## A New Algorithm for Learning From Examples

Summer project of Rodolfo Edward Pérez with advisor Prof Edre Boros

### Contents

#### What is learning from example?

Humans have a great ability to learn new concepts from a set of examples. For
instance, if shown a number of examples of New York style and Chicago style
pizzas, you will quickly learn to distinguish between the two varieties,
perhaps noticing the differenct in the crust thickness or the way the toppings
are positioned either within or on top of the cheese. One current topic of research in machine learning is the development
of algorithms which give computers some of the power of generalization that
humans naturally have. Essentially, an algorithm for learning from example
will tell a computer how to construct a mapping from a set of observable
variables (such as crust thickness, which toppings are present, and where they
are located) to a
classification (New York or Chicago style) when given a set of examples (a few
pizzas of each type).
Many such algorithms already exist, and some algorithms have advantages over
others in terms of the number of examples necessary to learn the concept, time
taken for the algorithm to run, memory requirements, accuracy of learning to
classify given examples, and accuracy of genearalization. Given the variaty of
standards by which the effectiveness of an alogrithm is measured, and the
relative youth of this field, the search for new algorithms for learning by
example is still very much a current area of research.
#### Description of the problem

This project treats only the case of learning functions from boolean
variables to a boolean classification. I have been implementing and testing
algorithms developed by my advisor, professor Boros. The goal for this project
is to develop an algorithm which runs in a reasonable amount of time and has a
high accuracy in generalization.

The basic idea of the algorithm is to build a function represented as a
logical circuit by creating one layer of gates at a time. The new gates are
designed to satisfy optimize a heuristic which balances accuracy on the
training examples with its ability to aid the other gates in the same layer to
distinguish the positive and negative examples. We are still experimenting
with the specifics of the algorithm, and more details will be posted later
when the algorithm is finalized.