arXiv Statistics ML
Tensor Network Moral Graph Recovery of Discrete Probability Distributions
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arXiv Machine Learning
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Parameterised graph theory for tensor networks: entanglement rerouting, structural simplification, and agnostic tomography
The paper applies parameterised graph theory to tensor networks, showing that cutwidth and tree‑cutwidth bound the bond‑dimension overhead needed to represent a tensor‑network state as a matrix product state or tree tensor network. It derives graph‑dependent upper bounds on the sample and computational complexity of tensor‑network tomography, introducing a new graph parameter called learning complexity. Finally, it extends the framework to an agnostic learner that approximates any state with a tensor‑network state of given bond dimension, providing explicit graph‑dependent complexity bounds.
arXiv AI
Sep 23
On Probabilistic Inference Through Parametric Tensor Decomposition in Base Tensor Networks
arXiv:2609.23774v1 Announce Type: new Abstract: Probabilistic inference is generally only tractable in low-treewidth graphical models, limiting its effective applicability in high-treewidth settings....
arXiv Machine Learning
Oct 21
Robust Latent Variable Graphical Models: Exact Recovery and Fundamental Limits
arXiv:2610.27010v1 Announce Type: cross Abstract: We study robust estimation of a Gaussian precision matrix that decomposes as a sparse matrix minus a symmetric, possibly indefinite, low-rank matrix,...
arXiv Machine Learning
Jun 2
Network Learning with Semi-relaxed Gromov-Wasserstein
arXiv:2606. 02223v1 Announce Type: new Abstract: Estimating the generative mechanism of large-scale networks is a fundamental challenge in statistical machine learning.
Hugging Face Trending Papers
Sep 10
Identifiability of Nonnegative Tensor Decompositions via Positive Scattering
The paper introduces a new concept called positive scattering to enhance identifiability of nonnegative tensor decompositions. By combining this scattering term with existing dimension-based conditions, the authors derive two sufficient criteria that guarantee minimality, nonnegative rank, and uniqueness for subsets of components. The key result is a positive splitting inequality that links dimension constraints with support-induced geometric rigidity, and the authors show that the scattering term’s mode costs are discrete, enabling an exact activation characterization via graph connectivity. This criterion can certify sparse nonnegative tensor decompositions that elude traditional Kruskal and Lovitz–Petrov conditions, even after reshaping, and reduces to familiar matrix results in the two-dimensional case.
arXiv Machine Learning
Jul 17
Spectral Concentration and Recovery in Sparse High-Dimensional Random Geometric Graphs
arXiv:2607. 14304v1 Announce Type: cross Abstract: We study sparse random geometric graphs generated by connecting pairs of high-dimensional vectors whose inner product exceeds a threshold.