Knowledge-guided Pattern Discovery via Coupled Tensor Factorizations
- URL: http://arxiv.org/abs/2608.13234v1
- Date: Thu, 13 Aug 2026 13:38:45 GMT
- Title: Knowledge-guided Pattern Discovery via Coupled Tensor Factorizations
- Abstract summary: We introduce a knowledge-guided approach that brings together data and computational models.<n>Our experiments on real metabolomics measurements demonstrate that guiding the analysis of such noisy data improves the pattern discovery performance.
- Score: 1.179778723980276
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: In order to understand complex systems such as the human metabolome or human brain, different sensing technologies are used, generating complex data. These datasets are often multiway, i.e., with more than two axes of variation such as a subjects by metabolites by time array. While tensor factorizations have successfully revealed interpretable patterns from such complex data, they have so far been mainly data-driven. On the other hand, there is more to data -- there are computational models (of these systems), which are rich sources of prior information. In this paper, we introduce a knowledge-guided approach that brings together data and computational models by jointly analyzing real data and simulated data (generated using a computational model) using coupled tensor factorizations with linear coupling. Our experiments on real metabolomics measurements demonstrate that guiding the analysis of such noisy data with simulated data improves the pattern discovery performance while also revealing potential discrepancies between data and computational models.
Related papers
- Diffusion Model for Manifold Data: Score Decomposition, Curvature, and Statistical Complexity [93.52679474816728]
Diffusion models have become a leading framework in generative modeling.<n>This paper investigates how diffusion models learn structured data, focusing on two key aspects: statistical complexity and influence of data geometric properties.<n>We also highlight the interplay of manifold curvature with the structures in the score function.
arXiv Detail & Related papers (2026-03-21T04:40:19Z) - From Entropy to Epiplexity: Rethinking Information for Computationally Bounded Intelligence [91.54446789584826]
Epiplexity is a formalization of information capturing what computationally bounded observers can learn from data.<n>We show how information can be created with computation, how it depends on the ordering of the data, and how likelihood modeling can produce more complex programs than present in the data generating process itself.
arXiv Detail & Related papers (2026-01-06T18:04:03Z) - Learning Divergence Fields for Shift-Robust Graph Representations [73.11818515795761]
In this work, we propose a geometric diffusion model with learnable divergence fields for the challenging problem with interdependent data.
We derive a new learning objective through causal inference, which can guide the model to learn generalizable patterns of interdependence that are insensitive across domains.
arXiv Detail & Related papers (2024-06-07T14:29:21Z) - Towards Theoretical Understandings of Self-Consuming Generative Models [56.84592466204185]
This paper tackles the emerging challenge of training generative models within a self-consuming loop.
We construct a theoretical framework to rigorously evaluate how this training procedure impacts the data distributions learned by future models.
We present results for kernel density estimation, delivering nuanced insights such as the impact of mixed data training on error propagation.
arXiv Detail & Related papers (2024-02-19T02:08:09Z) - Discovering Mixtures of Structural Causal Models from Time Series Data [23.18511951330646]
We propose a general variational inference-based framework called MCD to infer the underlying causal models.
Our approach employs an end-to-end training process that maximizes an evidence-lower bound for the data likelihood.
We demonstrate that our method surpasses state-of-the-art benchmarks in causal discovery tasks.
arXiv Detail & Related papers (2023-10-10T05:13:10Z) - Capturing dynamical correlations using implicit neural representations [85.66456606776552]
We develop an artificial intelligence framework which combines a neural network trained to mimic simulated data from a model Hamiltonian with automatic differentiation to recover unknown parameters from experimental data.
In doing so, we illustrate the ability to build and train a differentiable model only once, which then can be applied in real-time to multi-dimensional scattering data.
arXiv Detail & Related papers (2023-04-08T07:55:36Z) - A Data-Driven Method for Automated Data Superposition with Applications
in Soft Matter Science [0.0]
We develop a data-driven, non-parametric method for superposing experimental data with arbitrary coordinate transformations.
Our method produces interpretable data-driven models that may inform applications such as materials classification, design, and discovery.
arXiv Detail & Related papers (2022-04-20T14:58:04Z) - Mixed Effects Neural ODE: A Variational Approximation for Analyzing the
Dynamics of Panel Data [50.23363975709122]
We propose a probabilistic model called ME-NODE to incorporate (fixed + random) mixed effects for analyzing panel data.
We show that our model can be derived using smooth approximations of SDEs provided by the Wong-Zakai theorem.
We then derive Evidence Based Lower Bounds for ME-NODE, and develop (efficient) training algorithms.
arXiv Detail & Related papers (2022-02-18T22:41:51Z) - Multimodal Data Fusion in High-Dimensional Heterogeneous Datasets via
Generative Models [16.436293069942312]
We are interested in learning probabilistic generative models from high-dimensional heterogeneous data in an unsupervised fashion.
We propose a general framework that combines disparate data types through the exponential family of distributions.
The proposed algorithm is presented in detail for the commonly encountered heterogeneous datasets with real-valued (Gaussian) and categorical (multinomial) features.
arXiv Detail & Related papers (2021-08-27T18:10:31Z) - Model discovery in the sparse sampling regime [0.0]
We show how deep learning can improve model discovery of partial differential equations.
As a result, deep learning-based model discovery allows to recover the underlying equations.
We illustrate our claims on both synthetic and experimental sets.
arXiv Detail & Related papers (2021-05-02T06:27:05Z) - Learning ODE Models with Qualitative Structure Using Gaussian Processes [0.6882042556551611]
In many contexts explicit data collection is expensive and learning algorithms must be data-efficient to be feasible.
We propose an approach to learning a vector field of differential equations using sparse Gaussian Processes.
We show that this combination improves extrapolation performance and long-term behaviour significantly, while also reducing the computational cost.
arXiv Detail & Related papers (2020-11-10T19:34:07Z) - Lossless Compression of Structured Convolutional Models via Lifting [14.63152363481139]
We introduce a simple and efficient technique to detect the symmetries and compress the neural models without loss of any information.
We demonstrate through experiments that such compression can lead to significant speedups of structured convolutional models.
arXiv Detail & Related papers (2020-07-13T08:02:27Z)
This list is automatically generated from the titles and abstracts of the papers in this site.
This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.