mlsanityData to 14 Oct 2026

The Minimax Learning Rates of Normal and Ising Undirected Graphical Models

arXiv 1806.06887 ↗First posted 18 Jun 2018math.ST cs.LG stat.THcited by 11

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Abstract (arXiv)

Let G be an undirected graph with m edges and d vertices. We show that d-dimensional Ising models on G can be learned from n i.i.d. samples within expected total variation distance some constant factor of min1, √(m + d)/n, and that this rate is optimal. We show that the same rate holds for the class of d-dimensional multivariate normal undirected graphical models with respect to G. We also identify the optimal rate of min1, √m/n for Ising models with no external magnetic field.

Key facts. Cited by 11 papers in the map (data through 14 Oct 2026). First posted on arXiv 18 Jun 2018.

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Citing papers per year: 2021: 1; 2022: 2; 2023: 4; 2024: 1; 2025: 2; 2026: 1.

11 papers.

  1. 2023A Unified Approach to Learning Ising Models: Beyond Independence and Bounded Widthcited by 14
  2. 2023User-Level Differential Privacy With Few Examples Per Usercited by 12
  3. 2021Chow-Liu++: Optimal Prediction-Centric Learning of Tree Ising Modelscited by 9
  4. 2024Bypassing the Noisy Parity Barrier: Learning Higher-Order Markov Random Fields from Dynamicscited by 8
  5. 2022Learning and Testing Latent-Tree Ising Models Efficientlycited by 7
  6. 2023Learning finitely correlated states: stability of the spectral reconstructioncited by 4
  7. 2025Estimating Ising Models in Total Variation Distancecited by 3
  8. 2022Privately Estimating a Gaussian: Efficient, Robust and Optimalcited by 0
  9. 2023Interaction Screening and Pseudolikelihood Approaches for Tensor Learning in Ising Modelscited by 0
  10. 2025Robust Learnability of Sample-Compressible Distributions under Noisy or Adversarial Perturbationscited by 0
  11. 2026Information-Theoretic Bounds for Sparse Covariance Estimation in the Vertical-Split Distributed Modelcited by 0