This week, I read Jointly Combining Implicit Constraints Improves Temporal
Ordering by Nathanael Chambers and Dan Jurafsky. The paper proposes imposing
global constraints over the local pairwise order decisions. It proposes two
constraints (1) Transitivity and (2) Time expression normalization.

Transitivity. A soft classification (before, after and unknown) is done using
SVM and confidence scores are calculated for each pairwise events. The objective
function is maximized subject to the constraints that only one (before, after,
and unknown) is chosen. Transitivity is imposed over the connected components of
a digraph that r_1 + r_2 - r_3 \leq 0. Integer Linear Programming is used to
find the optimal solution. This however, didn't find any advantage over the
Timebank Corpus as the graph was very sparse and connected components were very
few. To eliminate this, they create a transitive closure.

The second global constraint that was imposed was normalizing the time
expressions to a single timeline. The document's publication date was considered
to be the current point in time, and phrases like "last month", "next Friday"
are normalized.

After using global as well as transitivity, the authors report 1-2% (absolute)
increase in accuracy