jurafsky&martin_3rdEd_17 (1).pdf

The a cost function f n is used to efficiently guide

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The A* cost function, f ( n ) , is used to efficiently guide the search to a solution. The f -cost has two components: g ( n ) , the exact cost of the partial solution repre- sented by the state n , and h ( n ) a heuristic approximation of the cost of a solution that makes use of n . When h ( n ) satisfies the criteria of not overestimating the actual cost, A* will find an optimal solution. Not surprisingly, the closer the heuristic can get to the actual cost, the more effective A* is at finding a solution without having to explore a significant portion of the solution space. When applied to parsing, search states correspond to edges representing com- pleted constituents. As with the PCKY algorithm, edges specify a constituent’s start and end positions, its grammatical category, and its f -cost. Here, the g component represents the current cost of an edge and the h component represents an estimate of the cost to complete a derivation that makes use of that edge. The use of A* for phrase structure parsing originated with (Klein and Manning, 2003a) , while the CCG approach presented here is based on (Lewis and Steedman, 2014) . Using information from a supertagger, an agenda and a parse table are initial- ized with states representing all the possible lexical categories for each word in the input, along with their f -costs. The main loop removes the lowest cost edge from the agenda and tests to see if it is a complete derivation. If it reflects a complete derivation it is selected as the best solution and the loop terminates. Otherwise, new states based on the applicable CCG rules are generated, assigned costs, and entered into the agenda to await further processing. The loop continues until a complete derivation is discovered, or the agenda is exhausted, indicating a failed parse. The algorithm is given in Fig. 13.11 .
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13.7 P ROBABILISTIC CCG P ARSING 235 function CCG-AS TAR -P ARSE ( words ) returns table or failure supertags S UPERTAGGER ( words ) for i from 1 to L ENGTH ( words ) do for all { A | ( words [ i ] , A , score ) 2 supertags } edge M AKE E DGE ( i - 1, i , A , score ) table I NSERT E DGE ( table , edge ) agenda I NSERT E DGE ( agenda , edge ) loop do if E MPTY ?( agenda ) return failure current P OP ( agenda ) if C OMPLETED P ARSE ?( current ) return table table I NSERT E DGE ( chart , edge ) for each rule in A PPLICABLE R ULES ( edge ) do successor A PPLY ( rule , edge ) if successor not 2 in agenda or chart agenda I NSERT E DGE ( agenda , successor ) else if successor 2 agenda with higher cost agenda R EPLACE E DGE ( agenda , successor ) Figure 13.11 A*-based CCG parsing. Heuristic Functions Before we can define a heuristic function for our A* search, we need to decide how to assess the quality of CCG derivations. For the generic PCFG model, we defined the probability of a tree as the product of the probability of the rules that made up the tree. Given CCG’s lexical nature, we’ll make the simplifying assumption that the probability of a CCG derivation is just the product of the probability of the supertags assigned to the words in the derivation, ignoring the rules used in the the derivation.
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