Research map / Learning theory and algorithms / Sample complexity
Concentration of Multilinear Functions of the Ising Model with Applications to Network Data
Read the paperCheck your idea against 108,967 papers
AI-extracted summary. Written by AI from the paper's title only (no summary yet). Numbers and claims can be wrong or missing context, so check the paper before you cite or build on it.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use concentration of lower-degree multilinear functions to bound martingale increments | Multilinear statistics of high-temperature Ising models without external fields · Degree-d multilinear functions | concentration radius: C_1\|a\|_\infty (n \log^2 n/\eta)^{d/2} | Helped |
| Use the proposed bilinear concentration analysis instead of the prior Lipschitz-based bound | Bilinear functions of high-temperature Ising models · No external field | concentration radius: O(n^{1.5}) -> 300\|a\|_\infty n \log^2 n / \eta + 2 | Helped |
| Center spins by their expectations | Bilinear functions of high-temperature Ising models with external fields · Arbitrary external fields | tail probability: 4\exp\left(-\frac{r}{c'n\log n} \right) | Helped |
| Use pairwise differences between two i.i.d. samples | Bilinear functions of high-temperature Ising models with external fields · Two i.i.d. Ising samples | tail probability: 4\exp\left(-\frac{r}{c'n\log n} \right) | Helped |
| Use uncentered bilinear statistics in the presence of an external field | Bilinear functions of high-temperature Ising models · Empty graph with a uniform external field | variance: c(h)n^3 | Hurt |
| Apply the bilinear tail analysis to an independent-spin example | Bilinear statistic f(X)=\sum_{u \neq v}X_uX_v · Empty graph | tail probability: \exp(-9/4)\exp\left(-\frac{9r}{8n} \right) | Mixed |
| Use multilinear statistics as tests of whether social-network choices follow an Ising model | Last.fm artist-listening data · Last.fm | test rejection | Mixed |
Closest papers by meaning
- Maximizing Influence in an Ising Network: A Mean-Field Optimal Solution (NeurIPS 2016 · similarity 0.88)
- Maximizing Activity in Ising Networks via the TAP Approximation (AAAI 2018 · similarity 0.87)
- Inference and Sampling of $K_33$-free Ising Models (ICML 2019 · similarity 0.86)
- Computational and Statistical Tradeoffs in Inferring Combinatorial Structures of Ising Model (ICML 2020 · similarity 0.86)
- Fast Wasserstein rates for estimating probability distributions of probabilistic graphical models (NeurIPS 2026 · similarity 0.83)
- DiPhon: Diffusion on Graphons for Scalable Graph Generation (NeurIPS 2026 · similarity 0.83)
Writing a paper in this area? scime draft is a free LaTeX editor with AI included, real-time co-authors and a check of your references and venue rules before you submit. It also imports OpenAI Prism projects.