# Functional Bayesian Tucker Decomposition for Continuous-indexed Tensor Data

arXiv: https://arxiv.org/abs/2311.04829 · HTML: https://mlsanity.com/paper/2311.04829/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 34 references that are in the map.
- First posted on arXiv 8 Nov 2023.

## Builds on (most cited first, 8 of 8)

- [Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domains](https://mlsanity.com/paper/2006.10739/) (2020)
- [Expectation Propagation for approximate Bayesian inference](https://mlsanity.com/paper/1301.2294/) (2013)
- [Low-Rank Tensor Function Representation for Multi-Dimensional Data Recovery](https://mlsanity.com/paper/2212.00262/) (2022)
- [Scalable Tucker Factorization for Sparse Tensors - Algorithms and Discoveries](https://mlsanity.com/paper/1710.02261/) (2017)
- [Optimization of Functions Given in the Tensor Train Format](https://mlsanity.com/paper/2209.14808/) (2022)
- [Streaming Factor Trajectory Learning for Temporal Tensor Decomposition](https://mlsanity.com/paper/2310.17021/) (2023)
- [Conditional Expectation Propagation](https://mlsanity.com/paper/1910.12360/) (2019)
- [Adaptive Granularity in Tensors: A Quest for Interpretable Structure](https://mlsanity.com/paper/1912.09009/) (2019)

## Built on by (most cited first, 10 of 10)

- [Generating Full-field Evolution of Physical Dynamics from Irregular Sparse Observations](https://mlsanity.com/paper/2505.09284/) (2025)
- [A Novel Approach to Temporal QoS Estimation via Extended Kalman Filter-Incorporated Latent Feature Analysis](https://mlsanity.com/paper/2606.23010/) (2026)
- [Continuous Representation Methods, Theories, and Applications: An Overview and Perspectives](https://mlsanity.com/paper/2505.15222/) (2025)
- [Functional Complexity-adaptive Temporal Tensor Decomposition](https://mlsanity.com/paper/2502.06164/) (2025)
- [Low-Rank Tensor Recovery via Variational Schatten-p Quasi-Norm and Jacobian Regularization](https://mlsanity.com/paper/2506.22134/) (2025)
- [When Bayesian Tensor Completion Meets Multioutput Gaussian Processes: Functional Universality and Rank Learning](https://mlsanity.com/paper/2512.21486/) (2025)
- [Neural Operator-Grounded Continuous Tensor Function Representation and Its Applications](https://mlsanity.com/paper/2603.01812/) (2026)
- [StreamPhy: Streaming Inference of High-Dimensional Physical Dynamics via State Space Models](https://mlsanity.com/paper/2605.07384/) (2026)
- [TRACE: Retrospective Streaming Generation of Physical Fields under Sparse Structured Sensing](https://mlsanity.com/paper/2608.26219/) (2026)
- [HarmoCore: Functional Latent Diffusion for Sparse Reconstruction of Oscillatory Wave Fields](https://mlsanity.com/paper/2609.00679/) (2026)

## Abstract (arXiv)

Tucker decomposition is a powerful tensor model to handle multi-aspect data. It demonstrates the low-rank property by decomposing the grid-structured data as interactions between a core tensor and a set of object representations (factors). A fundamental assumption of such decomposition is that there are finite objects in each aspect or mode, corresponding to discrete indexes of data entries. However, real-world data is often not naturally posed in this setting. For example, geographic data is represented as continuous indexes of latitude and longitude coordinates, and cannot fit tensor models directly. To generalize Tucker decomposition to such scenarios, we propose Functional Bayesian Tucker Decomposition (FunBaT). We treat the continuous-indexed data as the interaction between the Tucker core and a group of latent functions. We use Gaussian processes (GP) as functional priors to model the latent functions. Then, we convert each GP into a state-space prior by constructing an equivalent stochastic differential equation (SDE) to reduce computational cost. An efficient inference algorithm is developed for scalable posterior approximation based on advanced message-passing techniques. The advantage of our method is shown in both synthetic data and several real-world applications. We release the code of FunBaT at urlhttps://github.com/xuangu-fang/Functional-Bayesian-Tucker-Decomposition.