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1. LMLFM: Longitudinal Multi-Level Factorization Machine

   Liang, Junjie; Xu, Dongkuan; Sun, Yiwei; Honavar, Vasant G. (January 2020, Proceedings of the 34th AAAI Conference on Artficial Intelligence)

   We consider the problem of learning predictive models from longitudinal data, consisting of irregularly repeated, sparse observations from a set of individuals over time. Such data of- ten exhibit longitudinal correlation (LC) (correlations among observations for each individual over time), cluster correlation (CC) (correlations among individuals that have similar char- acteristics), or both. These correlations are often accounted for using mixed effects models that include fixed effects and random effects, where the fixed effects capture the regression parameters that are shared by all individuals, whereas random effects capture those parameters that vary across individuals. However, the current state-of-the-art methods are unable to se- lect the most predictive fixed effects and random effects from a large number of variables, while accounting for complex cor- relation structure in the data and non-linear interactions among the variables. We propose Longitudinal Multi-Level Factoriza- tion Machine (LMLFM), to the best of our knowledge, the first model to address these challenges in learning predictive mod- els from longitudinal data. We establish the convergence prop- erties, and analyze the computational complexity, of LMLFM. We present results of experiments with both simulated and real-world longitudinal data which show that LMLFM out- performs the state-of-the-art methods in terms of predictive accuracy, variable selection ability, and scalability to data with large number of variables. The code and supplemental material is available at https://github.com/junjieliang672/LMLFM. 

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2. Longitudinal Deep Kernel Gaussian Process Regression

   Liang, Junjie; Wu, Yanting; Xu, Dongxuan; Honavar, Vasant (January 2021, Proceedings of the AAAI Conference on Artificial Intelligence)

   null (Ed.)

   Gaussian processes offer an attractive framework for predictive modeling from longitudinal data, i.e., irregularly sampled, sparse observations from a set of individuals over time. However, such methods have two key shortcomings: (i) They rely on ad hoc heuristics or expensive trial and error to choose the effective kernels, and (ii) They fail to handle multilevel correlation structure in the data. We introduce Longitudinal deep kernel Gaussian process regression (L-DKGPR) to overcome these limitations by fully automating the discovery of complex multilevel correlation structure from longitudinal data. Specifically, L-DKGPR eliminates the need for ad hoc heuristics or trial and error using a novel adaptation of deep kernel learning that combines the expressive power of deep neural networks with the flexibility of non-parametric kernel methods. L-DKGPR effectively learns the multilevel correlation with a novel additive kernel that simultaneously accommodates both time-varying and the time-invariant effects. We derive an efficient algorithm to train L-DKGPR using latent space inducing points and variational inference. Results of extensive experiments on several benchmark data sets demonstrate that L-DKGPR significantly outperforms the state-of-the-art longitudinal data analysis (LDA) methods. 

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3. Spatial variability of site effects and its correlation with site response in Japan

   https://doi.org/10.3208/jgssp.v10.P2-25  

   Lorenzo-Velazquez, Cristina; Cabas, Ashly (January 2024, Japanese Geotechnical Society Special Publication)

   Local soil conditions depict an important role in regional seismic hazard assessments due to their influence on earthquake-induced ground shaking and deformation. The different levels of damage and site response at nearby locations correlate to site and geologic conditions variability, as has been reported after past earthquakes. Evaluating spatially variable ground motions (GMs) is key for earthquake reconnaissance efforts and regional seismic hazard assessments. This study focuses on the evaluation of spatial correlations in site parameters (e.g. time-averaged shear-wave velocity to a depth of 30 meters) at Kiban-Kyoshin Network (KiK-net), and their comparison to the observed spatial correlation residuals from ground motion intensity measures (IMs) from the Mw9.1 Tohoku earthquake. Current spatial correlation models treat site effects either as a fixed amplification factor or as randomized amplifications, but site effects are neither fixed nor random. Hence, geostatistical methods are used here to estimate spatial correlations between parameters that control site response and integrate their effects on resulting spatially variable ground motions. In this work, we evaluate the significance of the spatial correlation for different site parameters with respect to the GM amplification IMs residuals. 

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4. Dynamical Gaussian Process Latent Variable Model for Representation Learning from Longitudinal Data

   https://doi.org/10.1145/3412815.3416894  

   Le, Thanh; Honavar, Vasant (January 2020, ACM/IMS Conference on Foundations of Data Science)

   null (Ed.)

   Many real-world applications involve longitudinal data, consisting of observations of several variables, where different subsets of variables are sampled at irregularly spaced time points. We introduce the Longitudinal Gaussian Process Latent Variable Model (L-GPLVM), a variant of the Gaussian Process Latent Variable Model, for learning compact representations of such data. L-GPLVM overcomes a key limitation of the Dynamic Gaussian Process Latent Variable Model and its variants, which rely on the assumption that the data are fully observed over all of the sampled time points. We describe an effective approach to learning the parameters of L-GPLVM from sparse observations, by coupling the dynamical model with a Multitask Gaussian Process model for sampling of the missing observations at each step of the gradient-based optimization of the variational lower bound. We further show the advantage of the Sparse Process Convolution framework to learn the latent representation of sparsely and irregularly sampled longitudinal data with minimal computational overhead relative to a standard Latent Variable Model. We demonstrated experiments with synthetic data as well as variants of MOCAP data with varying degrees of sparsity of observations that show that L-GPLVM substantially and consistently outperforms the state-of-the-art alternatives in recovering the missing observations even when the available data exhibits a high degree of sparsity. The compact representations of irregularly sampled and sparse longitudinal data can be used to perform a variety of machine learning tasks, including clustering, classification, and regression. 

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5. A Novel Method for Detecting Intersectional DIF: Multilevel Random Item Effects Model with Regularized Gaussian Variational Estimation

   https://doi.org/10.1017/psy.2025.10046  

   Ren, He; Lyu, Weicong; Wang, Chun; Xu, Gongjun (September 2025, Psychometrika)

   Abstract Differential item functioning (DIF) screening has long been suggested to ensure assessment fairness. Traditional DIF methods typically focus on the main effects of demographic variables on item parameters, overlooking the interactions among multiple identities. Drawing on the intersectionality framework, we define intersectional DIF as deviations in item parameters that arise from the interactions among demographic variables beyond their main effects and propose a novel item response theory (IRT) approach for detecting intersectional DIF. Under our framework, fixed effects are used to account for traditional DIF, while random item effects are introduced to capture intersectional DIF. We further introduce the concept of intersectional impact, which refers to interaction effects on group-level mean ability. Depending on which item parameters are affected and whether intersectional impact is considered, we propose four models, which aim to detect intersectional uniform DIF (UDIF), intersectional UDIF with intersectional impact, intersectional non-uniform DIF (NUDIF), and intersectional NUDIF with intersectional impact, respectively. For efficient model estimation, a regularized Gaussian variational expectation-maximization algorithm is developed. Simulation studies demonstrate that our methods can effectively detect intersectional UDIF, although their detection of intersectional NUDIF is more limited. 

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