How deeply does Statistics Slam Dunk cover nonlinear mapping?

Defines departure from linearity, relates it to diminishing returns, and demonstrates it visually without developing formal mathematical models.

Nonlinear mapping

As explained in Statistics Slam Dunk

Nonlinearity is the property that a relationship cannot be represented adequately by a straight-line pattern or linear function.

A nonlinear mapping describes a relationship that departs from a straight, proportional pattern. It signals that changes in one quantity do not translate uniformly into changes in another. Inequality similarly departs from equal distribution, but focuses on unequal allocation rather than the shape of a relationship. section 15.4.1

NBA franchises and games played

NBA franchise participation from 1946 through 2020 forms a nonlinear relationship with games played: active franchises account for more than 98% of games, while a smaller group contributes a disproportionate share. A Pareto chart makes this diminishing-returns pattern visible and can identify where corrective action or additional effort will matter most. section 15.4.1 section 15.5

df4 %>%
 group_by(franchise) %>%
 summarize(games) %>%
ggplot(aes(x = franchise, y = games)) +
       theme(axis.text.x = element_text(angle = 90, 
                                        hjust = 1, vjust = 0.5)) +
       stat_pareto() +
 ggtitle("Pareto Chart: Games Played (1946-2020)") +
 xlab("") +
 ylab("Games Played") +
 theme(plot.title = element_text(face = "bold"))

Builds a Pareto chart in R with ggplot2 and ggQC to display franchise games and their cumulative nonlinear pattern. section 15.4.1

How Statistics Slam Dunk covers it

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Math and Architectures of Deep LearningA property of a function or layer whose output is not a linear transformation of its inputs.
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Machine Learning for Tabular Data: XGBoost, Deep Learning, and AIA nonlinear transformation maps inputs to outputs in a way that cannot be represented as a linear function.
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Graph Neural Networks in ActionA parameterized operation that maps inputs to outputs without preserving linearity, allowing a neural network to model nonlinear relationships.
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Deep Learning with PyTorch, Second EditionA process whose behavior cannot be represented as a simple linear relation between inputs and outputs.
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Statistics Every Programmer NeedsA nonlinear relationship is a relationship in which changes in one quantity are not represented by a linear function of another.
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Inside Deep Learning: Math, Algorithms, ModelsA transformation inserted between linear steps to let a neural network represent functions that are not purely linear.

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Related concepts

activation functionproduced by · An activation function maps a neural-network unit’s or layer’s input to an output, often introducing nonlinearity into the network’s computation.
80-20 ruleequivalent to · The 80-20 rule is an informal heuristic that roughly 80 percent of an outcome may be associated with 20 percent of its contributing causes or effort.
linear regressioncontrasts with · Linear regression is a statistical modeling method that estimates a continuous response as a linear combination of predictor variables and fitted coefficients.
mathematical functionkind of · A mathematical function is a mapping that assigns exactly one output to each permitted input in its domain.
expressive powerproduces · Expressive power is the capacity of a model, language, or system to represent or convey a range and complexity of functions, patterns, distinctions, or ideas.
perceptroncontrasts with · A perceptron is a single-layer computational model and linear classifier that combines weighted inputs with a bias and applies a threshold or activation rule.

This explainer was generated by Manning's knowledge graph from the text of Statistics Slam Dunk. The section links point to the parts of the book it draws on.