Yong Gao

Han Wang, Zhou Huang, Ganmin Yin et al.

The geographically weighted regression (GWR) is an essential tool for estimating the spatial variation of relationships between dependent and independent variables in geographical contexts. However, GWR suffers from the problem that classical linear regressions, which compose the GWR model, are more prone to be underfitting, especially for significant volume and complex nonlinear data, causing inferior comparative performance. Nevertheless, some advanced models, such as the decision tree and the support vector machine, can learn features from complex data more effectively while they cannot provide explainable quantification for the spatial variation of localized relationships. To address the above issues, we propose a geographically gradient boosting weighted regression model, GWRBoost, that applies the localized additive model and gradient boosting optimization method to alleviate underfitting problems and retains explainable quantification capability for spatially-varying relationships between geographically located variables. Furthermore, we formulate the computation method of the Akaike information score for the proposed model to conduct the comparative analysis with the classic GWR algorithm. Simulation experiments and the empirical case study are applied to prove the efficient performance and practical value of GWRBoost. The results show that our proposed model can reduce the RMSE by 18.3% in parameter estimation accuracy and AICc by 67.3% in the goodness of fit.

Congsong Zhang, Yong Gao, James Nastos

Backtracking has been widely used for solving problems in artificial intelligence (AI), including constraint satisfaction problems and combinatorial optimization problems. Good branching heuristics can efficiently improve the performance of backtracking by helping prune the search space and leading the search to the most promising direction. In this paper, we first propose a new graph neural network (GNN) model designed using the probabilistic method. From the GNN model, we introduce an approach to learn a branching heuristic for combinatorial optimization problems. In particular, our GNN model learns appropriate probability distributions on vertices in given graphs from which the branching heuristic is extracted and used in a backtracking search. Our experimental results for the (minimum) dominating-clique problem show that this learned branching heuristic performs better than the minimum-remaining-values heuristic in terms of the number of branches of the whole search tree. Our approach introduces a new way of applying GNNs towards enhancing the classical backtracking algorithm used in AI.