Research on Mathematical Modeling and Statistical Analysis of Complex Datasets Based on Machine Learning

Abstract

With the explosive growth of data scale, the high-dimensional sparsity, dynamic evolution and multi-source heterogeneity of complex data sets have brought great challenges to traditional statistical modeling methods. Machine learning provides a new paradigm for complex data modeling with its ability of nonlinear function approximation and automatic feature learning. However, the pure data-driven machine learning model has some problems such as poor interpretability and insufficient robustness. This article proposes a Dynamic Statistical Constrained Deep Learning (DSC-DL), which integrates techniques such as graph neural networks (GNN), Bayesian dynamic regularization, and multimodal variational encoders to address the challenges of complex data. DSC-DL deals with high-dimensional sparsity by structural feature selection and graph embedding dimension reduction technology, captures dynamic evolution by time-aware hidden variable modeling, and realizes multi-source heterogeneous fusion through joint variational inference and adaptive fusion mechanism. In this paper, the generalization error bound of DSC-DL under dependent identically distributed data is derived, which provides theoretical guarantee for its robustness. Experimental results on financial fraud detection, social topic prediction and cancer typing diagnosis show that DSC-DL can effectively handle complex data sets, and shows excellent prediction performance, robustness and interpretability.