Book Image

Mastering Machine Learning Algorithms. - Second Edition

By : Giuseppe Bonaccorso
Book Image

Mastering Machine Learning Algorithms. - Second Edition

By: Giuseppe Bonaccorso

Overview of this book

Mastering Machine Learning Algorithms, Second Edition helps you harness the real power of machine learning algorithms in order to implement smarter ways of meeting today's overwhelming data needs. This newly updated and revised guide will help you master algorithms used widely in semi-supervised learning, reinforcement learning, supervised learning, and unsupervised learning domains. You will use all the modern libraries from the Python ecosystem – including NumPy and Keras – to extract features from varied complexities of data. Ranging from Bayesian models to the Markov chain Monte Carlo algorithm to Hidden Markov models, this machine learning book teaches you how to extract features from your dataset, perform complex dimensionality reduction, and train supervised and semi-supervised models by making use of Python-based libraries such as scikit-learn. You will also discover practical applications for complex techniques such as maximum likelihood estimation, Hebbian learning, and ensemble learning, and how to use TensorFlow 2.x to train effective deep neural networks. By the end of this book, you will be ready to implement and solve end-to-end machine learning problems and use case scenarios.
Table of Contents (28 chapters)
26
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27
Index

Optimization algorithms

When we discussed the back-propagation algorithm in the previous chapter, we showed how the SGD strategy can be easily employed to train deep networks with large datasets. This method is quite robust and effective; however, the function to optimize is generally non-convex and the number of parameters is extremely large.

These conditions dramatically increase the probability of finding saddle points (instead of local minima) and can slow down the training process when the surface is almost flat (as shown in the following figure, where the point (0, 0) is a saddle point).

Example of saddle point in a hyperbolic paraboloid

Considering the previous example, as the function is f(x,y) = x2y2, the partial derivatives and the Hessian are:

Hence, the point the first partial derivatives vanishes at (0, 0), so the point is a candidate to be an extreme. However, the Hessian has the eigenvalues that are solutions of the equation , which leads...