[hts-users:01292] Re: Duration Modelling

[Simon King <Simon.King@xxxxxxxx>]

Paco Pinto wrote:
> Shouldn't all the questions be made in all the data subspaces ? 

No.

The questions to be asked in the tree, and the orders in which they are 
asked down each branch of the tree, are learned from data. They are 
chosen from a potentially long list of questions about the features (A, 
B, and C, in your example)

In your example tree, if A is false, then the next question that you 
should ask is about C, not B. This question ordering was chosen during 
learning because it maximised some objective function.

If you asked all the questions on all branches of the tree, all you 
would have would be a lookup table with one entry for every unique 
combination of A, B, and C. This would probably not work well in speech 
& language tasks, because we would typically not see all possible 
combinations of features in any finite  training data set, so there 
would be many entries in the table that we could not estimate a value for.

The decision tree solves this sparsity problem by effectively collapsing 
together certain rows or columns of this multi-dimensional table, so 
that it has fewer entries, and can therefore be estimated from a finite 
amount of data.

Decisions trees have the advantages of simplicity, low computational 
cost and being human readable, but they do have a significant weakness 
in that they subdivide the data set into ever small partitions during 
learning. Nevertheless, they often perform very well (e.g., 
letter-to-sound models).

Simon