AISTATS Experiments

Use this before submission when the empirical or simulation story is not yet locked.

Experiment audit

• Map each empirical claim to a table, figure, simulation, ablation, or robustness check.
• Include baselines that represent both ML practice and relevant statistical methods.
• Separate synthetic simulations that validate assumptions from real-data experiments that

show practical relevance.

• Report uncertainty for stochastic results: repeated runs, standard errors, confidence

intervals, paired tests, or bootstrap intervals when appropriate.

• Report dataset splits, preprocessing, metrics, hyperparameter search ranges, final chosen

settings, selection criteria, random seeds, hardware, software versions, and runtime.

• Add ablations for the mechanism, not just cosmetic variants.
• Audit for leakage, selection bias, multiple-comparison issues, and mismatch between

theoretical assumptions and empirical setup.

What experiments are for at this venue

• AISTATS experiments exist to validate theory, not to win leaderboards. One focused

simulation confirming a predicted rate outweighs five extra benchmark datasets.

• The strongest design triad: a synthetic study where assumptions hold exactly, a study where

they are deliberately violated, and a real-data study showing practical behavior.

• Reviewers, frequently statisticians, check whether the empirical regime — sample size,

dimension, noise level — matches the asymptotic regime of the theorems. A bound proven as n grows but tested only at n = 500 invites the question of relevance.

Theory-validation design table

| Theoretical claim | Matching experiment | Reject pattern avoided | |---|---|---| | Convergence rate in n | Log-log error versus n with fitted slope | "Rates asserted but never plotted" | | Confidence-interval coverage | Empirical coverage across many replications | "Nominal 95 percent never verified" | | Regret bound | Cumulative regret versus horizon, with the bound curve overlaid | "Bound and trajectory never compared" | | Robustness to misspecification | Violation-severity sweep | "Guarantees hold under assumptions the experiments quietly break" |

Vignette: a kernel conditional independence test

Suppose the paper proves finite-sample type-I error control under a boundedness assumption. The matching plan: simulate under the null at several sample sizes to verify size, sweep dependence strength for power curves, then inject heavy-tailed noise that breaks boundedness to map degradation — every panel tied to a numbered theorem or remark.

Statistical reporting floor

• Replication counts and seeds for every stochastic figure; captions must say whether bars

are standard errors, confidence intervals, or quantiles.

• Report the compute actually consumed rather than vague feasibility language.

Output format

text
[Experiment readiness] strong / adequate / weak
[Claim -> evidence map] <claim: table/figure/simulation>
[Missing statistical evidence] <uncertainty/test/seed/baseline>
[Reproducibility gaps] <hyperparameters/compute/data/code>
[Decision-critical next run] <one experiment or simulation>