box'' nature. On the other hand, probabilistic ``white box'' models, though interpretable, often suffer from a significant performance gap when compared to neural networks. To address this, we propose a novel quantum physics-based ``white box'' method that offers both accurate uncertainty quantification and enhanced interpretability. By mapping the kernel mean embedding (KME) of a time series data vector to a reproducing kernel Hilbert space (RKHS), we construct a tensor network-inspired 1D spin chain Hamiltonian, with the KME as one of its eigen-functions or eigen-modes. We then solve the associated Schr{ö}dinger equation and apply perturbation theory to quantify uncertainty, thereby improving the interpretability of tasks performed with the quantum tensor network-based model. We demonstrate the effectiveness of this methodology, compared to state-of-the-art ``white box" models, in change point detection and time series clustering, providing insights into the uncertainties associated with decision-making throughout the process. |
| title | A Quantum Tensor Network-Based Viewpoint for Modeling and Analysis of Time Series Data |
| topic | Machine Learning Information Theory |
| url | https://arxiv.org/abs/2511.13514 |