Book Image

Hands-On Mathematics for Deep Learning

By : Jay Dawani
Book Image

Hands-On Mathematics for Deep Learning

By: Jay Dawani

Overview of this book

Most programmers and data scientists struggle with mathematics, having either overlooked or forgotten core mathematical concepts. This book uses Python libraries to help you understand the math required to build deep learning (DL) models. You'll begin by learning about core mathematical and modern computational techniques used to design and implement DL algorithms. This book will cover essential topics, such as linear algebra, eigenvalues and eigenvectors, the singular value decomposition concept, and gradient algorithms, to help you understand how to train deep neural networks. Later chapters focus on important neural networks, such as the linear neural network and multilayer perceptrons, with a primary focus on helping you learn how each model works. As you advance, you will delve into the math used for regularization, multi-layered DL, forward propagation, optimization, and backpropagation techniques to understand what it takes to build full-fledged DL models. Finally, you’ll explore CNN, recurrent neural network (RNN), and GAN models and their application. By the end of this book, you'll have built a strong foundation in neural networks and DL mathematical concepts, which will help you to confidently research and build custom models in DL.
Table of Contents (19 chapters)
1
Section 1: Essential Mathematics for Deep Learning
7
Section 2: Essential Neural Networks
13
Section 3: Advanced Deep Learning Concepts Simplified

Exploring the various optimization methods

Now that you know what optimization is, it's time to explore some of the methods used in practice. We will not be covering the entire field of optimization because that would require an entire book to cover. We will only cover the essential optimization methods that are applicable to deep learning.

Least squares

Least squares is a subclass of convex optimization. It is classified as having no constraints and takes the following form:

Here, , are rows of A, and is our optimization variable.

We can also express this as a set of linear equations of the form. Therefore, .

The problem of least squares is very similar to that of maximum likelihood estimation.

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