| { | |
| "claims": [ | |
| "Theorem 4.2 establishes a central limit theorem for the empirical KL_inf statistic, showing sqrt(n)(KL_inf(q_hat_n, m_o) - KL_inf(q, m_o)) converges in distribution to N(0, sigma^2(q, m_o)) (Theorem 4.2).", | |
| "Theorem 4.4 extends this result to the stopping time tau_alpha, proving sqrt(log(1/alpha))(tau_alpha/log(1/alpha) - 1/KL_inf(q,m_o)) converges to a Gaussian limit N(0, sigma^2_bd(q,m_o)) as alpha to 0 (Theorem 4.4).", | |
| "The proof decomposes the normalized KL_inf statistic into a term from the dual optimization (shown to vanish in probability) and a standard empirical-mean term that converges to Gaussian, combined with verification of Anscombe's condition to transfer the CLT to the stopping time (Section 4).", | |
| "Proposition 4.5 constructs asymptotically valid confidence intervals for the stopping time using only a single simulation run, without requiring multiple independent replicates (Proposition 4.5).", | |
| "Numerical experiments on synthetic Beta and Bernoulli distributions and on real crop-yield data show empirical stopping-time distributions converging to the theoretical Gaussian limit, with stronger agreement at smaller significance levels alpha (Section 5)." | |
| ], | |
| "claims_dataset_sha256": "7c0373fbbfb98b5acdc2c0ac122d9d81431bd6b42dda76fa36a91b49ec4b7825", | |
| "claims_url": "https://icml-2026-agent-repro-challenge.static.hf.space/claims_anchored.json", | |
| "paper_id": "HMyCBL2yMV" | |
| } | |