We propose an adaptive sampling approach for multiple testing which aims to maximize statistical power while ensuring anytime false discovery control.

Multiple hypothesis testing is a significant problem in nearly all neuroimaging studies. In order to correct for this phenomena, we require a reliable estimate of the Family-Wise Error Rate (FWER). The well known Bonferroni correction method, while being simple to implement, is quite conservative, and can substantially under-power a study because it ignores dependencies between test statistics. Permutation testing, on the other hand, is an exact, non parametric method of estimating the FWER for a given α threshold, but for acceptably low thresholds the computational burden can be prohibitive. In this paper, we observe that permutation testing in fact amounts to populating the columns of a very large matrix P. By analyzing the spectrum of this matrix, under certain conditions, we see that P has a low-rank plus a low-variance residual decomposition which makes it suitable for highly sub–sampled -- on the order of 0.5% -- matrix completion methods.

Editors of academic journals and program chairs of conferences require peer reviewers to write their own reviews. However, there is growing concern about the rise of lazy reviewing practices, where reviewers use large language models (LLMs) to generate reviews instead of writing them independently. Existing tools for detecting LLM-generated content are not designed to differentiate between fully LLM-generated reviews and those merely polished by an LLM. In this work, we employ a straightforward approach to identify LLM-generated reviews - doing an indirect prompt injection via the paper PDF to ask the LLM to embed a watermark. Our focus is on presenting watermarking schemes and statistical tests that maintain a bounded family-wise error rate, when a venue evaluates multiple reviews, with a higher power as compared to standard methods like Bonferroni correction. These guarantees hold without relying on any assumptions about human-written reviews. We also consider various methods for prompt injection including font embedding and jailbreaking. We evaluate the effectiveness and various tradeoffs of these methods, including different reviewer defenses. We find a high success rate in the embedding of our watermarks in LLM-generated reviews across models. We also find that our approach is resilient to common reviewer defenses, and that the bounds on error rates in our statistical tests hold in practice while having the power to flag LLM-generated reviews, while Bonferroni correction is infeasible.

Effective spoken dialog systems should facilitate natural interactions with quick and rhythmic timing, mirroring human communication patterns. To reduce response times, previous efforts have focused on minimizing the latency in automatic speech recognition (ASR) to optimize system efficiency. However, this approach requires waiting for ASR to complete processing until a speaker has finished speaking, which limits the time available for natural language processing (NLP) to formulate accurate responses. As humans, we continuously anticipate and prepare responses even while the other party is still speaking. This allows us to respond appropriately without missing the optimal time to speak. In this work, as a pioneering study toward a conversational system that simulates such human anticipatory behavior, we aim to realize a function that can predict the forthcoming words and estimate the time remaining until the end of an utterance (EOU), using the middle portion of an utterance. To achieve this, we propose a training strategy for an encoder-decoder-based ASR system, which involves masking future segments of an utterance and prompting the decoder to predict the words in the masked audio. Additionally, we develop a cross-attention-based algorithm that incorporates both acoustic and linguistic information to accurately detect the EOU. The experimental results demonstrate the proposed model's ability to predict upcoming words and estimate future EOU events up to 300ms prior to the actual EOU. Moreover, the proposed training strategy exhibits general improvements in ASR performance.

In this paper, we address conditional testing problems through the conformal inference framework. We define the localized conformal p-values by inverting prediction intervals and prove their theoretical properties. These defined p-values are then applied to several conditional testing problems to illustrate their practicality. Firstly, we propose a conditional outlier detection procedure to test for outliers in the conditional distribution with finite-sample false discovery rate (FDR) control. We also introduce a novel conditional label screening problem with the goal of screening multivariate response variables and propose a screening procedure to control the family-wise error rate (FWER). Finally, we consider the two-sample conditional distribution test and define a weighted U-statistic through the aggregation of localized p-values. Numerical simulations and real-data examples validate the superior performance of our proposed strategies.

Feature attributions are ubiquitous tools for understanding the predictions of machine learning models. However, popular methods for scoring input variables such as SHAP and LIME suffer from high instability due to random sampling. Leveraging ideas from multiple hypothesis testing, we devise attribution methods that correctly rank the most important features with high probability. Our algorithm RankSHAP guarantees that the $K$ highest Shapley values have the proper ordering with probability exceeding $1-\alpha$. Empirical results demonstrate its validity and impressive computational efficiency. We also build on previous work to yield similar results for LIME, ensuring the most important features are selected in the right order.

Multiple hypothesis testing is a significant problem in nearly all neuroimaging studies. In order to correct for this phenomena, we require a reliable estimate of the Family-Wise Error Rate (FWER). The well known Bonferroni correction method, while being simple to implement, is quite conservative, and can substantially under-power a study because it ignores dependencies between test statistics. Permutation testing, on the other hand, is an exact, non parametric method of estimating the FWER for a given α threshold, but for acceptably low thresholds the computational burden can be prohibitive. In this paper, we observe that permutation testing in fact amounts to populating the columns of a very large matrix P. By analyzing the spectrum of this matrix, under certain conditions, we see that P has a low-rank plus a low-variance residual decomposition which makes it suitable for highly sub–sampled -- on the order of 0.5% -- matrix completion methods.

After initial release of a machine learning algorithm, the model can be fine-tuned by retraining on subsequently gathered data, adding newly discovered features, or more. Each modification introduces a risk of deteriorating performance and must be validated on a test dataset. It may not always be practical to assemble a new dataset for testing each modification, especially when most modifications are minor or are implemented in rapid succession. Recent works have shown how one can repeatedly test modifications on the same dataset and protect against overfitting by (i) discretizing test results along a grid and (ii) applying a Bonferroni correction to adjust for the total number of modifications considered by an adaptive developer. However, the standard Bonferroni correction is overly conservative when most modifications are beneficial and/or highly correlated. This work investigates more powerful approaches using alpha-recycling and sequentially-rejective graphical procedures (SRGPs). We introduce novel extensions that account for correlation between adaptively chosen algorithmic modifications. In empirical analyses, the SRGPs control the error rate of approving unacceptable modifications and approve a substantially higher number of beneficial modifications than previous approaches.

Multiple testing adjustment has gained in popularity with large scale datasets used for exploratory purposes. It is now a key consideration in statistical inference problems.

We consider the inference problem for high-dimensional linear models, when covariates have an underlying spatial organization reflected in their correlation. A typical example of such a setting is high-resolution imaging, in which neighboring pixels are usually very similar. Accurate point and confidence intervals estimation is not possible in this context with many more covariates than samples, furthermore with high correlation between covariates. This calls for a reformulation of the statistical inference problem, that takes into account the underlying spatial structure: if covariates are locally correlated, it is acceptable to detect them up to a given spatial uncertainty. We thus propose to rely on the $\delta$-FWER, that is the probability of making a false discovery at a distance greater than $\delta$ from any true positive. With this target measure in mind, we study the properties of ensembled clustered inference algorithms which combine three techniques: spatially constrained clustering, statistical inference, and ensembling to aggregate several clustered inference solutions. We show that ensembled clustered inference algorithms control the $\delta$-FWER under standard assumptions for $\delta$ equal to the largest cluster diameter. We complement the theoretical analysis with empirical results, demonstrating accurate $\delta$-FWER control and decent power achieved by such inference algorithms.