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Full-Text Articles in Physical Sciences and Mathematics
Parameter Estimation And Inference Of Spatial Autoregressive Model By Stochastic Gradient Descent, Gan Luan
Parameter Estimation And Inference Of Spatial Autoregressive Model By Stochastic Gradient Descent, Gan Luan
Dissertations
Stochastic gradient descent (SGD) is a popular iterative method for model parameter estimation in large-scale data and online learning settings since it goes through the data in only one pass. While SGD has been well studied for independent data, its application to spatially-correlated data largely remains unexplored. This dissertation develops SGD-based parameter estimation and statistical inference algorithms for the spatial autoregressive (SAR) model, a common model for spatial lattice data.
This research contains three parts. (I) The first part concerns SGD estimation and inference for the SAR mean regression model. A new SGD algorithm based on maximum likelihood estimator (MLE) …
Statistical Machine Learning Methods For Mining Spatial And Temporal Data, Fei Tan
Statistical Machine Learning Methods For Mining Spatial And Temporal Data, Fei Tan
Dissertations
Spatial and temporal dependencies are ubiquitous properties of data in numerous domains. The popularity of spatial and temporal data mining has thus grown with the increasing prevalence of massive data. The presence of spatial and temporal attributes not only provides complementary useful perspectives, but also poses new challenges to the representation and integration into the learning procedure. In this dissertation, the involved spatial and temporal dependencies are explored with three genres: sample-wise, feature-wise, and target-wise. A family of novel methodologies is developed accordingly for the dependency representation in respective scenarios.
First, dependencies among discrete, continuous and repeated observations are studied …