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Explore a comprehensive conference talk examining the evolution of geometric thinking in statistical modeling, from Francis Galton's pioneering 1886 elliptical visualizations to modern explainable artificial intelligence approaches. Discover how Galton's geometric insights into regression toward the mean and bivariate normal distributions established the foundation for classical multivariate analysis techniques including principal component analysis and canonical correlation, while profoundly influencing contemporary methods like diffusion models. Learn about the challenges that unstructured big data presents to traditional parsimonious statistical models and understand why deep learning models with billions of parameters sacrifice transparency for predictive excellence, creating the "black-box" dilemma central to explainable AI research. Examine a novel data molding perspective that moves beyond conventional data modeling approaches by shifting focus from "what the data is" to "what the data can be used for," leveraging the plasticity of unstructured big data through elementary geometric concepts. Investigate the connections between manifold learning, helical confounding, and liquid association while exploring two innovative concepts: mold-compliance and artificial-trait configurative-generation (ATCG). Understand how these concepts guide new algorithms for image data investigation that address prediction validity and within-class heterogeneity issues, and see how data molding transforms feature space extraction, shifting investigation focus from out-of-distribution detection to mold-violation analysis and from UMAP clustering to ATCG-induced hierarchical clustering methods.
