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1. Time‐varying feature selection for longitudinal analysis

   https://doi.org/10.1002/sim.8412  

   Xue, Lan; Shu, Xinxin; Shi, Peibei; Wu, Colin_O; Qu, Annie (November 2019, Statistics in Medicine)

   We propose time‐varying coefficient model selection and estimation based on the spline approach, which is capable of capturing time‐dependent covariate effects. The new penalty function utilizes local‐region information for varying‐coefficient estimation, in contrast to the traditional model selection approach focusing on the entire region. The proposed method is extremely useful when the signals associated with relevant predictors are time‐dependent, and detecting relevant covariate effects in the local region is more scientifically relevant than those of the entire region. Our simulation studies indicate that the proposed model selection incorporating local features outperforms the global feature model selection approaches. The proposed method is also illustrated through a longitudinal growth and health study from National Heart, Lung, and Blood Institute. 

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2. Physics-Constrained Dictionary Learning for Selective Laser Melting Process Monitoring

   Lu, Yanglong; Wang, Yan (May 2021, Proceedings of 2021 IISE Annual Conference & Expo)

   null (Ed.)

   Compressed sensing (CS) as a new data acquisition technique has been applied to monitor manufacturing processes. With a few measurements, sparse coefficient vectors can be recovered by solving an inverse problem and original signals can be reconstructed. Dictionary learning methods have been developed and applied in combination with CS to improve the sparsity level of the recovered coefficient vectors. In this work, a physics-constrained dictionary learning approach is proposed to solve both of reconstruction and classification problems by optimizing measurement, basis, and classification matrices simultaneously with the considerations of the application-specific restrictions. It is applied in image acquisitions in selective laser melting (SLM). The proposed approach includes the optimization in two steps. In the first stage, with the basis matrix fixed, the measurement matrix is optimized by determining the pixel locations for sampling in each image. The optimized measurement matrix only includes one non-zero entry in each row. The optimization of pixel locations is solved based on a constrained FrameSense algorithm. In the second stage, with the measurement matrix fixed, the basis and classification matrices are optimized based on the K-SVD algorithm. With the optimized basis matrix, the coefficient vector can be recovered with CS. The original signal can be reconstructed by the linear combination of the basis matrix and the recovered coefficient vector. The original signal can also be classified to identify different machine states by the linear combination of the classification matrix and the coefficient vector. 

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3. Geostatistical modeling of positive‐definite matrices: An application to diffusion tensor imaging

   https://doi.org/10.1111/biom.13445  

   Lan, Zhou; Reich, Brian J.; Guinness, Joseph; Bandyopadhyay, Dipankar; Ma, Liangsuo; Moeller, F. Gerard (June 2022, Biometrics)

   Abstract Geostatistical modeling for continuous point‐referenced data has extensively been applied to neuroimaging because it produces efficient and valid statistical inference. However, diffusion tensor imaging (DTI), a neuroimaging technique characterizing the brain's anatomical structure, produces a positive‐definite (p.d.) matrix for each voxel. Currently, only a few geostatistical models for p.d. matrices have been proposed because introducing spatial dependence among p.d. matrices properly is challenging. In this paper, we use the spatial Wishart process, a spatial stochastic process (random field), where each p.d. matrix‐variate random variable marginally follows a Wishart distribution, and spatial dependence between random matrices is induced by latent Gaussian processes. This process is valid on an uncountable collection of spatial locations and is almost‐surely continuous, leading to a reasonable way of modeling spatial dependence. Motivated by a DTI data set of cocaine users, we propose a spatial matrix‐variate regression model based on the spatial Wishart process. A problematic issue is that the spatial Wishart process has no closed‐form density function. Hence, we propose an approximation method to obtain a feasible Cholesky decomposition model, which we show to be asymptotically equivalent to the spatial Wishart process model. A local likelihood approximation method is also applied to achieve fast computation. The simulation studies and real data application demonstrate that the Cholesky decomposition process model produces reliable inference and improved performance, compared to other methods. 

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4. Estimation of Dynamic Networks for High-Dimensional Nonstationary Time Series

   https://doi.org/10.3390/e22010055  

   Xu, Mengyu; Chen, Xiaohui; Wu, Wei Biao (January 2020, Entropy)

   This paper is concerned with the estimation of time-varying networks for high-dimensional nonstationary time series. Two types of dynamic behaviors are considered: structural breaks (i.e., abrupt change points) and smooth changes. To simultaneously handle these two types of time-varying features, a two-step approach is proposed: multiple change point locations are first identified on the basis of comparing the difference between the localized averages on sample covariance matrices, and then graph supports are recovered on the basis of a kernelized time-varying constrained L 1 -minimization for inverse matrix estimation (CLIME) estimator on each segment. We derive the rates of convergence for estimating the change points and precision matrices under mild moment and dependence conditions. In particular, we show that this two-step approach is consistent in estimating the change points and the piecewise smooth precision matrix function, under a certain high-dimensional scaling limit. The method is applied to the analysis of network structure of the S&P 500 index between 2003 and 2008. 

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5. TIME-VARYING ESTIMATION AND DYNAMIC MODEL SELECTION WITH AN APPLICATION OF NETWORK DATA

   Lan Xue, Xinxin Shu (January 2020, Statistica sinica)

   In many biomedical and social science studies, it is important to identify and predict the dynamic changes of associations among network data over time. We propose a varying-coefficient model to incorporate time-varying network data, and impose a piecewise penalty function to capture local features of the network associations. The proposed approach is semi-parametric, and therefore flexible in modeling dynamic changes of association in network data problems. Furthermore, the approach can identify the time regions when dynamic changes of associations occur. To achieve a sparse network estimation at local time intervals, we implement a group penalization strategy involving parameters that overlap between groups. However, this makes the optimization process challenging for large-dimensional network data observed at many time points. We develop a fast algorithm, based on the smoothing proximal-gradient method, that is computationally efficient and accurate. We illustrate the proposed method through simulation studies and children's attention deficit hyperactivity disorder fMRI data, showing that the proposed method and algorithm recover dynamic network changes over time efficiently. 

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