Learning Internal Representations (PhD Thesis)

TL;DR

This thesis explores how learning shared representations across multiple tasks improves generalization in machine learning, providing theoretical bounds on sample efficiency and extending to hypothesis space biases.

Contribution

It introduces the concept of environment-based representation learning and derives bounds on sample sizes needed for effective generalization across tasks.

Findings

Learning a shared representation reduces the number of examples needed per task.

Bounds are established for the number of tasks and samples for effective representation learning.

Representation learning can be extended to other forms of hypothesis space bias.

Abstract

Most machine learning theory and practice is concerned with learning a single task. In this thesis it is argued that in general there is insufficient information in a single task for a learner to generalise well and that what is required for good generalisation is information about many similar learning tasks. Similar learning tasks form a body of prior information that can be used to constrain the learner and make it generalise better. Examples of learning scenarios in which there are many similar tasks are handwritten character recognition and spoken word recognition. The concept of the environment of a learner is introduced as a probability measure over the set of learning problems the learner might be expected to learn. It is shown how a sample from the environment may be used to learn a representation, or recoding of the input space that is appropriate for the environment. Learning a representation can equivalently be thought of as learning the appropriate features of the environment. Bounds are derived on the sample size required to ensure good generalisation from a representation learning process. These bounds show that under certain circumstances learning a representation appropriate for $n$ tasks reduces the number of examples required of each task by a factor of $n$. Once a representation is learnt it can be used to learn novel tasks from the same environment, with the result that far fewer examples are required of the new tasks to ensure good generalisation. Bounds are given on the number of tasks and the number of samples from each task required to ensure that a representation will be a good one for learning novel tasks. The results on representation learning are generalised to cover any form of automated hypothesis space bias.