Pattern Recognition and Neural Networks
This book uses tools from statistical decision theory and computational learning theory to create  a rigorous foundation for the theory of neural networks. On the theoretical side,Pattern Recognition and  Neural Networksemphasizes probability and statistics. Almost all the results have proofs that are often  original. On the application side, the emphasis is on pattern recognition. Most of the examples are from real  world problems. In addition to the more common types of networks, the book has chapters on decision trees  and belief networks from the machine-learning field. This book is intended for use in graduate courses that  teach statistics and engineering. A strong background in statistics is needed to fully appreciate the  theoretical developments and proofs. However, undergraduate-level linear algebra, calculus, and  probability knowledge is sufficient to follow the book.