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

Essential concepts in statistics

While probability allows us to measure and calculate the odds of events or outcomes occurring, statistics allows us to make judgments and decisions given data generated by some unknown probability model. We use the data to learn the properties of the underlying probabilistic model. We call this process parametric inference.

Estimation

In estimation, our objective is given n iid samples with the same distribution as X (the probability model). If the PDF and probability mass function (PMF) is , we need to find θ.

Formally, we define a statistic as an estimate of θ.

A statistic is a function, T, of the data, , so that our estimate is . Therefore, T(x) is the sampling distribution...