Changes from Classical Statistics to Modern Statistics and Data Science

• URL: http://arxiv.org/abs/2211.03756v1
• Date: Sun, 30 Oct 2022 21:35:53 GMT
• Title: Changes from Classical Statistics to Modern Statistics and Data Science
• Authors: Kai Zhang, Shan Liu, and Momiao Xiong
• Abstract summary: The Euclidean assumption is not appropriate for non Euclidean data. We are expected to marry statistics with AI, develop a unified theory of modern statistics and drive next generation of AI and data science.
• Score: 24.38352029124892
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

Related papers

• Beyond Euclid: An Illustrated Guide to Modern Machine Learning with Geometric, Topological, and Algebraic Structures [3.5357133304100326]
  Modern machine learning encounters richly structured data that is inherently nonEuclidean. Extracting knowledge from such non-Euclidean data requires a broader mathematical perspective. We propose a graphical taxonomy that integrates recent advances into an intuitive unified framework.
  arXiv  Detail & Related papers  (2024-07-12T17:48:36Z)
• A Triumvirate of AI Driven Theoretical Discovery [0.0]
  We argue that while the theorist is in no way in danger of being replaced by AI in the near future, the hybrid of human expertise and AI algorithms will become an integral part of theoretical discovery.
  arXiv  Detail & Related papers  (2024-05-30T11:57:00Z)
• Discovering Interpretable Physical Models using Symbolic Regression and Discrete Exterior Calculus [55.2480439325792]
  We propose a framework that combines Symbolic Regression (SR) and Discrete Exterior Calculus (DEC) for the automated discovery of physical models. DEC provides building blocks for the discrete analogue of field theories, which are beyond the state-of-the-art applications of SR to physical problems. We prove the effectiveness of our methodology by re-discovering three models of Continuum Physics from synthetic experimental data.
  arXiv  Detail & Related papers  (2023-10-10T13:23:05Z)
• Stretched and measured neural predictions of complex network dynamics [2.1024950052120417]
  Data-driven approximations of differential equations present a promising alternative to traditional methods for uncovering a model of dynamical systems. A recently employed machine learning tool for studying dynamics is neural networks, which can be used for data-driven solution finding or discovery of differential equations. We show that extending the model's generalizability beyond traditional statistical learning theory limits is feasible.
  arXiv  Detail & Related papers  (2023-01-12T09:44:59Z)
• A Survey of Deep Learning for Mathematical Reasoning [71.88150173381153]
  We review the key tasks, datasets, and methods at the intersection of mathematical reasoning and deep learning over the past decade. Recent advances in large-scale neural language models have opened up new benchmarks and opportunities to use deep learning for mathematical reasoning.
  arXiv  Detail & Related papers  (2022-12-20T18:46:16Z)
• Neurocompositional computing: From the Central Paradox of Cognition to a new generation of AI systems [120.297940190903]
  Recent progress in AI has resulted from the use of limited forms of neurocompositional computing. New, deeper forms of neurocompositional computing create AI systems that are more robust, accurate, and comprehensible.
  arXiv  Detail & Related papers  (2022-05-02T18:00:10Z)
• EINNs: Epidemiologically-Informed Neural Networks [75.34199997857341]
  We introduce a new class of physics-informed neural networks-EINN-crafted for epidemic forecasting. We investigate how to leverage both the theoretical flexibility provided by mechanistic models as well as the data-driven expressability afforded by AI models.
  arXiv  Detail & Related papers  (2022-02-21T18:59:03Z)
• Modeling Item Response Theory with Stochastic Variational Inference [8.369065078321215]
  We introduce a variational Bayesian inference algorithm for Item Response Theory (IRT) Applying this method to five large-scale item response datasets yields higher log likelihoods and higher accuracy in imputing missing data. The algorithm implementation is open-source, and easily usable.
  arXiv  Detail & Related papers  (2021-08-26T05:00:27Z)
• An Extensible Benchmark Suite for Learning to Simulate Physical Systems [60.249111272844374]
  We introduce a set of benchmark problems to take a step towards unified benchmarks and evaluation protocols. We propose four representative physical systems, as well as a collection of both widely used classical time-based and representative data-driven methods.
  arXiv  Detail & Related papers  (2021-08-09T17:39:09Z)
• Model-Based Deep Learning [155.063817656602]
  Signal processing, communications, and control have traditionally relied on classical statistical modeling techniques. Deep neural networks (DNNs) use generic architectures which learn to operate from data, and demonstrate excellent performance. We are interested in hybrid techniques that combine principled mathematical models with data-driven systems to benefit from the advantages of both approaches.
  arXiv  Detail & Related papers  (2020-12-15T16:29:49Z)
• Learning Theory for Inferring Interaction Kernels in Second-Order Interacting Agent Systems [17.623937769189364]
  We develop a complete learning theory which establishes strong consistency and optimal nonparametric min-max rates of convergence for the estimators. The numerical algorithm presented to build the estimators is parallelizable, performs well on high-dimensional problems, and is demonstrated on complex dynamical systems.
  arXiv  Detail & Related papers  (2020-10-08T02:07:53Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.