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A ILP for Event Coreference Resolution
Let  $\lambda$  refers the set of all event mentions in a document and  $p_{ij}$  equals the score from the local pairwise classifier denoting event mentions 'i' and 'j' are coreferential. We formulate the baseline objective function that minimizes equation 1.
$$
\begin{array}{l} \Theta_ {B} = \sum_ {i \in \lambda , j \in \lambda} - l o g \left(p _ {i j}\right) x _ {i j} - l o g \left(1 - p _ {i j}\right) (\neg x _ {i j}) \tag {1} \\ s. t. \quad x _ {i j} \in \{0, 1 \} \\ \end{array}
$$
We then add constituent objective functions (equation 2) and new constraints to the baseline objective to incorporate document-level content structure, including repetitions of headline events in main content  $(\Theta_{M})$  as well as in consequence, previous event and current context  $(\Theta_{C})$ , intra-type coreference chains in non-main contents  $(\Theta_{L})$  and exclusion of singletons from event coreferential chains  $(\Theta_{S})$  while reinforcing non-singletons to have more coreferential mentions  $(\Theta_{N})$ .
$$
\Theta = \Theta_ {B} + K _ {M} \Theta_ {M} + K _ {C} \Theta_ {C} + K _ {L} \Theta_ {L} + K _ {S} \Theta_ {S} + K _ {N} \Theta_ {N} \tag {2}
$$
The weighting parameters for all the constituent objective functions were obtained through grid search. We first preset all the values to 0.5 and then searched each parameter in the multiples of 0.5 over the range from 0.5 to 5. We found that the best performance was obtained for  $K_{M} = 3.0$ ,  $K_{C} = 1.0$ ,  $K_{S} = 2.5$  and  $K_{N} = 0.5$ . Also, the best values for  $K_{L}$  are 0.5 for content types M2-C1 and 1.0 for content types C2-D8.
A.1 Infusing Singletons Score in the ILP Forumlation
Intuitively, coreferential event mentions and singletons are exclusive to each other. However, enforcing such mutual exclusion would be extremely unstable when both system predicted singletons
and event coreference scores are imperfect. Therefore, we simply discourage singletons from being included in any coreference chains and encourage non-singletons to form more coreferential links in our model by adding two constituent objective functions  $\Theta_S$  and  $\Theta_N$  (equation 3).
$$
\Theta_ {S} = \sum_ {i \in \lambda , j \in \lambda , i \vee j \in S} x _ {i j}; \Theta_ {N} = - \sum_ {i \in \lambda , j \in \lambda , i \wedge j \in N} x _ {i j} \tag {3}
$$
Where  $S$  and  $N$  are predicted singletons and nonsingletons from content-structure aware singleton classifier. The relaxed  $\Theta_S$  and  $\Theta_N$  based implementation allows violations for predicted singletons when its pairwise coreference score with an event mention is high.
A.2 Incorporating Content Types in the ILP Forumlation
As evident from the analysis, main, consequence, previous event and current context content types favor coreferential event mentions with headline event. Furthermore, if an event chain starts in one of the C1-D4 content types, it tend to have coreferential event mentions within the same content type or sometimes in the main content. We model above correlations between main and non-main content types and event coreference chains through their respective objective functions and constraints.
Main Events: for the event pairs with the first event mention from headline and the second one from main content sentences, we define a simple objective function (equation 4) that add the negative sum of their indicator variables to the main objective function.
$$
\Theta_ {M} = - \sum_ {i \in \xi_ {H}, j \in \xi_ {M}} x _ {i j} \tag {4}
$$
Here,  $\xi_{H}$  and  $\xi_{M}$  indicate event mentions in headline and main content sentences respectively. By minimizing  $\Theta_{M}$  in global objective function, our model encourages coreferential mentions between the headline and main content sentences.
Similarly, we define  $\Theta_C$  that encourages coreferential mentions between the headline and sentences from consequence, previous event and current context content types (equation 5).
$$
\Theta_ {C} = - \sum_ {i \in \xi_ {H}, j \in \xi_ {R}} x _ {i j} \tag {5}
$$
Here,  $\xi_{R}$  indicate event mentions in one of the consequence, previous event or current context content types.
Intra-type Events: for each non-main content type  $T$ , we define the objective function  $\Theta_L$  and corresponding constraint (equation 6) to penalize event chains that start in that non-main content type sentence but include event mentions from other non-main type sentences.
$$
\Theta_ {L} = \sum_ {i \in \xi_ {T}} Y _ {i}
$$
$$
s. t. \quad \Gamma_ {i} - Y _ {i} \leq M \gamma_ {i} \tag {6}
$$
$$
\Gamma_ {i} = \sum_ {i \in \xi_ {T}, j \notin (\xi_ {M} \cup \xi_ {T})} x _ {i j} ; \gamma_ {i} = \sum_ {k \notin \xi_ {T}, i \in \xi_ {T}} x _ {k i}
$$
First, we define an ILP variable  $Y_{i}$  for each event  $i$  in  $\xi_{T}$ , where  $\xi_{T}$  represents events in a non-main content type  $T \in C1-D4$ , and add that to the objective function  $\Theta_{L}$ . Then, through the constraint in equation 6, we set the value of  $Y_{i}$  to  $\Gamma_{i}$  when  $\lambda_{i}$  is 0.  $\Gamma_{i}$  equals the number of subsequent coreferential event mentions of event  $i$  in sentences of other non-main types.  $\gamma_{i}$  equals the number of antecedent coreferential even mentions of event  $i$  in sentences of main or other non-main types. By minimizing  $Y_{i}$  in  $\Theta_{L}$ , we discourage an event chain starting in a C1-D4 content type-sentence from forming coreferential links with subsequent event mentions in other non-main types.