Book Image

Deep Learning with Theano

By : Christopher Bourez
Book Image

Deep Learning with Theano

By: Christopher Bourez

Overview of this book

This book offers a complete overview of Deep Learning with Theano, a Python-based library that makes optimizing numerical expressions and deep learning models easy on CPU or GPU. The book provides some practical code examples that help the beginner understand how easy it is to build complex neural networks, while more experimented data scientists will appreciate the reach of the book, addressing supervised and unsupervised learning, generative models, reinforcement learning in the fields of image recognition, natural language processing, or game strategy. The book also discusses image recognition tasks that range from simple digit recognition, image classification, object localization, image segmentation, to image captioning. Natural language processing examples include text generation, chatbots, machine translation, and question answering. The last example deals with generating random data that looks real and solving games such as in the Open-AI gym. At the end, this book sums up the best -performing nets for each task. While early research results were based on deep stacks of neural layers, in particular, convolutional layers, the book presents the principles that improved the efficiency of these architectures, in order to help the reader build new custom nets.
Table of Contents (22 chapters)
Deep Learning with Theano
Credits
About the Author
Acknowledgments
About the Reviewers
www.PacktPub.com
Customer Feedback
Preface
Index

Classification loss function


The loss function is an objective function to minimize during training to get the best model. Many different loss functions exist.

In a classification problem, where the target is to predict the correct class among k classes, cross-entropy is commonly used as it measures the difference between the real probability distribution, q, and the predicted one, p, for each class:

Here, i is the index of the sample in the dataset, n is the number of samples in the dataset, and k is the number of classes.

While the real probability of each class is unknown, it can simply be approximated in practice by the empirical distribution, that is, randomly drawing a sample out of the dataset in the dataset order. The same way, the cross-entropy of any predicted probability, p, can be approximated by the empirical cross-entropy:

Here, is the probability estimated by the model for the correct class of example .

Accuracy and cross-entropy both evolve in the same direction but measure...