Stratified Sampling

Building a co-registered SAR-optical corpus for self-supervised Earth Observation is above all an acquisition problem, yet the main multi-modal datasets are collected opportunistically, with no per-stratum quota control and no mechanism against the geographic dropout that non-uniform cloud cover leaves behind. We present Deficit-Driven Stratified Acquisition (DDSA), an algorithm that treats building a co-registered Sentinel-1/Sentinel-2 corpus as a constrained maximum-coverage problem over a hemisphere-corrected (class x season x region) stratification, enforces strict temporal pairing and a multi-stage quality gate, and closes the loop during acquisition with a human-in-the-loop deficit-repair stage. Measured on its own product, the algorithm yields three results a single-pass acquisition cannot report. Deficit-driven ordering makes a partial run a covering one: it holds every one of the 192 strata populated from the first few percent of the budget, where an abundance-first order leaves most strata empty until the end. Whether a failed attempt can be recovered depends on the temporal persistence of its cause, not the kind of defect: geometric failures such as nodata are among the most repairable (eta = 41.4%) while cloud is among the least (eta = 18.8%), because a cloudy location is cloudy on most dates of its season. The repair loop supplies 39.5% of the released pairs at no measurable quality cost, with 89.8% surviving manual review. The quality guarantee has a price: 2,928,370 acquisition attempts produced 740,746 released pairs. We release the corpus, STRATA-S12, with STAC/PDS4-aligned FAIR sidecars, and a pre-registered linear-probe check confirms it is fit for self-supervised pre-training. A metadata-level coverage comparison against SSL4EO-S12 and SEN12MS situates the corpus over a shared frame; systematic cross-corpus and cross-method comparison is left to follow-up work.

Evaluating large language models (LLMs) on AMLworld's smallest test splits is costly because each of over a million targets requires a separate graph prompt. Sampling reduces this cost, but small balanced subsets change unweighted precision and F1. We introduce AMLworld-Compact, an evaluation set that retains every illicit test transaction and samples benign transactions from supervised-score strata. Its HT-Coreset protocol reduces evaluation targets by 271x and 611x on HI-Small and LI-Small. Horvitz-Thompson weights give unbiased full-test confusion-count estimates for fixed predictions; recall is exact, while precision and F1 are ratio estimates. In a held-out study using Graph Feature Preprocessor (GFP) features, one boosted-tree family defines strata for evaluating the other over 500 draws per configuration. At the released sizes, F1 RMSE is 0.00-2.58 percentage points versus 4.44-7.41 for uniform sampling with HT weights; conservative intervals remain broad. Under the evaluated graph prompts, seven open-weight LLMs have weighted precision near the predict-all-illicit baseline. In an outcome-stratified audit of 1,000 HI-Small few-shot outputs from one run per model, lexical checks pass for 84.5% of correct and 56.2% of incorrect binary verdicts, so these markers do not establish correctness. We release the evaluation sets, construction code, and audit tools at https://huggingface.co/datasets/typhoon-ai/AMLworldCompactEval and https://github.com/nat-nischw/AMLworld-Compact.

Validating an LLM-as-a-judge requires estimating its agreement with humans, yet annotation budgets rarely allow every item to be multiply labeled. We prove that this overlap sparsity is the first-order determinant of wrong deployment decisions: at 5% pairwise overlap, wrong-decision rates reach 25% and the probability of selecting the wrong best judge among ten candidates is 65%. The two actionable levers are overlap quantity and allocation. For quantity, we derive a minimum-overlap formula showing $ρ\geq 0.25$ suffices for non-borderline judges while borderline cases remain fundamentally hard. For allocation, a zero-cost stratified scheme halves false-rejection rates relative to random sampling when strata are informative. We validate on 10 LLM judges across four evaluation matrices spanning visual assessment, causal reasoning, and summarization.

Online controlled experiments, or A/B tests, are widely used to estimate causal effects on digital platforms. A central challenge is to improve experimental sensitivity, or statistical power, without increasing the experimental sample size. Stratified sampling is a classical variance reduction technique; however, its effectiveness depends critically on how the strata are constructed. We thus propose an optimization-based stratification framework for stratified sampling using optimal multi-way decision trees. Our method, called Optimal Multi-way Stratification Trees (OMST), formulates stratification as a path-selection problem over a feature graph. The selected paths define interpretable stratification rules and are optimized using an exact variance-minimizing binary optimization formulation under continuous proportional allocation and a Neyman-type optimal allocation. We incorporate supervised optimal binning to generate outcome-relevant candidate splits for numerical features. Furthermore, we introduce reduction procedures for redundant candidate paths and assignment constraints, substantially reducing the optimization problem size. Experiments on both a real-world and a simulated dataset demonstrate that OMST achieves comparable or superior variance reduction to existing methods while maintaining shallow and interpretable stratification trees.

Randomized experiments are often run in one population to guide decisions in another. Allocating by experimental proportions wastes budget on groups that rarely appear in deployment, whereas allocating by deployment proportions under-samples groups that are hard to measure precisely. We propose TWNA (Target-Weighted Neyman Allocation), a two-stage stratified design that uses pilot estimates of group--arm outcome variances to allocate final-stage sample sizes and treatment probabilities for target-weighted group average treatment effect (GATE) precision. The oracle rule has a closed form and balances deployment importance with statistical difficulty; the plug-in rule recovers it as pilot variance estimates stabilize. We also extend TWNA to handle uncertainty about deployment composition, remaining robust whether the target mix is roughly known or entirely unknown. Finally, we distinguish this weight robustness from a pilot-robust variant for skewed, rare-event, or contaminated outcomes. Simulations and real-covariate benchmarks show the largest gains when groups are both deployment-important and difficult to measure.

Metamodels are instrumental in reducing the computational burden associated with nested reliability analyses and optimization loops in Performance-Based Risk Optimization (PBRO) of structures under stochastic loads. In this context, stochastic emulators are particularly useful because they approximate response distributions while accounting for the intrinsic stochasticity of the simulator. Among these methods, Stochastic Polynomial Chaos Expansion (SPCE) is especially attractive because it does not require replications of nonlinear analyses at fixed input conditions. However, SPCE may present limitations in accurately representing extreme responses in the tails of structural response distributions. To address this limitation, this study proposes a framework that combines Generalized Stratified Sampling (GSS) with SPCE. The GSS scheme partitions the input space into strata according to the intensity of the hazard, improving the representation of extreme responses, while independent SPCE emulators are trained within each stratum. The conditional exceedance probabilities estimated in each stratum are then recombined using the total probability theorem to evaluate the probabilistic constraints. The proposed GSS-SPCE framework is applied to the optimal design of buckling-restrained brace cross-sectional areas in a two-story steel building. The objective is to minimize the initial construction cost while satisfying prescribed probabilistic performance constraints. Results show that the proposed framework accurately estimates structural response distributions, including their tail regions, while substantially reducing the number of nonlinear model evaluations required for PBRO.

Opinionated text - spanning product reviews, hotel feedback, and social posts - captures rich signals about user experiences, preferences, and concerns. However, the scale, redundancy, and imbalance of such corpora make it challenging to analyze opinions effectively, particularly when the goal is to generate summaries that remain faithful to the diversity of viewpoints expressed. This paper presents a framework that preserves semantics in LLM-based opinion summarization while minimizing token usage. We combine multidimensional classification (e.g., sentiment, topics) with a family of stratified sampling strategies to select compact yet representative subsets of opinions before prompting the LLM. Tailored prompts then produce balanced summaries that surface the salient aspects expressed in the opinions (e.g., strengths and weaknesses of products/hotels). Experiments on Amazon product reviews, Tripadvisor hotel reviews, and X/Twitter posts demonstrate that our method significantly reduces token usage and computational cost while consistently outperforming traditional AI-based and standard LLM summarization baselines in terms of content coverage, balance, and semantic preservation.

Pretrained diffusion models serve as frozen teachers feeding downstream pipelines such as text-to-3D, single-step distillation, and data attribution. The teacher gradients these pipelines consume are Monte Carlo (MC) expectations over noise levels and Gaussian noise samples; their estimator variance dominates compute cost because each draw requires expensive upstream work (rendering, simulation, encoding). We introduce CARV, a compute-aware variance-accounting framework that motivates a hierarchical MC estimator: amortize the expensive upstream computation over cheap diffusion-noise resamples, sharpened by timestep importance sampling and a stratified-inverse-CDF construction. In our text-to-3D distillation and attribution experiments, CARV delivers 2-3x effective compute multipliers (most from amortized reuse; ~25% additional from IS+stratification) without changing the objective; in single-step distillation, the same techniques cut gradient variance by an order of magnitude but do not improve downstream FID, marking the regime where MC variance is no longer the bottleneck.

We study the expected star discrepancy under a newly designed class of non-equal volume partitions. The main contributions are twofold. First, we establish a strong partition principle for the star discrepancy, showing that our newly designed non-equal volume partitions yield stratified sampling point sets with lower expected star discrepancy than classical jittered sampling. Specifically, we prove that $\mathbb{E}(D^{*}_{N}(Z)) < \mathbb{E}(D^{*}_{N}(Y))$, where $Y$ and $Z$ represent jittered sampling and our non-equal volume partition sampling, respectively. Second, we derive explicit upper bounds for the expected star discrepancy under our non-equal volume partition models, which improve upon existing bounds for jittered sampling. Our results provide a theoretical foundation for using non-equal volume partitions in high-dimensional numerical integration.

The critical need for transparent and trustworthy machine learning in cybersecurity operations drives the development of this integrated Explainable AI (XAI) framework. Our methodology addresses three fundamental challenges in deploying AI for threat detection: handling massive datasets through Strategic Sampling Methodology that preserves class distributions while enabling efficient model development; ensuring experimental rigor via Automated Data Leakage Prevention that systematically identifies and removes contaminated features; and providing operational transparency through Integrated XAI Implementation using SHAP analysis for model-agnostic interpretability across algorithms. Applied to the CIC-IDS2017 dataset, our approach maintains detection efficacy while reducing computational overhead and delivering actionable explanations for security analysts. The framework demonstrates that explainability, computational efficiency, and experimental integrity can be simultaneously achieved, providing a robust foundation for deploying trustworthy AI systems in security operations centers where decision transparency is paramount.