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There are two problems in modern science:

 too many people use different terminology to solve the same problems;

 even more people use the same terminology to address completely different

issues.

Anonymous

In recent years, there has been an explosive growth of methods for learning

(or estimating dependencies) from data. This is not surprising given the prolifera￾tion of

 low-cost computers (for implementing such methods in software)

 low-cost sensors and database technology (for collecting and storing data)

 highly computer-literate application experts (who can pose ‘‘interesting’’

application problems)

A learning method is an algorithm (usually implemented in software) that esti￾mates an unknown mapping (dependency) between a system’s inputs and outputs

from the available data, namely from known (input, output) samples. Once such

a dependency has been accurately estimated, it can be used for prediction of future

system outputs from the known input values. This book provides a unified descrip￾tion of principles and methods for learning dependencies from data.

Methods for estimating dependencies from data have been traditionally explored

in diverse fields such as statistics (multivariate regression and classification), engi￾neering (pattern recognition), and computer science (artificial intelligence, machine

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learning, and, more recently, data mining). Recent interest in learning from data has

resulted in the development of biologically motivated methodologies, such as

artificial neural networks, fuzzy systems, and wavelets.

Unfortunately, developments in each field are seldom related to other fields,

despite the apparent commonality of issues and methods. The mere fact that

hundreds of ‘‘new’’ methods are being proposed each year at various conferences

and in numerous journals suggests a certain lack of understanding of the basic

issues common to all such methods.

The premise of this book is that there are just a handful of important principles

and issues in the field of learning dependencies from data. Any researcher or

practitioner in this field needs to be aware of these issues in order to successfully

apply a particular methodology, understand a method’s limitations, or develop new

techniques.

This book is an attempt to present and discuss such issues and principles (common to all methods) and then describe representative popular methods originating

from statistics, neural networks, and pattern recognition. Often methods developed

in different fields can be related to a common conceptual framework. This approach

enables better understanding of a method’s properties, and it has methodological

advantages over traditional ‘‘cookbook’’ descriptions of various learning algorithms.

Many aspects of learning methods can be addressed under a traditional statistical

framework. At the same time, many popular learning algorithms and learning

methodologies have been developed outside classical statistics. This happened

for several reasons:

1. Traditionally, the statistician’s role has been to analyze the inferential

limitations of the structural model constructed (proposed) by the application-domain expert. Consequently, the conceptual approach (adopted in

statistics) is parameter estimation for model identification. For many reallife problems that require flexible estimation with finite samples, the

statistical approach is fundamentally flawed. As shown in this book, learning

with finite samples should be based on the framework known as risk

minimization, rather than density estimation.

2. Statisticians have been late to recognize and appreciate the importance of

computer-intensive approaches to data analysis. The growing use of computers has fundamentally changed the traditional boundaries between a statistician (data modeler) and a user (application expert). Nowadays, engineers

and computer scientists successfully use sophisticated empirical datamodeling techniques (i.e., neural nets) to estimate complex nonlinear

dependencies from the data.

3. Statistics (being part of mathematics) has developed into a closed discipline,

with its own scientific jargon and academic objectives that favor analytic

proofs rather than practical methods for learning from data.