1. A class of kernel-based scalable algorithms for data science
- Author
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LeFloch, Philippe G., Mercier, Jean-Marc, and Miryusupov, Shohruh
- Subjects
Mathematics - Numerical Analysis - Abstract
We present several generative and predictive algorithms based on the RKHS (reproducing kernel Hilbert spaces) methodology, which most importantly are scalable in the following sense. It is well recognized that the RKHS methodology leads one to efficient and robust algorithms for numerous tasks in data science, statistics, and scientific computations.However, the standard implementations remain difficult to scale to encompass large data sets. In this paper, we introduce a simple and robust, divide-and-conquer approach which applies to large scale data sets and relies on suitably formulated, kernel-based algorithms: we distinguish between extrapolation, interpolation, and optimal transport steps. We explain how to select the best algorithms in specific applications thanks to some feedback, mainly consisting of perfomance criteria. Our main focus for the applications and challenging problems arising in industrial applications, such as the generation of mesh for efficient numerical simulations, the design of generators of conditional distributions, the transition probability matrix for statistic or stochastic applications, as well as various tasks of interest to the artificial intelligence community. Indeed, the proposed algorithms are relevant for supervised or unsupervised learning, generative methods, and reinforcement learning., Comment: 15 pages
- Published
- 2024