The knockoff filter introduced by Barber and Cand\`es 2016 is an elegant framework for controlling the false discovery rate in variable selection. While empirical results indicate that this methodology is not too conservative, there is no conclusive theoretical result on its power. When the predictors are i.i.d.\ Gaussian, it is known that as the signal to noise ratio tend to infinity, the knockoff filter is consistent in the sense that one can make FDR go to 0 and power go to 1 simultaneously. In this work we study the case where the predictors have a general covariance matrix $\bsigma$. We introduce a simple functional called \emph{effective signal deficiency (ESD)} of the covariance matrix of the predictors that predicts consistency of various variable selection methods. In particular, ESD reveals that the structure of the precision matrix plays a central role in consistency and therefore, so does the conditional independence structure of the predictors. To leverage this connection, we introduce \emph{Conditional Independence knockoff}, a simple procedure that is able to compete with the more sophisticated knockoff filters and that is defined when the predictors obey a Gaussian tree graphical models (or when the graph is sufficiently sparse). Our theoretical results are supported by numerical evidence on synthetic data.

Sample size calculations for power analysis are critical for clinical research and trial design, yet their complexity and reliance on statistical expertise create barriers for many researchers. We introduce PowerGPT, an AI-powered system integrating large language models (LLMs) with statistical engines to automate test selection and sample size estimation in trial design. In a randomized trial to evaluate its effectiveness, PowerGPT significantly improved task completion rates (99.3% vs. 88.9% for test selection, 99.3% vs. 77.8% for sample size calculation) and accuracy (94.1% vs. 55.4% in sample size estimation, p < 0.001), while reducing average completion time (4.0 vs. 9.3 minutes, p < 0.001). These gains were consistent across various statistical tests and benefited both statisticians and non-statisticians as well as bridging expertise gaps. Already under deployment across multiple institutions, PowerGPT represents a scalable AI-driven approach that enhances accessibility, efficiency, and accuracy in statistical power analysis for clinical research.

The knockoff filter introduced by Barber and Cand\ es 2016 is an elegant framework for controlling the false discovery rate in variable selection. While empirical results indicate that this methodology is not too conservative, there is no conclusive theoretical result on its power. When the predictors are i.i.d.\ Gaussian, it is known that as the signal to noise ratio tend to infinity, the knockoff filter is consistent in the sense that one can make FDR go to 0 and power go to 1 simultaneously. In this work we study the case where the predictors have a general covariance matrix \bsigma . We introduce a simple functional called \emph{effective signal deficiency (ESD)} of the covariance matrix of the predictors that predicts consistency of various variable selection methods.

This study's first purpose is to provide quantitative evidence that would incentivize researchers to instead use the more robust method of nested cross-validation. The second purpose is to present methods and MATLAB codes for doing power analysis for ML-based analysis during the design of a study. Monte Carlo simulations were used to quantify the interactions between the employed cross-validation method, the discriminative power of features, the dimensionality of the feature space, and the dimensionality of the model. Four different cross-validations (single holdout, 10-fold, train-validation-test, and nested 10-fold) were compared based on the statistical power and statistical confidence of the ML models. Distributions of the null and alternative hypotheses were used to determine the minimum required sample size for obtaining a statistically significant outcome ({\alpha}=0.05, 1-\b{eta}=0.8). Statistical confidence of the model was defined as the probability of correct features being selected and hence being included in the final model. Our analysis showed that the model generated based on the single holdout method had very low statistical power and statistical confidence and that it significantly overestimated the accuracy. Conversely, the nested 10-fold cross-validation resulted in the highest statistical confidence and the highest statistical power, while providing an unbiased estimate of the accuracy. The required sample size with a single holdout could be 50% higher than what would be needed if nested cross-validation were used. Confidence in the model based on nested cross-validation was as much as four times higher than the confidence in the single holdout-based model. A computational model, MATLAB codes, and lookup tables are provided to assist researchers with estimating the sample size during the design of their future studies.

Many ethical frameworks require artificial intelligence (AI) systems to be explainable. Explainable AI (XAI) models are frequently tested for their adequacy in user studies. Since different people may have different explanatory needs, it is important that participant samples in user studies are large enough to represent the target population to enable generalizations. However, it is unclear to what extent XAI researchers reflect on and justify their sample sizes or avoid broad generalizations across people. We analyzed XAI user studies (n = 220) published between 2012 and 2022. Most studies did not offer rationales for their sample sizes. Moreover, most papers generalized their conclusions beyond their target population, and there was no evidence that broader conclusions in quantitative studies were correlated with larger samples. These methodological problems can impede evaluations of whether XAI systems implement the explainability called for in ethical frameworks. We outline principles for more inclusive XAI user studies.

In the experimental sciences, statistical power analyses are often used before data collection to determine the required sample size. However, traditional power analyses can be costly when data are difficult or expensive to collect. We propose synthetic power analyses; a framework for estimating statistical power at various sample sizes, and empirically explore the performance of synthetic power analysis for sample size selection in cognitive neuroscience experiments. To this end, brain imaging data is synthesized using an implicit generative model conditioned on observed cognitive processes. Further, we propose a simple procedure to modify the statistical tests which result in conservative statistics. Our empirical results suggest that synthetic power analysis could be a low-cost alternative to pilot data collection when the proposed experiments share cognitive processes with previously conducted experiments.

Despite its importance to experimental design, statistical power (the probability that, given a real effect, an experiment will reject the null hypothesis) has largely been ignored by the NLP community. Underpowered experiments make it more difficult to discern the difference between statistical noise and meaningful model improvements, and increase the chances of exaggerated findings. By meta-analyzing a set of existing NLP papers and datasets, we characterize typical power for a variety of settings and conclude that underpowered experiments are common in the NLP literature. In particular, for several tasks in the popular GLUE benchmark, small test sets mean that most attempted comparisons to state of the art models will not be adequately powered. Similarly, based on reasonable assumptions, we find that the most typical experimental design for human rating studies will be underpowered to detect small model differences, of the sort that are frequently studied. For machine translation, we find that typical test sets of 2000 sentences have approximately 75% power to detect differences of 1 BLEU point. To improve the situation going forward, we give an overview of best practices for power analysis in NLP and release a series of notebooks to assist with future power analyses.

The knockoff filter introduced by Barber and Cand\ es 2016 is an elegant framework for controlling the false discovery rate in variable selection. While empirical results indicate that this methodology is not too conservative, there is no conclusive theoretical result on its power. When the predictors are i.i.d.\ Gaussian, it is known that as the signal to noise ratio tend to infinity, the knockoff filter is consistent in the sense that one can make FDR go to 0 and power go to 1 simultaneously. In this work we study the case where the predictors have a general covariance matrix $\bsigma$. We introduce a simple functional called \emph{effective signal deficiency (ESD)} of the covariance matrix of the predictors that predicts consistency of various variable selection methods.