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1. 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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2. Modeling of Collective Cell Behaviors Interacting With Extracellular Matrix Using Dual Faceted Linearization

   https://doi.org/10.1115/DSCC2018-9164  

   Mayalu, Michaëlle N. ; Kim, Min-Cheol ; Asada, H. Harry ( September 2018 , 2018 ASME Dynamic Systems and Control Conference)

   Cells interacting over an extracellular matrix (ECM) exhibit emergent behaviors, which are often observably different from single-cell dynamics. Fibroblasts embedded in a 3-D ECM, for example, compact the surrounding gel and generate an anisotropic strain field, which cannot be observed in single cellinduced gel compaction. This emergent matrix behavior results from collective intracellular mechanical interaction and is crucial to explain the large deformations and mechanical tensions that occur during embryogenesis, tissue development and wound healing. Prediction of multi-cellular interactions entails nonlinear dynamic simulation, which is prohibitively complex to compute using first principles especially as the number of cells increase. Here, we introduce a new methodology for predicting nonlinear behaviors of multiple cells interacting mechanically through a 3D ECM. In the proposed method, we first apply Dual- Faceted Linearization to nonlinear dynamic systems describing cell/matrix behavior. Using this unique linearization method, the original nonlinear state equations can be expressed with a pair of linear dynamic equations by augmenting the independent state variables with auxiliary variables which are nonlinearly dependent on the original states. Furthermore, we can find a reduced order latent space representation of the dynamic equations by orthogonal projection onto the basis of a lower dimensional linear manifold within the augmented variable space. Once converted to latent variable equations, we superpose multiple dynamic systems to predict their collective behaviors. The method is computationally efficient and accurate as demonstrated through its application for prediction of emergent cell induced ECM compaction. 

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3. Disentangling ferroelectric domain wall geometries and pathways in dynamic piezoresponse force microscopy via unsupervised machine learning

   https://doi.org/10.1088/1361-6528/ac2f5b  

   Kalinin, Sergei V ; Steffes, James J ; Liu, Yongtao ; Huey, Bryan D ; Ziatdinov, Maxim ( November 2021 , Nanotechnology)

   Abstract Domain switching pathways in ferroelectric materials visualized by dynamic piezoresponse force microscopy (PFM) are explored via variational autoencoder, which simplifies the elements of the observed domain structure, crucially allowing for rotational invariance, thereby reducing the variability of local polarization distributions to a small number of latent variables. For small sampling window sizes the latent space is degenerate, and variability is observed only in the direction of a single latent variable that can be identified with the presence of domain wall. For larger window sizes, the latent space is 2D, and the disentangled latent variables can be generally interpreted as the degree of switching and complexity of domain structure. Applied to multiple consecutive PFM images acquired while monitoring domain switching, the polarization switching mechanism can thus be visualized in the latent space, providing insight into domain evolution mechanisms and their correlation with the microstructure. 

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4. Regression of binary network data with exchangeable latent errors

   https://doi.org/10.1017/nws.2023.12  

   Marrs, Frank W ; Fosdick, Bailey K ( September 2023 , Network Science)

   Undirected, binary network data consist of indicators of symmetric relations between pairs of actors. Regression models of such data allow for the estimation of effects of exogenous covariates on the network and for prediction of unobserved data. Ideally, estimators of the regression parameters should account for the inherent dependencies among relations in the network that involve the same actor. To account for such dependencies, researchers have developed a host of latent variable network models; however, estimation of many latent variable network models is computationally onerous and which model is best to base inference upon may not be clear. We propose the probit exchangeable (PX) model for undirected binary network data that is based on an assumption of exchangeability, which is common to many of the latent variable network models in the literature. The PX model can represent the first two moments of any exchangeable network model. We leverage the EM algorithm to obtain an approximate maximum likelihood estimator of the PX model that is extremely computationally efficient. Using simulation studies, we demonstrate the improvement in estimation of regression coefficients of the proposed model over existing latent variable network models. In an analysis of purchases of politically aligned books, we demonstrate political polarization in purchase behavior and show that the proposed estimator significantly reduces runtime relative to estimators of latent variable network models, while maintaining predictive performance. 

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5. Modeling Dynamic Missingness of Implicit Feedback for Recommendation

   Menghan Wang, Mingming Gong ( December 2018 , Advances in neural information processing systems)

   Implicit feedback is widely used in collaborative filtering methods for recommendation. It is well known that implicit feedback contains a large number of values that are missing not at random (MNAR); and the missing data is a mixture of negative and unknown feedback, making it difficult to learn users’ negative preferences. Recent studies modeled exposure, a latent missingness variable which indicates whether an item is exposed to a user, to give each missing entry a confidence of being negative feedback. However, these studies use static models and ignore the information in temporal dependencies among items, which seems to be an essential underlying factor to subsequent missingness. To model and exploit the dynamics of missingness, we propose a latent variable named “user intent” to govern the temporal changes of item missingness, and a hidden Markov model to represent such a process. The resulting framework captures the dynamic item missingness and incorporate it into matrix factorization (MF) for recommendation. We also explore two types of constraints to achieve a more compact and interpretable representation of user intents. Experiments on real-world datasets demonstrate the superiority of our method against state-of-the-art recommender systems. 

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