1 Introduction: Numerical Machine Learning

The goal of this course is to enable you to build systems that do something, rather than encyclopedic coverage.

1.1 Problems we will be able to address using material from this course

1.1.1 Regression/Function approximation/Curve fitting

• model financial markets to predict which stocks will go up and by how much.
• model the economy to predict the growth of the economy.
• model the weather to predict how much rainfall will occur next year.
• model robot arm dynamics to improve control accuracy.
• image warping and morphing in graphics
• model a car engine to increase fuel efficiency and reduce emissions.
• model how a car steers to automatically drive a car: part of the Intelligent Vehicle Highway System.

1.1.2 Pattern recognition/Classification

• optical character recognition (OCR):
  • printed (output of scanner or fax machine).
  • hand printed.
  • cursive
• speech recognition.
• vision (object recognition)
• fault detection and identification
• medical diagnosis

1.1.3 Reinforcement learning

• Learn to play games: backgammon, checkers, chess, pacman, ...
• Program complex systems using rewards and punishment: ``Good house, bad house''

1.1.4 Clustering/Unsupervised Learning/Self-Organization

1.2 Philosophy

1.2.1 Learning from examples is fundamental

The dream is to program computers by simply giving them examples of desired behavior, or just rewards and punishment.

1.2.2 Representations are functions

See Appendix 1 for a description of the notation used. Our representation is a function that maps an input to an output. Improving the representation means correcting how inputs are mapped to outputs.

Vector input

Our representation of the input data and queries is a vector of numbers . In classification this is called a ``feature'' vector. Typical input types:

• Discrete unordered measurement (categorical measurment): gender, species, political party, college attended, country of origin.
• Discrete ordered measurement: number of children.
• Continuous measurement (continuity implies an ordering): temperature, income, height, weight.
• Time series: Stock prices over last N weeks, pen location during handwriting, speech. [FIGURE 1 GOES HERE]
• Image: Computer image of a face, a fax. [FIGURE 2 GOES HERE]

Output

In regression the output y is a continuous variable. In classification it is an assignment of the input to a particular class. Multiple outputs can be handled by separately handling each one.

Geometric point of view

• FIGURE: fitting curves. 1D, 2D
• FIGURE: Decision surfaces 2D.

1.2.3 Smoothness is the constraint

1.2.4 Learning is Numerical Optimization

The representations are trained by making them correctly handle the examples. This leads to training by gradient descent, with the criteria to minimize being the mismatch between the predicted and actual outputs for each example.

1.2.5 Classification is Regression

We will handle classification problems for the most part by transforming them into regression problems. More on this in the chapter on classification.

1.3 Methods

Brings together techniques from

• Statistics
• Pattern Recognition
• Optimization
• Numerical analysis/Numerical methods.
• Neural Networks
• Function Approximation Theory
• Control Theory
• Operations Research
• Machine Learning
• Artificial Intelligence

See ``relevant courses'' list.

1.4 Relationship to statistics

Statistics: Know form of function, just don't know parameters. Noise is major issue. Learning: error caused by both wrong form and noise. If you repeated observations, would you get same data?

1.5 Big questions

1.5.1 Why learn?

Learn to handle complex systems

We want to deal with complex systems we don't fully understand.

Learn to reduce needed apriori knowledge

We don't have needed apriori knowledge, or it is to expensive to gather/generate apriori knowledge.

1.5.2 How far can numerical approaches go?

When does the geometric and viewpoint run out of gas?

1.5.3 What is the difference between numeric and symbolic approaches?

Categorical vs. Ordered inputs?

  
Figure 1.1: A classification of tasks.

Categorical values Examples of categorical values: sex is one of male or female, nationality is one of US, Canadian, Mexican, ..., Categorical values can naturally be represented by symbols.

Ordered values are either continuous real values, or discrete values that have a natural ordering, such as the number of people in a room. Ordered discrete values can be represented by symbols, although symbolic representations typically ignore the ordering of the values.

Figure 1.1 attempts to sort out different kinds of tasks:

• categorical inputs, categorical outputs: classification, if small enough can be done by enumeration. This is where AI lives: symbols in, symbols out.
• categorical inputs, ordered outputs: this really means that the outputs will be categorical as well, perhaps after some averaging. An example of this type of problem is predicting the height of citizens of different countries. Aside from averaging over all the data to get a default height, It is not clear how to make use of knowledge of the average height of Russian citizens to improve our estimate of the average height of US citizens.
• ordered inputs, categorical outputs: classification
• ordered inputs, ordered outputs: regression

About this document ...

This document was generated using the LaTeX2HTML translator Version 96.1-d (Mar 10, 1996) Copyright © 1993, 1994, 1995, 1996, Nikos Drakos, Computer Based Learning Unit, University of Leeds.

The command line arguments were:
latex2html -split 0 -t NML: Introduction -no_navigation -show_section_numbers introduction.

The translation was initiated by Christopher G. Atkeson on Thu Mar 28 23:58:36 EST 1996