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1. A continuous statistical-geometric framework for normative and impaired gaits

   https://doi.org/10.1098/rsif.2022.0402  

   Swaminathan, Krithika; Tolkova, Irina; Baker, Lauren; Arumukhom Revi, Dheepak; Awad, Louis N.; Walsh, Conor J.; Mahadevan, L. (November 2022, Journal of The Royal Society Interface)

   A quantitative analysis of human gait patterns in space–time provides an opportunity to observe variability within and across individuals of varying motor capabilities. Impaired gait significantly affects independence and quality of life, and thus a large part of clinical research is dedicated to improving gait through rehabilitative therapies. Evaluation of these paradigms relies on understanding the characteristic differences in the kinematics and underlying biomechanics of impaired and unimpaired locomotion, which has motivated quantitative measurement and analysis of the gait cycle. Previous analysis has largely been limited to a statistical comparison of manually selected pointwise metrics identified through expert knowledge. Here, we use a recent statistical-geometric framework, elastic functional data analysis (FDA), to decompose kinematic data into continuous ‘amplitude’ (spatial) and ‘phase’ (temporal) components, which can then be integrated with established dimensionality reduction techniques. We demonstrate the utility of elastic FDA through two unsupervised applications to post-stroke gait datasets. First, we distinguish between unimpaired, paretic and non-paretic gait presentations. Then, we use FDA to reveal robust, interpretable groups of differential response to exosuit assistance. The proposed methods aim to benefit clinical practice for post-stroke gait rehabilitation, and more broadly, to automate the quantitative analysis of motion. 

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2. Distinct value computations support rapid sequential decisions

   https://doi.org/10.1038/s41467-023-43250-x  

   Mah, Andrew; Schiereck, Shannon S.; Bossio, Veronica; Constantinople, Christine M. (November 2023, Nature Communications)

   Abstract The value of the environment determines animals’ motivational states and sets expectations for error-based learning^1–3. How are values computed? Reinforcement learning systems can store or cache values of states or actions that are learned from experience, or they can compute values using a model of the environment to simulate possible futures³. These value computations have distinct trade-offs, and a central question is how neural systems decide which computations to use or whether/how to combine them^4–8. Here we show that rats use distinct value computations for sequential decisions within single trials. We used high-throughput training to collect statistically powerful datasets from 291 rats performing a temporal wagering task with hidden reward states. Rats adjusted how quickly they initiated trials and how long they waited for rewards across states, balancing effort and time costs against expected rewards. Statistical modeling revealed that animals computed the value of the environment differently when initiating trials versus when deciding how long to wait for rewards, even though these decisions were only seconds apart. Moreover, value estimates interacted via a dynamic learning rate. Our results reveal how distinct value computations interact on rapid timescales, and demonstrate the power of using high-throughput training to understand rich, cognitive behaviors. 

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3. Federated Choquet Regression with LASSO for Outcome Prediction in Multisite Longitudinal Trial Data

   https://doi.org/10.1145/3761824  

   Lomasov, Semyon; Fang, Hua; Wang, Honggang (October 2025, ACM Transactions on Computing for Healthcare)

   Aggregating person-level data across multiple clinical study sites is often constrained by privacy regulations, necessitating the development of decentralized modeling approaches in biomedical research. To address this requirement, a federated nonlinear regression algorithm based on the Choquet integral has been introduced for outcome prediction. This approach avoids reliance on prior statistical assumptions about data distribution and captures feature interactions, reflecting the non-additive nature of biomedical data characteristics. This work represents the first theoretical application of Choquet integral regression to multisite longitudinal trial data within a federated learning framework. The Multiple Imputation Choquet Integral Regression with LASSO (MIChoquet-LASSO) algorithm is specifically designed to reduce overfitting and enable variable selection in federated learning settings. Its performance has been evaluated using synthetic datasets, publicly available biomedical datasets, and proprietary longitudinal randomized controlled trial data. Comparative evaluations were conducted against benchmark methods, including ordinary least squares (OLS) regression and Choquet-OLS regression, under various scenarios such as model misspecification and both linear and nonlinear data structures in non-federated and federated contexts. Mean squared error was used as the primary performance metric. Results indicate that MIChoquet-LASSO outperforms compared models in handling nonlinear longitudinal data with missing values, particularly in scenarios prone to overfitting. In federated settings, Choquet-OLS underperforms, whereas the federated variant of the model, FEDMIChoquet-LASSO, demonstrates consistently better performance. These findings suggest that FEDMIChoquet-LASSO offers a reliable solution for outcome prediction in multisite longitudinal trials, addressing challenges such as missing values, nonlinear relationships, and privacy constraints while maintaining strong performance within the federated learning framework. 

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4. Statistical Significance for Hierarchical Clustering

   https://doi.org/10.1111/biom.12647  

   Kimes, Patrick K.; Liu, Yufeng; Hayes, David Neil; Marron, James Stephen (January 2017, Biometrics)

   Summary Cluster analysis has proved to be an invaluable tool for the exploratory and unsupervised analysis of high-dimensional datasets. Among methods for clustering, hierarchical approaches have enjoyed substantial popularity in genomics and other fields for their ability to simultaneously uncover multiple layers of clustering structure. A critical and challenging question in cluster analysis is whether the identified clusters represent important underlying structure or are artifacts of natural sampling variation. Few approaches have been proposed for addressing this problem in the context of hierarchical clustering, for which the problem is further complicated by the natural tree structure of the partition, and the multiplicity of tests required to parse the layers of nested clusters. In this article, we propose a Monte Carlo based approach for testing statistical significance in hierarchical clustering which addresses these issues. The approach is implemented as a sequential testing procedure guaranteeing control of the family-wise error rate. Theoretical justification is provided for our approach, and its power to detect true clustering structure is illustrated through several simulation studies and applications to two cancer gene expression datasets. 

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5. Precise unbiased estimation in randomized experiments using auxiliary observational data

   https://doi.org/10.1515/jci-2022-0011  

   Gagnon-Bartsch, Johann A.; Sales, Adam C.; Wu, Edward; Botelho, Anthony F.; Erickson, John A.; Miratrix, Luke W.; Heffernan, Neil T. (January 2023, Journal of Causal Inference)

   Abstract Randomized controlled trials (RCTs) admit unconfounded design-based inference – randomization largely justifies the assumptions underlying statistical effect estimates – but often have limited sample sizes. However, researchers may have access to big observational data on covariates and outcomes from RCT nonparticipants. For example, data from A/B tests conducted within an educational technology platform exist alongside historical observational data drawn from student logs. We outline a design-based approach to using such observational data for variance reduction in RCTs. First, we use the observational data to train a machine learning algorithm predicting potential outcomes using covariates and then use that algorithm to generate predictions for RCT participants. Then, we use those predictions, perhaps alongside other covariates, to adjust causal effect estimates with a flexible, design-based covariate-adjustment routine. In this way, there is no danger of biases from the observational data leaking into the experimental estimates, which are guaranteed to be exactly unbiased regardless of whether the machine learning models are “correct” in any sense or whether the observational samples closely resemble RCT samples. We demonstrate the method in analyzing 33 randomized A/B tests and show that it decreases standard errors relative to other estimators, sometimes substantially. 

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