1 Boosting-based parse re-ranking with subtree features Taku Kudo Jun Suzuki Hideki Isozaki NTT Communication Science Labs.

2 Discriminative methods for parsing have shown a remarkable performance compared to traditional generative models, e.g., PCFG two approaches  re-ranking [Collins 00, Collins 02] discriminative machine learning algorithms are used to rerank n-best outputs of generative/conditional parsers.  dynamic programming Max margin parsing [Tasker 04]

3 Reranking Let x be an input sentence, and y be a parse tree for x Let G(x) be a function that returns a set of n- best results for x A re-ranker gives a score to each sentence and selects the result which has the highest score x: I buy cars with money …. y1y1 y2y2 y3y3 n-best results G(x)

4 Scoring with linear model is a feature function that maps output y into space is a parameter vector (weights) modeled with training data

5 Two issues in linear model [1/2] How to estimate the weights ?  try to minimize a loss for given training data  definition of loss: ME SVMs Boosting

6 Two issues in linear model [2/2] How to define the feature set ?  use all subtrees Pros: - natural extension of CFG rules - can capture long contextual information Cons: naïve enumerations give huge complexities

7 A question for all subtrees Do we always need all subtrees?  only a small set of subtrees is informative  most subtrees are redundant Goal: automatic feature selection from all subtrees  can perform fast parsing  can give good interpretation to selected subtrees Boosting meets our demand!

8 Why Boosting? Different regularization strategies for  L1 (Boosting) better when most given features are irrelevant can remove redundant features  L2 (SVMs) better when most given features are relevant uses features as much as they can Boosting meets our demand, because most subtrees are irrelevant and redundant

9 RankBoost [Freund03] Current weights Next weights Update feature k with an increment δ select the optimal pair that minimizes the Loss

10 How to find the optimal subtree?  Set of all subtrees is huge  Need to find the optimal subtree efficiently A variant of Branch-and-Bound Define a search space in which the whole set of subtrees is given Find the optimal subtree by traversing this search space Prune the search space by proposing a criterion

11 Ad-hoc techniques Size constraints  Use subtrees whose size is less than s (s = 6~8) Frequency constraints  Use subtrees that occur no less than f times in training data (f = 2 ~ 5) Pseudo iterations  After several 5- or 10-iterations of boosting, we alternately perform 100- or 300 pseudo iterations, in which the optimal subtee is selected from the cache that maintains the features explored in the previous iterations.

12 Relation to previous work Boosting vs Kernel methods [Collins 00] Boosting vs Data Oriented Parsing [Bod 98]

13 Kernels [Collins 00] Kernel methods reduce the problem into the dual form that only depends on dot products of two instances (parsed trees) Pros  No need to provide explicit feature vector  A dynamic programming is used to calculate dot products between trees, which is very efficient! Cons  Require a large number of kernel evaluations in testing  Parsing is slow  Difficult to see which features are relevant

14 DOP [Bod 98] DOP is not based on re-ranking DOP deals with the all the subtrees representation explicitly like our method Pros  high accuracy Cons  exact computation is NP-complete  cannot always provide sparse feature representation  very slow since the number of subtrees the DOP uses is huge

15 Kernels vs DOP vs Boosting KernelDOPBoosting How to enumerate all the subtrees? implicitlyexplicitly Complexity in training polynomialNP-hard (worst case) Branch-and-bound Sparse feature representations No Yes Parsing speed slow fast Can see relevant features? NoYes, but difficult because of redundant features Yes

16 Experiments WSJ parsing Shallow parsing

17 Experiments WSJ parsing  Standard data: training: 2-21, test 23 of PTB  Model2 of Collins 99 was used to obtain n-best results  exactly the same setting as [Collins 00 (Kernels)] Shallow parsing  CoNLL 2000 shared task  training:15-18, test: 20 of PTB  CRF-based parser [Sha 03] was used to obtain n-best results

18 Tree representations WSJ parsing  lexicalized tree  each non-terminal has a special node labeled with a head word Shallow parsing  right-branching tree where adjacent phrases are child/parent relation  special node for right/left boundaries

19 Results: WSJ parsing LR/LP = labeled recall/precision. CBs is the average number of cross brackets per sentence. 0 CBs, and 2CBs are the percentage of sentences with 0 or 2 crossing brackets, respectively Comparable to other methods Better than kernel method that uses all subtree representations with different parameter estimation

20 Results: Shallow parsing Comparable to other methods Our method is also comparable to Zhang’s method even without extra linguistic features Fβ=1 is a harmonic mean between precision and recall

21 Advantages Compact feature set  WSJ parsing: ~ 8,000  Shallow parsing: ~ 3,000  Kernels implicitly use a huge number of features Parsing is very fast  WSJ parsing: sec./sentence  Shallow parsing: sec./sentence (n-best parsing time is NOT included)

22 Advantages, cont’d Sparse feature representations allow us to analyze which kinds of subtrees are relevant Shallow parsing positive subtrees negative subtrees positive subtrees WSJ parsing

23 Conclusions All subtrees are potentially used as features Boosting  L1 norm regularization performs automatic feature selection Branch and bound  enables us to find the optimal subtrees efficiently Advantages:  comparable accuracy to other parsing methods  fast parsing  good interpretability

24 Efficient computation

25 Right most extension [Asai02, Zaki02] Extend a given tree of size (n-1) by adding a new node to obtain trees of size n  a node is added to the right-most-path  a node is added as the rightmost sibling b a c a b 56 c 3 b a c ab 56 c 3 b a c ab 56 c 3 b a c ab 56 c 3 rightmost- path t 7 7 7

26 Right most extension, cont. Recursive applications of right most extensions create a search space

27 Pruning For all propose an upper bound such that Can prune the node t if, where is a suboptimal gain Pruning strategy μ(t )=0.4 implies the gain of any supertree of t is no grater than 0.4

28 Upper bound of the gain

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