mlsanityData to 7 Oct 2026

Changes from Classical Statistics to Modern Statistics and Data Science

arXiv 2211.03756 ↗First posted 30 Oct 2022stat.ME cs.LGcited by 0

On the map: Diffusion models → Diffusion foundations and sampling

Abstract (arXiv)

A coordinate system is a foundation for every quantitative science, engineering, and medicine. Classical physics and statistics are based on the Cartesian coordinate system. The classical probability and hypothesis testing theory can only be applied to Euclidean data. However, modern data in the real world are from natural language processing, mathematical formulas, social networks, transportation and sensor networks, computer visions, automations, and biomedical measurements. The Euclidean assumption is not appropriate for non Euclidean data. This perspective addresses the urgent need to overcome those fundamental limitations and encourages extensions of classical probability theory and hypothesis testing , diffusion models and stochastic differential equations from Euclidean space to non Euclidean space. Artificial intelligence such as natural language processing, computer vision, graphical neural networks, manifold regression and inference theory, manifold learning, graph neural networks, compositional diffusion models for automatically compositional generations of concepts and demystifying machine learning systems, has been rapidly developed. Differential manifold theory is the mathematic foundations of deep learning and data science as well. We urgently need to shift the paradigm for data analysis from the classical Euclidean data analysis to both Euclidean and non Euclidean data analysis and develop more and more innovative methods for describing, estimating and inferring non Euclidean geometries of modern real datasets. A general framework for integrated analysis of both Euclidean and non Euclidean data, composite AI, decision intelligence and edge AI provide powerful innovative ideas and strategies for fundamentally advancing AI. We are expected to marry statistics with AI, develop a unified theory of modern statistics and drive next generation of AI and data science.

Key facts. No citing papers in the map yet (data through 7 Oct 2026). Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models. Builds on 86 of its 150 references that are in the map. First posted on arXiv 30 Oct 2022.

Builds on

86 of 150 references.

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