The Rising Influence of Rising Affluence

[semi_infinite]

How things come full circle - Note from Mike Grossman -


Mike Grossman
2:15?AM (6 hours ago)
to Mike

Non-Newtonian calculus is used in the doctoral dissertation on artificial intelligence by Michael Valenzuela at the University of Arizona. The dissertation is called ”Machine learning, optimization, and anti-training with sacrificial data“. (In computer science, machine learning is a branch of artificial intelligence.) It includes sections called “Non-Newtonian Derivations”, Non-Newtonian Models”, and “Applications of Non-Newtonian Calculus”.

From the dissertation: “Traditionally the machine learning community has viewed the No Free Lunch (NFL) theorems for search and optimization as a limitation. I review, analyze, and unify the NFL theorem with the many frameworks to arrive at necessary conditions for improving black-box optimization, model selection, and machine learning in general. I review meta-learning literature to determine when and how meta-learning can bene?t machine learning. We generalize meta-learning, in context of the NFL theorems, to arrive at a novel technique called Anti-Training with Sacri?cial Data (ATSD). My technique applies at the meta level to arrive at domain speci?c algorithms and models. I also show how to generate sacri?cial data. An extensive case study is presented. … For algorithms designed to operate on non-combinatorial problems, derivatives or second order assumptions are often exploited. However, both the derivatives and de?nition of second order depends on which calculus is used. Commonly classical additive calculus is used resulting in the common quadratic model and the classical derivative. This need not be the case. Grossman and Katz [Non-Newtonian Calculus] mention several alternative calculi including: geometric, anageometric, bigeometric, quadratic, anaquadratic, biquadratic, harmonic, anaharmonic, and biharmonic. … Non-Newtonian calculus has been used to derive optimization algorithms that perform better than traditional Newton based methods for Expectation-Maximization algorithms. However, Non-Newtonian calculus goes beyond simply being useful for optimization, it is useful for the other half of learning: modeling. The second order approximation using geometric calculus may produce the Gaussian curve … . The nth order approximation using bigeometric calculus produces an nth polynomial on a log-log plot.… Non-Newtonian generalized Taylor expansions produce nth order models, which are rarely polynomials. … Non-Newtonian models sometimes make sense to use. Non-Newtonian models follow from non-Newtonian calculi. … Here are a few rules of thumb for non-Newtonian models. If a meta-model is primarily concerned with learning probabilities, non-parametric distributions, or anything else where the multiplication is the primary operation, then the geometric calculi may be of interest. If working in a domain where the squares are additive, as is common the case when estimating the variance of a sum of independent random variables, then the quadratic calculi may produce meaningful models.”

https://www.researchgate.net/publication/301692116_Machine_Learning_Optimization_and_Anti-Training_with_Sacrificial_Data

8:56?AM (0 minutes ago)
to Mike

Hah. I wonder if ChatGPT and BARD implementation of NNC will result in a better answer about "What's NNC?" Nah - it will just be faster. LOL.