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complexity theory

Why the simplest explanation is always the best

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PreambleThe simplest explanation is always the best among the explanations that are representative.  It is called the principle of parsimony,  Occam's razor. It is the bedrock of scientific enlightenment. There is a recent development that people start to do a category error to discard this...

machine learning data science overfitting complexity complexity theory interpretable machine learning bayesian statistics. statistical models evalutionary computation overgenearlisation

Resolution of misconception of overfitting: Differentiating learning curves from Occam curves

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Preamble Occam (Wikipedia)A misconception that overfitted model can be identified with the  amount of generalisation gap between model's training and test sets over its learning curves is still out there. Even in some prominent online lectures and blog posts, this misconception is now repeated...

machine learning deep learning occam's razor complexity theory interpretable machine learning statistical mechanics

Periodic Spectral Ergodicity Accurately Predicts Deep Learning Generalisation

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Preamble     Dali (1931), The Persistence of Memory (Wikipedia)One of the new mathematical concepts arise due to understanding of deep learning is called periodic spectral ergodicity (PSE). The cascading PSE (cPSE) propagates over deep learning layers which can also be used as a complexity...

deep learning random matrix theory periodic spectral ergodicity complexity theory spectral ergodicity quantum mechanics random matrices ergodic hypothesis

A New Matrix Mathematics for Deep Learning : Random Matrix Theory of Deep Learning

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Preamble     Figure: Definition of Randomness (Compagner 1991, Delft University)Development of deep learning systems (DLs)  increased our hopes to develop more autonomous systems. Based on the hierarchal learning of representations, deep learning defies the basic learning theory that beg the...

machine learning deep learning linear algebra random matrix theory complexity theory probabilistic models ergodic hypothesis complex networks multidimensional arrays freeman dyson ising-lenz model

Shifting Modern Data Science Forward: Dijkstra principle for data science

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Kindly reposted to KDnuggets by Gregory Piatetsky-Shapiro with the title Data science is not about data -applying Dijkstra principle to data science and enhancements.PreludeDijkstra in Zurich, 1984 (Wikipedia)Edsger Dijkstra was a Dutch theoretical physicist turned computer scientist, and probably...

machine learning data science statistics complexity theory scientific computing computer science dijkstra