Abstract
The models we have studied thus far in the book have all been linear. In this chapter, we begin our foray into nonlinear models by formally introducing features as mathematical functions that transform the input data. We discuss two main approaches to defining features: feature engineering that is driven by the domain knowledge of human experts and feature learning that is fully driven by the data itself. A discussion of the latter approach naturally leads to the introduction of deep neural networks as the main driver of recent advances in the field.
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Notes
- 1.
In this section, we only consider the case of two-class or binary classification. Multi-class classification follows similarly and is left out here to avoid repetition.
- 2.
Typically, a bias parameter w 0 is also included in this linear combination.
- 3.
According to the chain rule, if we have y = f 1(u) and u = f 2(x), then the derivative of the composition of f 1 and f 2, i.e., f 1(f 2(x)), can be found as
$$\displaystyle \begin{aligned} \frac{\text{d}\,y}{\text{d}\,x} = \frac{\text{d}\,y}{\text{d}\,u} \times \frac{\text{d}\,u}{\text{d}\,x}. \end{aligned}$$ - 4.
The interested reader is encouraged to see [3] and references therein.
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Watt J, Borhani R, Katsaggelos AK. Machine learning refined: foundations, algorithms, and applications. Cambridge: Cambridge University Press; 2020
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Borhani, R., Borhani, S., Katsaggelos, A.K. (2022). From Feature Engineering to Deep Learning. In: Fundamentals of Machine Learning and Deep Learning in Medicine. Springer, Cham. https://doi.org/10.1007/978-3-031-19502-0_6
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DOI: https://doi.org/10.1007/978-3-031-19502-0_6
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