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

Convolutional operators

Even if we work only with finite and discrete convolutions, it's useful to start providing the standard definition based on integrable functions. For simplicity, let's suppose that f(t) and k(t) are two real functions of a single variable with support in . The convolution of f(t) and k(t) (conventionally denoted as f(t) * k(t)), which we are going to call a kernel, is defined as follows:

The expression may not be very easy to understand without a mathematical background, but it can become exceptionally simple with a few considerations. First of all, the integral sums all values of ; therefore, the convolution is a function of the remaining variable, t. The second fundamental element is a sort of dynamic property: the kernel is reversed () and transformed into a function of a new variable, . Without deep mathematical knowledge, it's possible to understand that this operation shifts the function along the (independent variable) axis...