Machine Learning: Origins, Developments and Implications
First published:
ISBN: 978-1-78272-445-2
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Useful tools
Useful tools
Preface
Introduction: human-machine entanglement
Machine learning: origins
Useful tools
Decision trees
Introduction to neural networks
Back-propagation
Regularisation
Optimisation
Building neural networks
Early applications of machine learning
Interpreting neural network decisions
Predicting corporate bond returns
Deep learning networks
Applications of deep learning networks
Machine intelligence
Consciousness
The future and its challenges
Artificial intelligence and the military
Final thoughts
Appendix
Epilogue
Acknowledgements
This chapter presents several of the mathematical and statistical algorithms that underlie machine learning computation. Readers having no experience of logarithms, probability density distributions or regression will find this useful for understanding the concepts presented in subsequent chapters. Those familiar with these tools may wish to skip this chapter.
3.1 LOGARITHMS AND EXPONENTS
Consider first exponential functions. These are often used in the activation functions of artificial neurons. An exponential function is a mathematical expression in the form:
where x is a variable and a is a constant called the base of the function, which is typically greater than zero. A commonly used exponential function base is the transcendental number e, also called Euler’s number, which is approximately equal to 2.71828. The domain of an exponential function is the set of all real numbers; the range is the set of all positive real numbers. Another popular logarithmic base is 10.
Parts (a) and (b) of Figure 3.1 present examples of exponential growth and decay functions. As illustrated in the graph of the growth function f (x), the exponential function increases rapidly
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