On-Line Learning of Predictive Compositional Hierarchies
          
                            Karl Pfleger
                    Department of Computer Science
                         Stanford University

Abstract:

Language, music, spatial configurations, event chronologies, action
sequences, and many other types of data exhibit hierarchical compositional
structure, in which high-level entities represent combinations of lower-level
entities. Compositional (or part-whole) relationships, like taxonomic (is-a)
relationships, also serve as critical components of representation for
artificial intelligence. Existing work with hand-built compositional
hierarchies demonstrates the abilities of these structures to make predictive
inferences that smoothly integrate bottom-up and top-down influences,
spanning multiple levels of spatial or temporal resolution. However, unlike
taxonomies, for which numerous basic learning algorithms exist, there has not
been analogous foundational work on learning predictive compositional
hierarchies. My research demonstrates that predictive compositional
hierarchies can also be learned purely from primitive data in a way that is
general, unsupervised, and on-line (incrementally seeing a little data at a
time), with the ability at any point to make predictions about unseen data.

I define a new framework, which is basic and quite general, for on-line
learning of unsegmented sequence data. Systems capable of performing the task
well will have many possible uses resulting from their ability to fill in
missing data, resolve ambiguities, detect anomalies, etc. I introduce two
examples of new learning systems for this task, both employing compositional
hierarchies but based on different classes of traditional learning models.
The first, based on symmetric recurrent neural networks with probabilistic
semantics, provides a novel on-line structure modification rule for such
networks. The second, based on n-grams, introduces several contributions,
including an on-line method for selecting and storing only high-frequency
patterns, a method for weighting the statistical reliability of empirical
frequency estimates with different ages, and two unique methods for utilizing
lower-order models when combining n-grams.

The essence of on-line compositional hierarchy learning is the bottom-up
identification of frequently occurring repeated patterns in data, which
enables the future discovery of even larger patterns. Both systems introduced
are capable of composing larger and larger patterns (or chunks) as they see
more data, with no prespecified bound but nonetheless using less storage
space than that taken by the data itself. This hierarchical process has the
potential to scale automatically from fine-grained, low-level data to
coarser, high-level representations tuned to the statistical characteristics
of the environment, thereby bridging a gap that has proved to be one of the
largest stumbling blocks on the way to creating significantly more complex
and intelligent autonomous agents.