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1. Robustness Metric for Robust Design Optimization Under Time- and Space-Dependent Uncertainty Through Metamodeling

   https://doi.org/https://doi.org/10.1115/1.4045599  

   Xinpeng Wei, Xiaoping Du (January 2020, Journal of mechanical design)

   Product performance varies with respect to time and space in many engineering applications. This paper discusses how to measure and evaluate the robustness of a product or component when its quality characteristics (QCs) are functions of random variables, random fields, temporal variables, and spatial variables. At first, the existing time-dependent robustness metric is extended to the present time- and space-dependent problem. The robustness metric is derived using the extreme value of the quality characteristics with respect to temporal and spatial variables for the nominal-the-better type quality characteristics. Then, a metamodel-based numerical procedure is developed to evaluate the new robustness metric. The procedure employs a Gaussian Process regression method to estimate the expected quality loss that involves the extreme quality characteristics. The expected quality loss is obtained directly during the regression model building process. Four examples are used to demonstrate the robustness analysis method. The proposed method can be used for robustness analysis during robust design optimization (RDO) under time- and space-dependent uncertainty. 

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2. Real-time detection of clustered events in video-imaging data with applications to additive manufacturing

   https://doi.org/10.1080/24725854.2021.1882013  

   Yan, Hao; Grasso, Marco; Paynabar, Kamran; Colosimo, Bianca Maria (January 2021, IISE Transactions)

   The use of video-imaging data for in-line process monitoring applications has become popular in industry. In this framework, spatio-temporal statistical process monitoring methods are needed to capture the relevant information content and signal possible out-of-control states. Video-imaging data are characterized by a spatio-temporal variability structure that depends on the underlying phenomenon, and typical out-of-control patterns are related to events that are localized both in time and space. In this article, we propose an integrated spatio-temporal decomposition and regression approach for anomaly detection in video-imaging data. Out-of-control events are typically sparse, spatially clustered and temporally consistent. The goal is not only to detect the anomaly as quickly as possible (“when”) but also to locate it in space (“where”). The proposed approach works by decomposing the original spatio-temporal data into random natural events, sparse spatially clustered and temporally consistent anomalous events, and random noise. Recursive estimation procedures for spatio-temporal regression are presented to enable the real-time implementation of the proposed methodology. Finally, a likelihood ratio test procedure is proposed to detect when and where the anomaly happens. The proposed approach was applied to the analysis of high-sped video-imaging data to detect and locate local hot-spots during a metal additive manufacturing process. 

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3. REDS: Random ensemble deep spatial prediction

   https://doi.org/10.1002/env.2780  

   Daw, Ranadeep; Wikle, Christopher_K (December 2022, Environmetrics)

   Abstract There has been a great deal of recent interest in the development of spatial prediction algorithms for very large datasets and/or prediction domains. These methods have primarily been developed in the spatial statistics community, but there has been growing interest in the machine learning community for such methods, primarily driven by the success of deep Gaussian process regression approaches and deep convolutional neural networks. These methods are often computationally expensive to train and implement and consequently, there has been a resurgence of interest in random projections and deep learning models based on random weights—so called reservoir computing methods. Here, we combine several of these ideas to develop the random ensemble deep spatial (REDS) approach to predict spatial data. The procedure uses random Fourier features as inputs to an extreme learning machine (a deep neural model with random weights), and with calibrated ensembles of outputs from this model based on different random weights, it provides a simple uncertainty quantification. The REDS method is demonstrated on simulated data and on a classic large satellite data set. 

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4. Spatially and Robustly Hybrid Mixture Regression Model for Inference of Spatial Dependence

   https://doi.org/10.1109/ICDM51629.2021.00013  

   Chang, Wennan; Dang, Pengdao; Wan, Changlin; Lu, Xiaoyu; Fang, Yue; Zhao, Tong; Zang, Yong; Li, Bo; Zhang, Chi; Cao, Sha (December 2021, 2021 IEEE International Conference on Data Mining (ICDM))

   In this paper, we propose a Spatial Robust Mixture Regression model to investigate the relationship between a response variable and a set of explanatory variables over the spatial domain, assuming that the relationships may exhibit complex spatially dynamic patterns that cannot be captured by constant regression coefficients. Our method integrates the robust finite mixture Gaussian regression model with spatial constraints, to simultaneously handle the spatial non-stationarity, local homogeneity, and outlier contaminations. Compared with existing spatial regression models, our proposed model assumes the existence a few distinct regression models that are estimated based on observations that exhibit similar response-predictor relationships. As such, the proposed model not only accounts for non-stationarity in the spatial trend, but also clusters observations into a few distinct and homogenous groups. This provides an advantage on interpretation with a few stationary sub-processes identified that capture the predominant relationships between response and predictor variables. Moreover, the proposed method incorporates robust procedures to handle contaminations from both regression outliers and spatial outliers. By doing so, we robustly segment the spatial domain into distinct local regions with similar regression coefficients, and sporadic locations that are purely outliers. Rigorous statistical hypothesis testing procedure has been designed to test the significance of such segmentation. Experimental results on many synthetic and real-world datasets demonstrate the robustness, accuracy, and effectiveness of our proposed method, compared with other robust finite mixture regression, spatial regression and spatial segmentation methods. 

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5. Regression from Dependent Observations

   Daskalakis, Constantinos; Dikkala, Nishanth; Panageas, Ioannis (January 2019, 51st Annual ACM Symposium on the Theory of Computing)

   The standard linear and logistic regression models assume that the response variables are independent, but share the same linear relationship to their corresponding vectors of covariates. The assumption that the response variables are independent is, however, too strong. In many applications, these responses are collected on nodes of a network, or some spatial or temporal domain, and are dependent. Examples abound in financial and meteorological applications, and dependencies naturally arise in social networks through peer effects. Regression with dependent responses has thus received a lot of attention in the Statistics and Economics literature, but there are no strong consistency results unless multiple independent samples of the vectors of dependent responses can be collected from these models. We present computationally and statistically efficient methods for linear and logistic regression models when the response variables are dependent on a network. Given one sample from a networked linear or logistic regression model and under mild assumptions, we prove strong consistency results for recovering the vector of coefficients and the strength of the dependencies, recovering the rates of standard regression under independent observations. We use projected gradient descent on the negative log-likelihood, or negative log-pseudolikelihood, and establish their strong convexity and consistency using concentration of measure for dependent random variables. 

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