Module treetransforms

source code

A collection of methods for tree (grammar) transformations used in parsing natural language.

Although many of these methods are technically grammar transformations (ie. Chomsky Norm Form), when working with treebanks it is much more natural to visualize these modifications in a tree structure. Hence, we will do all transformation directly to the tree itself. Transforming the tree directly also allows us to do parent annotation. A grammar can then be simply induced from the modified tree.

The following is a short tutorial on the available transformations.

1. Chomsky Normal Form (binarization)

   It is well known that any grammar has a Chomsky Normal Form (CNF) equivalent grammar where CNF is defined by every production having either two non-terminals or one terminal on its right hand side. When we have hierarchically structured data (ie. a treebank), it is natural to view this in terms of productions where the root of every subtree is the head (left hand side) of the production and all of its children are the right hand side constituents. In order to convert a tree into CNF, we simply need to ensure that every subtree has either two subtrees as children (binarization), or one leaf node (non-terminal). In order to binarize a subtree with more than two children, we must introduce artificial nodes.

   There are two popular methods to convert a tree into CNF: left factoring and right factoring. The following example demonstrates the difference between them. Example:

   Original       Right-Factored     Left-Factored
   
        A              A                      A 
      / | \          /   \                  /   \ 
     B  C  D   ==>  B    A|<C-D>   OR   A|<B-C>  D 
                          /  \          /  \ 
                         C    D        B    C
   

2. Parent Annotation

   In addition to binarizing the tree, there are two standard modifications to node labels we can do in the same traversal: parent annotation and Markov order-N smoothing (or sibling smoothing).

   The purpose of parent annotation is to refine the probabilities of productions by adding a small amount of context. With this simple addition, a CYK (inside-outside, dynamic programming chart parse) can improve from 74% to 79% accuracy. A natural generalization from parent annotation is to grandparent annotation and beyond. The tradeoff becomes accuracy gain vs. computational complexity. We must also keep in mind data sparcity issues. Example:

   Original       Parent Annotation 
   
        A                A^<?>            
      / | \             /   \            
     B  C  D   ==>  B^<A>    A|<C-D>^<?>     where ? is the 
                               /  \          parent of A
                           C^<A>   D^<A>   
   

3. Markov order-N smoothing

   Markov smoothing combats data sparcity issues as well as decreasing computational requirements by limiting the number of children included in artificial nodes. In practice, most people use an order 2 grammar. Example:

    Original       No Smoothing       Markov order 1   Markov order 2   etc.
    
     __A__            A                      A                A 
    / /|\ \         /   \                  /   \            /   \  
   B C D E F  ==>  B    A|<C-D-E-F>  ==>  B   A|<C>  ==>   B  A|<C-D>
                          /   \               /   \            /   \  
                         C    ...            C    ...         C    ...
   

   Annotation decisions can be thought about in the vertical direction (parent, grandparent, etc) and the horizontal direction (number of siblings to keep). Parameters to the following functions specify these values. For more information see:

   Dan Klein and Chris Manning (2003) "Accurate Unlexicalized Parsing", ACL-03. http://www.aclweb.org/anthology/P03-1054

4. Unary Collapsing

   Collapse unary productions (ie. subtrees with a single child) into a new non-terminal (Tree node). This is useful when working with algorithms that do not allow unary productions, yet you do not wish to lose the parent information. Example:

     A         
     |
     B   ==>   A+B
    / \        / \  
   C   D      C   D