Frame-Semantic Parsing

FrameNet (Fillmore, Johnson, and Petruck 2003) is a linguistic resource storing considerable information about lexical and predicate-argument semantics in English. Grounded in the theory of frame semantics (Fillmore 1982), it suggests—but does not formally define—a semantic representation that blends representations familiar from word-sense disambiguation (Ide and Véronis 1998) and semantic role labeling (SRL; Gildea and Jurafsky 2002). Given the limited size of available resources, accurately producing richly structured frame-semantic structures with high coverage will require data-driven techniques beyond simple supervised classification, such as latent variable modeling, semi-supervised learning, and joint inference.

In this article, we present a computational and statistical model for frame-semantic parsing, the problem of extracting from text semantic predicate-argument structures such as those shown in Figure 1. We aim to predict a frame-semantic representation with two statistical models rather than a collection of local classifiers, unlike earlier approaches (Baker, Ellsworth, and Erk 2007). We use a probabilistic framework that cleanly integrates the FrameNet lexicon and limited available training data. The probabilistic framework we adopt is highly amenable to future extension through new features, more relaxed independence assumptions, and additional semi-supervised models.

Carefully constructed lexical resources and annotated data sets from FrameNet, detailed in Section 3, form the basis of the frame structure prediction task. We decompose this task into three subproblems: target identification (Section 4), in which frame-evoking predicates are marked in the sentence; frame identification (Section 5), in which the evoked frame is selected for each predicate; and argument identification (Section 6), in which arguments to each frame are identified and labeled with a role from that frame. Experiments demonstrating favorable performance to the previous state of the art on SemEval 2007 and FrameNet data sets are described in each section. Some novel aspects of our approach include a latent-variable model (Section 5.2) and a semi-supervised extension of the predicate lexicon (Section 5.5) to facilitate disambiguation of words not in the FrameNet lexicon; a unified model for finding and labeling arguments (Section 6) that diverges from prior work in semantic role labeling; and an exact dual decomposition algorithm (Section 7) that collectively predicts all the arguments of a frame together, thereby incorporating linguistic constraints in a principled fashion.

Our open-source parser, named SEMAFOR (Semantic Analyzer of Frame Representations)¹ achieves the best published results to date on the SemEval 2007 frame-semantic structure extraction task (Baker, Ellsworth, and Erk 2007). Herein, we also present results on newly released data with FrameNet 1.5, the latest edition of the lexicon. Some of the material presented in this article has appeared in previously published conference papers: Das et al. (2010) presented the basic model, Das and Smith (2011) described semi-supervised lexicon expansion, Das and Smith (2012) demonstrated a sparse variant of lexicon expansion, and Das, Martins, and Smith (2012) presented the dual decomposition algorithm for constrained joint argument identification. We present here a synthesis of those results and several additional details:

• 1. 

  The set of features used in the two statistical models for frame identification and argument identification.

• 2. 

  Details of a greedy beam search algorithm for argument identification that avoids illegal argument overlap.

• 3. 

  Error analysis pertaining to the dual decomposition argument identification algorithm, in contrast with the beam search algorithm.

• 4. 

  Results on full frame-semantic parsing using graph-based semi-supervised learning with sparsity-inducing penalties; this expands the small FrameNet predicate lexicon, enabling us to handle unknown predicates.

Our primary contributions are the use of efficient structured prediction techniques suited to shallow semantic parsing problems, novel methods in semi-supervised learning that improve the lexical coverage of our parser, and making frame-semantic structures a viable computational semantic representation usable in other language technologies. To set the stage, we next consider related work in the automatic prediction of predicate-argument semantic structures.

In this section, we will focus on previous scientific work relevant to the problem of frame-semantic parsing. First, we will briefly discuss work done on PropBank-style semantic role labeling, following which we will concentrate on the more relevant problem of frame-semantic structure extraction. Next, we review previous work that has used semi-supervised learning for shallow semantic parsing. Finally, we discuss prior work on joint structure prediction relevant to frame-semantic parsing.

Since Gildea and Jurafsky (2002) pioneered statistical semantic role labeling, there has been a great deal of computational work using predicate-argument structures for semantics. The development of PropBank (Kingsbury and Palmer 2002), followed by CoNLL shared tasks on semantic role labeling (Carreras and Màrquez 2004, 2005) boosted research in this area. Figure 2(a) shows an annotation from PropBank. PropBank annotations are closely tied to syntax, because the data set consists of the phrase-structure syntax trees from the Wall Street Journal section of the Penn Treebank (Marcus, Marcinkiewicz, and Santorini 1993) annotated with predicate-argument structures for verbs. In Figure 2(a), the syntax tree for the sentence is marked with various semantic roles. The two main verbs in the sentence, created and pushed, are the predicates. For the former, the constituent more than 1.2 million jobs serves as the semantic role ARG1 and the constituent In that time serves as the role ARGM-TMP. Similarly for the latter verb, roles ARG1, ARG2, ARGM-DIR, and ARGM-TMP are shown in the figure. PropBank defines core roles ARG0 through ARG5, which receive different interpretations for different predicates. Additional modifier roles ARGM-* include ARGM-TMP (temporal) and ARGM-DIR (directional), as shown in Figure 2(a). The PropBank representation therefore has a small number of roles, and the training data set comprises some 40,000 sentences, thus making the semantic role labeling task an attractive one from the perspective of machine learning.

There are many instances of influential work on semantic role labeling using PropBank conventions. Pradhan et al. (2004) present a system that uses support vector machines (SVMs) to identify the arguments in a syntax tree that can serve as semantic roles, followed by classification of the identified arguments to role names via a collection of binary SVMs. Punyakanok et al. (2004) describe a semantic role labeler that uses integer linear programming for inference and uses several global constraints to find the best suited predicate-argument structures. Joint modeling for semantic role labeling with discriminative log-linear models is presented by Toutanova, Haghighi, and Manning (2005), where global features looking at all arguments of a particular verb together are incorporated into a dynamic programming and reranking framework. The Computational Linguistics special issue on semantic role labeling (Màrquez et al. 2008) includes other interesting papers on the topic, leveraging the PropBank conventions for labeling shallow semantic structures. Recently, there have been initiatives to predict syntactic dependencies as well as PropBank-style predicate-argument structures together using one joint model (Surdeanu et al. 2008; Hajič et al. 2009).

Here, we focus on the related problem of frame-semantic parsing. Note from the annotated semantic roles for the two verbs in the sentence of Figure 2(a) that it is unclear what the core roles ARG1 or ARG2 represent linguistically. To better understand the roles' meaning for a given verb, one has to refer to a verb-specific file provided along with the PropBank corpus. Although collapsing these verb-specific core roles into tags ARG0-ARG5 leads to a small set of classes to be learned from a reasonable sized corpus, analysis shows that the roles ARG2–ARG5 serve many different purposes for different verbs. Yi, Loper, and Palmer (2007) point out that these four roles are highly overloaded and inconsistent, and they mapped them to VerbNet (Schuler 2005) thematic roles to get improvements on the SRL task. Recently, Bauer and Rambow (2011) presented a method to improve the syntactic subcategorization patterns for FrameNet lexical units using VerbNet. Instead of working with PropBank, we focus on shallow semantic parsing of sentences in the paradigm of frame semantics (Fillmore 1982), to which we turn next.

The FrameNet lexicon (Fillmore, Johnson, and Petruck 2003) contains rich linguistic information about lexical items and predicate-argument structures. A semantic frame present in this lexicon includes a list of lexical units, which are associated words and phrases that can potentially evoke it in a natural language utterance. Each frame in the lexicon also enumerates several roles corresponding to facets of the scenario represented by the frame. In a frame-analyzed sentence, predicates evoking frames are known as targets, and a word or phrase filling a role is known as an argument. Figure 2(b) shows frame-semantic annotations for the same sentence as in Figure 2(a). (In the figure, for example, the Cardinal_numbers frame, “M” denotes the role Multiplier and “E” denotes the role Entity.) Note that the verbs created and pushed evoke the frames Intentionally_create and Cause_change_position_on_a_scale, respectively. The corresponding lexical units² from the FrameNet lexicon, create.v and push.v, are also shown. The PropBank analysis in Figure 2(a) also has annotations for these two verbs. While PropBank labels the roles of these verbs with its limited set of tags, the frame-semantic parse labels each frame's arguments with frame-specific roles shown in the figure, making it immediately clear what those arguments mean. For example, for the Intentionally_create frame, more than 1.2 million jobs is the Created_entity, and In that time is the Time when the jobs were created. FrameNet also allows non-verbal words and phrases to evoke semantic frames: in this sentence, million evokes the frame Cardinal_numbers and doubles as its Number argument, with 1.2 as Multiplier, jobs as the Entity being quantified, and more than as the Precision of the quantity expression.

Whereas PropBank contains verbal predicates and NomBank (Meyers et al. 2004) contains nominal predicates, FrameNet counts these as well as allowing adjectives, adverbs, and prepositions among its lexical units. Finally, FrameNet frames organize predicates according to semantic principles, both by allowing related terms to evoke a common frame (e.g., push.v, raise.v, and growth.n for Cause_change_position_on_a_scale) and by defining frames and their roles within a hierarchy (see Figure 3). PropBank does not explicitly encode relationships among predicates.

Most early work on frame-semantic parsing has made use of the exemplar sentences in the FrameNet corpus (see Section 3.1), each of which is annotated for a single frame and its arguments. Gildea and Jurafsky (2002) presented a discriminative model for arguments given the frame; Thompson, Levy, and Manning (2003) used a generative model for both the frame and its arguments. Fleischman, Kwon, and Hovy (2003) first used maximum entropy models to find and label arguments given the frame. Shi and Mihalcea (2004) developed a rule-based system to predict frames and their arguments in text, and Erk and Padó (2006) introduced the Shalmaneser tool, which uses naive Bayes classifiers to do the same. Other FrameNet SRL systems (Giuglea and Moschitti 2006, for instance) have used SVMs. Most of this work was done on an older, smaller version of FrameNet, containing around 300 frames and fewer than 500 unique semantic roles. Unlike this body of work, we experimented with the larger SemEval 2007 shared task data set, and also the newer FrameNet 1.5,³ which lists 877 frames and 1,068 role types—thus handling many more labels, and resulting in richer frame-semantic parses.

Recent work in frame-semantic parsing—in which sentences may contain multiple frames which need to be recognized along with their arguments—was undertaken as the SemEval 2007 task 19 of frame-semantic structure extraction (Baker, Ellsworth, and Erk 2007). This task leveraged FrameNet 1.3, and also released a small corpus containing a little more than 2,000 sentences with full text annotations. The LTH system of Johansson and Nugues (2007), which we use as our baseline (Section 3.4), had the best performance in the SemEval 2007 task in terms of full frame-semantic parsing. Johansson and Nugues broke down the task as identifying targets that could evoke frames in a sentence, identifying the correct semantic frame for a target, and finally determining the arguments that fill the semantic roles of a frame. They used a series of SVMs to classify the frames for a given target, associating unseen lexical items to frames and identifying and classifying token spans as various semantic roles. Both the full text annotation corpus as well as the FrameNet exemplar sentences were used to train their models. Unlike Johansson and Nugues, we use only the full text annotated sentences as training data, model the whole problem with only two statistical models, and obtain significantly better overall parsing scores. We also model the argument identification problem using a joint structure prediction model and use semi-supervised learning to improve predicate coverage. We also present experiments on recently released FrameNet 1.5 data.

In other work based on FrameNet, Matsubayashi, Okazaki, and Tsujii (2009) investigated various uses of FrameNet's taxonomic relations for learning generalizations over roles; they trained a log-linear model on the SemEval 2007 data to evaluate features for the subtask of argument identification. Another line of work has sought to extend the coverage of FrameNet by exploiting VerbNet and WordNet (Shi and Mihalcea 2005; Giuglea and Moschitti 2006; Pennacchiotti et al. 2008) and by projecting entries and annotations within and across languages (Boas 2002; Fung and Chen 2004; Pado and Lapata 2005; Fürstenau and Lapata 2009b). Others have explored the application of frame-semantic structures to tasks such as information extraction (Moschitti, Morarescu, and Harabagiu 2003; Surdeanu et al. 2003), textual entailment (Burchardt and Frank 2006; Burchardt et al. 2009), question answering (Narayanan and Harabagiu 2004; Shen and Lapata 2007), and paraphrase recognition (Padó and Erk 2005).

Although there has been a significant amount of work in supervised shallow semantic parsing using both PropBank- and FrameNet-style representations, a few improvements over vanilla supervised methods using unlabeled data are notable. Fürstenau and Lapata (2009b) present a method of projecting predicate-argument structures from some seed examples to unlabeled sentences, and use a linear program formulation to find the best alignment explaining the projection. Next, the projected information as well as the seeds are used to train statistical model(s) for SRL. The authors ran experiments using a set of randomly chosen verbs from the exemplar sentences of FrameNet and found improvements over supervised methods. In an extension to this work, Fürstenau and Lapata (2009a) present a method for finding examples for unseen verbs using a graph alignment method; this method represents sentences and their syntactic analysis as graphs and graph alignment is used to project annotations from seed examples to unlabeled sentences. This alignment problem is again modeled as a linear program. Fürstenau and Lapata (2012) present an detailed expansion of the aforementioned papers. Although this line of work presents a novel direction in the area of SRL, the published approach does not yet deal with non-verbal predicates and does not evaluate the presented methods on the full text annotations of the FrameNet releases.

Deschacht and Moens (2009) present a technique of incorporating additional information from unlabeled data by using a latent words language model. Latent variables are used to model the underlying representation of words, and parameters of this model are estimated using standard unsupervised methods. Next, the latent information is used as features for an SRL model. Improvements over supervised SRL techniques are observed with the augmentation of these extra features. The authors also compare their method with the aforementioned two methods of Fürstenau and Lapata (2009a, 2009b) and show relative improvements. Experiments are performed on the CoNLL 2008 shared task data set (Surdeanu et al. 2008), which follows the PropBank conventions and only labels verbal and nominal predicates—in contrast to our work, which includes most lexicosyntactic categories. A similar approach is presented by Weston, Ratle, and Collobert (2008), who use neural embeddings of words, which are eventually used for SRL; improvements over state-of-the-art PropBank-style SRL systems are observed.

Recently, there has been related work in unsupervised semantic role labeling (Lang and Lapata 2010, 2011; Titov and Klementiev 2012) that attempts to induce semantic roles automatically from unannotated data. This line of work may be useful in discovering new semantic frames and roles, but here we stick to the concrete representation provided in FrameNet, without seeking to expand its inventory of semantic types. We present a new semi-supervised technique to expand the set of lexical items with the potential semantic frames that they could evoke; we use a graph-based semi-supervised learning framework to achieve this goal (Section 5.5).

Most high-performance SRL systems that use conventions from PropBank (Kingsbury and Palmer 2002) and NomBank (Meyers et al. 2004) utilize joint inference for semantic role labeling (Màrquez et al. 2008). To our knowledge, the separate line of work investigating frame-semantic parsing has not previously dealt with joint inference. A common trait in prior work, both in PropBank and FrameNet conventions, has been the use of a two-stage model that identifies arguments first, then labels them, often using dynamic programming or integer linear programs (ILPs); we treat both problems together here.⁴

Recent work in natural language processing (NLP) problems has focused on ILP formulations for complex structure prediction tasks like dependency parsing (Riedel and Clarke 2006; Martins, Smith, and Xing 2009; Martins et al. 2010), sequence tagging (Roth and Yih 2004), as well as PropBank SRL (Punyakanok et al. 2004). Whereas early work in this area focused on declarative formulations tackled with off-the-shelf solvers, Rush et al. (2010) proposed subgradient-based dual decomposition (also called Lagrangian relaxation) as a way of exploiting the structure of the problem and existing combinatorial algorithms. The method allows the combination of models that are individually tractable, but not jointly tractable, by solving a relaxation of the original problem. Since then, dual decomposition has been used to build more accurate models for dependency parsing (Koo et al. 2010), combinatory categorical grammar supertagging and parsing (Auli and Lopez 2011), and machine translation (Chang and Collins 2011; DeNero and Macherey 2011; Rush and Collins 2011).

Recently, Martins et al. (2011b) showed that the success of subgradient-based dual decomposition strongly relies on breaking down the original problem into a “good” decomposition, that is, one with few overlapping components. This leaves out many declarative constrained problems, for which such a good decomposition is not readily available. For those, Martins et al. 2011b proposed the Alternating Directions Dual Decomposition (AD³) algorithm, which retains the modularity of previous methods, but can handle thousands of small overlapping components. We adopt that algorithm as it perfectly suits the problem of argument identification, as we observe in Section 7.⁵ We also contribute an exact branch-and-bound technique wrapped around AD³.

Before delving into the details of our modeling framework, we describe in detail the structure of the FrameNet lexicon and the data sets used to train our models.

We consider frame-semantic parsing resources consisting of a lexicon and annotated sentences with frame-semantic structures, evaluation strategies, and previous baselines.

The FrameNet lexicon is a taxonomy of manually identified general-purpose semantic frames for English.⁶ Listed in the lexicon with each frame are a set of lemmas (with parts of speech) that can denote the frame or some aspect of it—these are called lexical units (LUs). In a sentence, word or phrase tokens that evoke a frame are known as targets. The set of LUs listed for a frame in FrameNet may not be exhaustive; we may see a target in new data that does not correspond to an LU for the frame it evokes. Each frame definition also includes a set of frame elements, or roles, corresponding to different aspects of the concept represented by the frame, such as participants, props, and attributes. We use the term argument to refer to a sequence of word tokens annotated as filling a frame role. Figure 1 shows an example sentence from the training data with annotated targets, LUs, frames, and role-argument pairs. The FrameNet lexicon also provides information about relations between frames and between roles (e.g., inheritance). Figure 3 shows a subset of the relations between five frames and their roles.

Accompanying most frame definitions in the FrameNet lexicon is a set of lexicographic exemplar sentences (primarily from the British National Corpus) annotated for that frame. Typically chosen to illustrate variation in argument realization patterns for the frame in question, these sentences only contain annotations for a single frame.

In preliminary experiments, we found that using exemplar sentences directly to train our models hurt performance as evaluated on SemEval 2007 data, which formed a benchmark for comparison with previous state of the art. This was a noteworthy observation, given that the number of exemplar sentences is an order of magnitude larger than the number of sentences in training data that we consider in our experiments (Section 3.2). This is presumably because the exemplars are not representative as a sample, do not have complete annotations, and are not from a domain similar to the test data. Instead, we make use of these exemplars in the construction of features (Section 5.2).

In our experiments on frame-semantic parsing, we use two sets of data:

• 1. 

  SemEval 2007 data: In benchmark experiments for comparison with previous state of the art, we use a data set that was released as part of the SemEval 2007 shared task on frame-semantic structure extraction (Baker, Ellsworth, and Erk 2007). Full text annotations in this data set consisted of a few thousand sentences containing multiple targets, each annotated with a frame and its arguments. The then-current version of the lexicon (FrameNet 1.3) was used for the shared task as the inventory of frames, roles, and lexical units (Figure 3 illustrates a small portion of the lexicon). In addition to the frame hierarchy, FrameNet 1.3 also contained 139,439 exemplar sentences containing one target each. Statistics of the data used for the SemEval 2007 shared task are given in the first column of Table 1. A total of 665 frame types and 720 role types appear in the exemplars and the training portion of the data. We adopted the same training and test split as the SemEval 2007 shared task; however, we removed four documents from the training set⁷ for development. Table 2 shows some additional information about the SemEval data set; the variety of lexicosyntactic categories of targets stands in marked contrast with the PropBank-style SRL data and task.

• 2. 

  FrameNet 1.5 release: A more recent version of the FrameNet lexicon was released in 2010.⁸ We also test our statistical models (only frame identification and argument identification) on this data set to get an estimate of how much improvement additional data can provide. Details of this data set are shown in the second column of Table 1. Of the 78 documents in this release with full text annotations, we selected 55 (19,582 targets) for training and held out the remaining 23 (4,458 targets) for testing. There are fewer target annotations per sentence in the test set than the training set.⁹ Das and Smith (2011, supplementary material) give the names of the test documents for fair replication of our work. We also randomly selected 4,462 targets from the training data for development of the argument identification model (Section 6.1).

Preprocessing. We preprocessed sentences in our data set with a standard set of annotations: POS tags from MXPOST (Ratnaparkhi 1996) and dependency parses from the MST parser (McDonald, Crammer, and Pereira 2005); manual syntactic parses are not available for most of the FrameNet-annotated documents. We used WordNet (Fellbaum 1998) for lemmatization. Our models treat these pieces of information as observations. We also labeled each verb in the data as having active or passive voice, using code from the SRL system described by Johansson and Nugues (2008).

Automatic annotations of frame-semantic structure can be broken into three parts: (1) targets, the words or phrases that evoke frames; (2) the frame type, defined in the lexicon, evoked by each target; and (3) the arguments, or spans of words that serve to fill roles defined by each evoked frame. These correspond to the three subtasks in our parser, each described and evaluated in turn: target identification (Section 4), frame identification (Section 5, not unlike word-sense disambiguation), and argument identification (Section 6, essentially the same as semantic role labeling).

The standard evaluation script from the SemEval 2007 shared task calculates precision, recall, and F₁-measure for frames and arguments; it also provides a score that gives partial credit for hypothesizing a frame related to the correct one. We present precision, recall, and F₁-measure microaveraged across the test documents, report labels-only matching scores (spans must match exactly), and do not use named entity labels.¹⁰ More details can be found in the task description paper from SemEval 2007 (Baker, Ellsworth, and Erk 2007). For our experiments, statistical significance is measured using a reimplementation of Dan Bikel's randomized parsing evaluation comparator, a stratified shuffling test whose original implementation¹¹ is accompanied by the following description (quoted verbatim, with explanations of our use of the test given in square brackets):

A strong baseline for frame-semantic parsing is the system presented by Johansson and Nugues (2007, hereafter J&N'07), the best system in the SemEval 2007 shared task. That system is based on a collection of SVMs. They used a set of rules for target identification which we describe in Appendix A. For frame identification, they used an SVM classifier to disambiguate frames for known frame-evoking words. They used WordNet synsets to extend the vocabulary of frame-evoking words to cover unknown words, and then used a collection of separate SVM classifiers—one for each frame—to predict a single evoked frame for each occurrence of a word in the extended set.

J&N'07 followed Xue and Palmer (2004) in dividing the argument identification problem into two subtasks: First, they classified candidate spans as to whether they were arguments or not; then they assigned roles to those that were identified as arguments. Both phases used SVMs. Thus, their formulation of the problem involves a multitude of independently trained classifiers that share no information—whereas ours uses two log-linear models, each with a single set of parameters shared across all contexts, to find a full frame-semantic parse.

We compare our models with J&N'07 using the benchmark data set from SemEval 2007. However, because we are not aware of any other work using the FrameNet 1.5 full text annotations, we report our results on that data set without comparison to any other system.

Target identification is the problem of deciding which word tokens (or word token sequences) evoke frames in a given sentence. In other semantic role labeling schemes (e.g., PropBank), simple part-of-speech criteria typically distinguish targets from non-targets. But in frame semantics, verbs, nouns, adjectives, and even prepositions can evoke frames under certain conditions. One complication is that semantically impoverished support predicates (such as make in make a request) do not evoke frames in the context of a frame-evoking, syntactically dependent noun (request). Furthermore, only temporal, locative, and directional senses of prepositions evoke frames.¹²

Preliminary experiments using a statistical method for target identification gave unsatisfactory results; instead, we followed J&N'07 in using a small set of rules to identify targets. First, we created a master list of all the morphological variants of targets that appear in the exemplar sentences and a given training set. For a sentence in new data, we considered as candidate targets only those substrings that appear in this master list. We also did not attempt to capture discontinuous frame targets: for example, we treat there would have been as a single span even though the corresponding LU is there be.v.¹³

Next, we pruned the candidate target set by applying a series of rules identical to the ones described by Johansson and Nugues (2007, see Appendix A), with two exceptions. First, they identified locative, temporal, and directional prepositions using a dependency parser so as to retain them as valid LUs. In contrast, we pruned all types of prepositions because we found them to hurt our performance on the development set due to errors in syntactic parsing. In a second departure from their target extraction rules, we did not remove the candidate targets that had been tagged as support verbs for some other target. Note that we used a conservative white list that filters out targets whose morphological variants were not seen either in the lexicon or the training data.¹⁴ Therefore, when this conservative process of automatic target identification is used, our system loses the capability to predict frames for completely unseen LUs, despite the fact that our powerful frame identification model (Section 5) can accurately label frames for new LUs.¹⁵

Results.Table 3 shows results on target identification tested on the SemEval 2007 test set; our system gains 3 F₁ points over the baseline. This is statistically significant with p < 0.01. Our results are also significant in terms of precision (p < 0.05) and recall (p < 0.01). There are 85 distinct LUs for which the baseline fails to identify the correct target while our system succeeds. A considerable proportion of these units have more than one token (e.g., chemical and biological weapon.n, ballistic missile.n), which J&N'07 do not model. The baseline also does not label variants of there be.v (e.g., there are and there has been), which we correctly label as targets. Some examples of other single token LUs that the baseline fails to identify are names of months, LUs that belong to the Origin frame (e.g., iranian.a), and directions (e.g., north.a or north-south.a).¹⁶

Given targets, our parser next identifies their frames, using a statistical model.

FrameNet specifies a great deal of structural information both within and among frames. For frame identification we make use of frame-evoking lexical units, the (lemmatized and POS-tagged) words and phrases listed in the lexicon as referring to specific frames. For example, listed with the Bragging frame are 10 LUs, including boast.n, boast.v, boastful.a, brag.v, and braggart.n. Of course, due to polysemy and homonymy, the same LU may be associated with multiple frames; for example, gobble.v is listed under both the Ingestion and Make_noise frames. We thus term gobble.v an ambiguous LU. All targets in the exemplar sentences, our training data, and most in our test data, correspond to known LUs. (See Section 5.4 for statistics of unknown LUs in the test sets.)

To incorporate frame-evoking expressions found in the training data but not the lexicon—and to avoid the possibility of lemmatization errors—our frame identification model will incorporate, via a latent variable, features based directly on exemplar and training targets rather than LUs. Let be the set of (unlemmatized and automatically POS-tagged) targets found in the exemplar sentences of the lexicon and/or the sentences in our training set. Let be the subset of these targets annotated as evoking a particular frame f.¹⁷ Let and denote the lemmatized versions of and , respectively. Then, we write and to indicate that this inflected verb boasted and its lemma boast have been seen to evoke the Bragging frame. Significantly, however, another target, such as toot your own horn, might be used elsewhere to evoke this frame. We thus face the additional hurdle of predicting frames for unknown words.

In producing full text annotations for the SemEval 2007 data set, annotators created several domain-critical frames that were not already present in version 1.3 of the lexicon. For our experiments we omit frames attested in neither the training data nor the exemplar sentences from the lexicon.¹⁸ This leaves a total of 665 frames for the SemEval 2007 data set and a total of 877 frames for the FrameNet 1.5 data set.

For a given sentence x with frame-evoking targets t, let t_i denote the ith target (a word sequence).¹⁹ Let denote its lemma. We seek a list f = 〈f₁, …, f_m〉 of frames, one per target. In our model, the set of candidate frames for t_i is defined to include every frame f such that —or if , then every known frame (the latter condition applies for 4.7% of the annotated targets in the SemEval 2007 development set). In both cases, we let be the set of candidate frames for the ith target in x. We denote the entire set of frames in the lexicon as .

Previous work has exploited WordNet for better coverage during frame identification (Burchardt, Erk, and Frank 2005; Johansson and Nugues 2007,e.g., by expanding the set of targets using synsets), and others have sought to extend the lexicon itself. We differ in our use of a latent variable to incorporate lexical-semantic features in a discriminative model, relating known lexical units to unknown words that may evoke frames. Here we are able to take advantage of the large inventory of partially annotated exemplar sentences. Note that this model makes an independence assumption: Each frame is predicted independently of all others in the document. In this way the model is similar to J&N'07. However, ours is a single conditional model that shares features and weights across all targets, frames, and prototypes, whereas the approach of J&N'07 consists of many separately trained models. Moreover, our model is unique in that it uses a latent variable to smooth over frames for unknown or ambiguous LUs.

Frame identification features depend on the preprocessed sentence x, the prototype ℓ and its WordNet lexical-semantic relationship with the target t_i, and of course the frame f. Our model uses binary features, which are detailed in Table 4.

SemEval 2007 Data. On the SemEval 2007 data set, we evaluate the performance of our frame identification model given gold-standard targets and automatically identified targets (Section 4); see Table 5. Together, our target and frame identification outperform the baseline by 4 F₁ points. To compare the frame identification stage in isolation with that of J&N'07, we ran our frame identification model with the targets identified by their system as input. With partial matching, our model achieves a relative improvement of 0.6% F₁ over J&N'07, as shown in the third row of Table 5 (though this is not significant). Note that for exact matching, the F₁ score of the automatic targets setting is better than the gold target setting. This is due to the fact that there are many unseen predicates in the test set on which the frame identification model performs poorly; however, for the automatic targets that are mostly seen in the lexicon and training data, the model gets high precision, resulting in better overall F₁ score.

Our frame identification model thus performs on par with the previous state of the art for this task, and offers several advantages over J&N's formulation of the problem: It requires only a single model, learns lexical-semantic features as part of that model rather than requiring a preprocessing step to expand the vocabulary of frame-evoking words, and is probabilistic, which can facilitate global reasoning.

In the SemEval 2007 data set, for gold-standard targets, 210 out of 1,059 lemmas were not present in the white list that we used for target identification (see Section 4). Our model correctly identifies the frames for 4 of these 210 lemmas. For 44 of these lemmas, the evaluation script assigns a score of 0.5 or more, suggesting that our model predicts a closely related frame. Finally, for 190 of the 210 lemmas, a positive score is assigned by the evaluation script. This suggests that the hidden variable model helps in identifying related (but rarely exact) frames for unseen targets, and explains why under exact—but not partial—frame matching, the F₁ score using automatic targets is commensurate with the score for oracle targets.²⁶

For automatically identified targets, the F₁ score falls because the model fails to predict frames for unseen lemmas. However, our model outperforms J&N'07 by 4 F₁ points. The partial frame matching F₁ score of our model represents a significant improvement over the baseline (p < 0.01). The precision and recall measures are significant as well (p < 0.05 and p < 0.01, respectively). However, because targets identified by J&N'07 and frames classified by our frame identification model resulted in scores on par with the baseline, we note that the significant results follow due to better target identification. Note from the results that the automatic target identification model shows an increase in precision, at the expense of recall. This is because the white list for target identification restricts the model to predict frames only for known LUs. If we label the subset of test set with already seen LUs (seen only in the training set, excluding the exemplars) with their corresponding most frequent frame, we achieve an exact match accuracy between 52.9% and 91.2%, depending on the accuracy of the unseen LUs (these bounds assume, respectively, that they are all incorrectly labeled or all correctly labeled).

FrameNet 1.5 Release. The bottom three rows of Table 5 show results on the full text annotation test set of the FrameNet 1.5 release. Because the number of annotations nearly doubled, we see large improvements in frame identification accuracy. Note that we only evaluate with gold targets as input to frame identification. (As mentioned in Section 3.2, some documents in the test set have not been annotated for all targets, so evaluating automatic target identification would not be informative.) We found that 50.1% of the targets in the test set were ambiguous (i.e., they associated with more than one frame either in FrameNet or our training data). On these targets, the exact frame identification accuracy is 73.10% and the partial accuracy is 85.77%, which indicates that the frame identification model is robust to target ambiguity. On this data set, the most frequent frame baseline achieves an exact match accuracy between 74.0% and 88.1%, depending on the accuracy of the unseen LUs.

We conducted further experiments with ablation of the latent variable in our frame identification model. Recall that the decoding objective used to choose a frame by marginalizing over a latent variable ℓ, whose values range over targets known to associate with the frame f being considered (see Equations (1) and (2)) in training. How much do the prototypes, captured by the latent variable, contribute to performance? Instead of treating ℓ as a marginalized latent variable, we can fix its value to the observed target.

An immediate effect of this choice is a blow-up in the number of features; we must instantiate features (see Table 4) for all 4,194 unique targets observed in training. Because each of these features needs to be associated with all 877 frames in the partition function of Equation (2), the result is an 80-fold blowup of the feature space (the latent variable model had 465,317 features). Such a model is not computationally feasible in our engineering framework, so we considered a model using only features observed to fire at some point in the training data (called “supported” features),²⁷ resulting in only 72,058 supported features. In Table 5, we see a significant performance drop (on both exact and partial matching accuracy) with this latent variable–free model, compared both with our latent variable model with all features and with only supported features (of which there are 165,200). This establishes that the latent variable in our frame identification model helps in terms of accuracy, and lets us use a moderately sized feature set incorporating helpful unsupported features.

Finally, in our test set, we found that 144 out of the 4,458 annotated targets were unseen, and our full frame identification model only labeled 23.1% of the frames correctly for those unseen targets; in terms of partial match accuracy, the model achieved a score of 46.6%. This, along with the results on the SemEval 2007 unseen targets, shows that there is substantial opportunity for improvement when unseen targets are presented to the system. We address this issue next.

We next address the poor performance of our frame identification model on targets that were unseen as LUs in FrameNet or as instances in training data, and briefly describe a technique for expanding the set of lexical units with potential semantic frames that they can associate with. These experiments were carried out on the FrameNet 1.5 data only. We use a semi-supervised learning (SSL) technique that uses a graph constructed from labeled and unlabeled data. The widely used graph-based SSL framework—see Bengio, Delalleau, and Le Roux (2006) and Zhu (2008) for introductory material on this topic—has been shown to perform better than several other semi-supervised algorithms on benchmark data sets (Chapelle, Schölkopf, and Zien 2006, chapter 21). The method constructs a graph where a small portion of vertices correspond to labeled instances, and the rest are unlabeled. Pairs of vertices are connected by weighted edges denoting the similarity between the pair. Traditionally, Markov random walks (Szummer and Jaakkola 2001; Baluja et al. 2008) or optimization of a loss function based on smoothness properties of the graph (e.g., Corduneanu and Jaakkola 2003; Zhu, Ghahramani, and Lafferty 2003; Subramanya and Bilmes 2008) are performed to propagate labels from the labeled vertices to the unlabeled ones. In our work, we are interested in multi-class generalizations of graph-propagation algorithms suitable for NLP applications, where each graph vertex can assume one or more out of many possible labels (Subramanya and Bilmes 2008; Talukdar and Crammer 2009). For us, graph vertices correspond to natural language types (not tokens) and undirected edges between them are weighted using a similarity metric. Recently, this set-up has been used to learn soft labels on natural language types (say, word n-grams or in our case, syntactically disambiguated predicates) from seed data, resulting in large but noisy lexicons, which are used to constrain structured prediction models. Applications have ranged from domain adaptation of sequence models (Subramanya, Petrov, and Pereira 2010) to unsupervised learning of POS taggers by using bilingual graph-based projections (Das and Petrov 2011).

We describe our approach to graph construction, propagation for lexicon expansion, and the use of the result to impose constraints on frame identification.

We construct a graph with lexical units as vertices. Thus, each vertex corresponds to a lemmatized word or phrase appended with a coarse POS tag. We use two resources for graph construction. First, we take all the words and phrases present in a dependency-based thesaurus constructed using syntactic cooccurrence statistics (Lin 1998), and aggregate words and phrases that share the same lemma and coarse POS tag. To construct this resource, Lin used a corpus containing 64 million words that was parsed with a fast dependency parser (Lin 1993, 1994), and syntactic contexts were used to find similar lexical items for a given word or phrase. Lin separately treated nouns, verbs, and adjectives/adverbs, so these form the three parts of the thesaurus. This resource gave us a list of possible LUs, much larger in size than the LUs present in FrameNet data.

The second component of graph construction comes from FrameNet itself. We scanned the exemplar sentences in FrameNet 1.5 and the training section of the full text annotations and gathered a distribution over frames for each LU appearing in FrameNet data. For a pair of LUs, we measured the Euclidean distance between their frame distributions. This distance was next converted to a similarity score and interpolated with the similarity score from Lin's dependency thesaurus. We omit further details about the interpolation and refer the reader to full details given in Das and Smith (2011).

For each LU, we create a vertex and link it to the K nearest neighbor LUs under the interpolated similarity metric. The resulting graph has 64,480 vertices, 9,263 of which are labeled seeds from FrameNet 1.5 and 55,217 of which are unlabeled. Each vertex has a possible set of labels corresponding to the 877 frames defined in the lexicon. Figure 4 shows an excerpt from the constructed graph.

For targets t_i in test data whose LUs are not present in the graph (and hence in supervised data), is the set of all frames. Note that in this semi-supervised extension of our frame identification inference procedure, we introduced several hyperparameters, namely, μ, ν, K (the number of nearest neighbors for each vertex included in the graph) and M (the number of highest scoring frames per vertex according to the induced frame distribution). We choose these hyperparameters using cross-validation by tuning the frame identification accuracy on unseen targets. (Different values of the first three hyperparameters were chosen for the different graph objectives and we omit their values here for brevity; M turned out to be 2 for all models.)

Table 6 shows frame identification accuracy, both using exact match as well as partial match. Performance is shown on the portion of the test set containing unknown LUs, as well as the whole test set. The final column presents lexicon size in terms of the set of truncated frame distributions (filtered according to the top M frames in q_v for a vertex v) for all the LUs in a graph. For comparison with a semi-supervised baseline, we consider a self-trained system. For this system, we used the supervised frame identification system to label 70,000 sentences from the English Gigaword corpus with frame-semantic parses. For finding targets in a raw sentence, we used a relaxed target identification scheme, where we marked as potential frame-evoking units all targets seen in the lexicon and all other words which were not prepositions, particles, proper nouns, foreign words, or WH-words. We appended these automatic annotations to the training data, resulting in 711,401 frame annotations, more than 36 times the annotated data. These data were next used to train a frame identification model.²⁸ This set-up is very similar to that of Bejan (2009) who used self-training to improve frame identification. In our setting, however, self-training hurts relative to the fully supervised approach (Table 6).

Note that for the unknown part of the test set the graph-based objectives outperform both the supervised model as well as the self-training baseline by a margin of ∼20% absolute. The best model is UJSF-ℓ_1,2, and its performance is significantly better than the supervised model (p < 0.01). It also produces a smaller lexicon (using the sparsity-inducing penalty) than NGF-ℓ₂, requiring less memory during frame identification inference. The small footprint can be attributed to the removal of LUs for which all frame components were zero (q_i = 0). The improvements of the graph-based objectives over the supervised and the self-trained models are modest for the whole test set, but the best model still has statistically significant improvements over the supervised model (p < 0.01).

Given a sentence x = 〈x₁, …, x_n〉, the set of targets t = 〈t₁, …, t_m〉, and a list of evoked frames f = 〈f₁, …, f_m〉 corresponding to each target, argument identification is the task of choosing which of each f_i's roles are filled, and by which parts of x. This task is most similar to the problem of semantic role labeling, but uses a richer set of frame-specific labels than PropBank annotations.

Let denote frame f_i's roles (named frame element types) observed in an exemplar sentence and/or our training set. A subset of each frame's roles are marked as core roles; these roles are conceptually and/or syntactically necessary for any given use of the frame, though they need not be overt in every sentence involving the frame. These are roughly analogous to the core arguments ARG0–ARG5 in PropBank. Non-core roles—analogous to the various ARGM-* in PropBank—loosely correspond to syntactic adjuncts, and carry broadly applicable information such as the time, place, or purpose of an event. The lexicon imposes some additional structure on roles, including relations to other roles in the same or related frames, and semantic types with respect to a small ontology (marking, for instance, that the entity filling the protagonist role must be sentient for frames of cognition). Figure 3 illustrates some of the structural elements comprising the frame lexicon by considering the Cause_to_make_noise frame.

We identify a set of spans that are candidates for filling any role . In principle, could contain any subsequence of x, but in this work we only consider the set of contiguous spans that (a) contain a single word or (b) comprise a valid subtree of a word and all its descendants in the dependency parse produced by the MST parser. This covers approximately 80% of arguments in the development data for both data sets.

The empty span, denoted ∅, is also included in , since some roles are not explicitly filled; in the SemEval 2007 development data, the average number of roles an evoked frame defines is 6.7, but the average number of overt arguments is only 1.7.²⁹ In training, if a labeled argument is not a subtree of the dependency parse, we add its span to .³⁰

Out of the overt argument spans in the training data, 12% are duplicates, having been used by some previous frame in the sentence (supposing some arbitrary ordering of frames). Our role-filling model, unlike a sentence-global argument detection-and-classification approach,³¹ permits this sort of argument sharing among frames. Word tokens belong to an average of 1.6 argument spans, including the quarter of words that do not belong to any argument.

Appending together the local inference decisions from Equation (7) gives us the best mapping for target t. Features for our log-linear model (Equation (8)) depend on the preprocessed sentence x; the target t; a role r of frame f; and a candidate argument span .³² For features using the head word of the target t or a candidate argument span s, we use the heuristic described in footnote 20 for selecting the head of non-subtree spans.

Table 7 lists the feature templates used in our model. Every feature template has a version that does not take into account the role being filled (so as to incorporate overall biases). The ◐ symbol indicates that the feature template also has a variant that is conjoined with r, the name of the role being filled; and • indicates that the feature template additionally has a variant that is conjoined with both r and f, the name of the frame.³³ The role-name-only variants provide for smoothing over frames for common types of roles such as Time and Place; see Matsubayashi, Okazaki, and Tsujii (2009) for a detailed analysis of the effects of using role features at varying levels of granularity. Certain features in our model rely on closed-class POS tags, which are defined to be all Penn Treebank tags except for cd and tags that start with v, n, j, or r. Finally, the features that encode a count or a number are binned into groups: (−∞, −20], [−19, −10], [−9, −5], −4, −3, −2, −1, 0, 1, 2, 3, 4, [5,9], [10,19], [20, ∞).

On the FrameNet 1.5 release, we trained this model using L-BFGS (Liu and Nocedal 1989) and ran it for 1,000 iterations. C was tuned on the development data, and we obtained best results for C = 1.0. We did not use stochastic gradient descent for this data set as the number of training instances increased and parallelization of L-BFGS on a multicore setup implementing MPI (Gropp, Lusk, and Skjellum 1994) gave faster training speeds.

Naive prediction of roles using Equation (7) may result in overlap among arguments filling different roles of a frame, because the argument identification model fills each role independently of the others. We want to enforce the constraint that two roles of a single frame cannot be filled by overlapping spans.³⁵ Toutanova, Haghighi, and Manning (2005) presented a dynamic programming algorithm to prevent overlapping arguments for SRL; however, their approach used an orthogonal view to the argument identification stage, wherein they labeled phrase-structure tree constituents with semantic roles. That formulation admitted a dynamic programming approach; our formulation of finding the best argument span for each role does not.

To eliminate illegal overlap, we adopt the beam search technique detailed in Algorithm 1. The algorithm produces a set of k-best hypotheses for a frame instance's full set of role-span pairs, but uses an approximation in order to avoid scoring an exponential number of hypotheses. After determining which roles are most likely not explicitly filled, it considers each of the other roles in turn: In each iteration, hypotheses incorporating a subset of roles are extended with high-scoring spans for the next role, always maintaining k alternatives. We set k=10,000 as the beam width.³⁶

Performance of the argument identification model is presented in Table 8 for both data sets in consideration. We analyze them here.

SemEval 2007 Data: For the SemEval data set, the table shows how performance varies given different types of input: correct targets and correct frames, correct targets but automatically identified frames, and ultimately, no oracle input (the full frame parsing scenario). Rows 1–2 isolate the argument identification task from the frame identification task. Given gold targets and frames, our argument identification model (without beam search) gets an F₁ score of 68.09%; when beam search is applied, this increases to 68.46%, with a noticeable increase in precision. Note that an estimated 19% of correct arguments are excluded because they are neither single words nor complete subtrees (see Section 6.1) of the automatic dependency parses.³⁷

Qualitatively, the problem of candidate span recall seems to be largely due to syntactic parse errors.³⁸ Although our performance is limited by errors when using the syntactic parse to determine candidate spans, it could still improve; this suggests that the model has trouble discriminating between good and bad arguments, and that additional feature engineering or jointly decoding arguments of a sentence's frames may be beneficial.

Rows 3–4 show the effect of automatic supervised frame identification on overall frame parsing performance. There is a 22% absolute decrease in F₁ (18% when partial credit is given for related frames), suggesting that improved frame identification or joint prediction of frames and arguments is likely to have a sizeable impact on overall performance. Rows 4–6 compare our full model (target, frame, and argument identification) with the baseline, showing significant improvement of more than 4.4 F₁ points for both exact and partial frame matching. As with frame identification, we compared the argument identification stage with that of J&N'07 in isolation, using the automatically identified targets and frames from the latter as input to our model. As shown in row 5, with partial frame matching, this gave us an F₁ score of 48.1% on the test set—significantly better (p < 0.05) than 45.6%, the full parsing result from J&N'07 (row 6 in Table 8). This indicates that our argument identification model—which uses a single discriminative model with a large number of features for role filling (rather than argument labeling)—is more accurate than the previous state of the art.

FrameNet 1.5 Release: Rows 7–12 show results on the newer data set, which is part of the FrameNet 1.5 release. As in the frame identification results of Table 5, we do not show results using predicted targets, as we only test the performance of the statistical models. First, we observe that for results with gold frames, the F₁ score is 79.08% with naive decoding, which is significantly higher than the SemEval counterpart. This indicates that increased training data greatly improves performance on the task. We also observe that beam search improves precision by nearly 2%, while getting rid of overlapping arguments. When both model frames and model arguments are used, we get an F₁ score of 68.45%, which is encouraging in comparison to the best results we achieved on the SemEval 2007 data set. Semi-supervised lexicon expansion for frame identification further improves parsing performance. We observe the best results when the UJSF-ℓ_1,2 graph objective is used for frame identification, significantly outperforming the fully supervised model on parsing (p < 0.001) for all evaluation metrics. The improvements with SSL can be explained by noting that frame identification performance goes up when the graph objectives are used, which carries over to argument identification. Figure 5 shows an example where the graph-based model UJSF-ℓ_1,2 corrects an error made by the fully supervised model for the unseen LU discrepancy.n, both for frame identification and full frame-semantic parsing.

The argument identification strategy described in the previous section does not capture some facets of semantic knowledge represented declaratively in FrameNet. In this section, we present an approach that exploits such knowledge in a principled, unified, and intuitive way. In prior NLP research using FrameNet, these interactions have been largely ignored, though they have the potential to improve the quality and consistency of semantic analysis. The beam search technique (Algorithm 1) handles one kind of constraint: avoiding argument overlaps. It is, however, approximate and cannot handle other forms of constraints.

Here, we present an algorithm that exactly identifies the best full collection of arguments of a target given its semantic frame. Although we work within the conventions of FrameNet, our approach is generalizable to other SRL frameworks. We model argument identification as constrained optimization, where the constraints come from expert knowledge encoded in FrameNet. Following prior work on PropBank-style SRL that dealt with similar constrained problems (Punyakanok et al. 2004; Punyakanok, Roth, and Yih 2008, inter alia), we incorporate this declarative knowledge in an integer linear program.

Because general-purpose ILP solvers are proprietary and do not fully exploit the structure of the problem, we turn to a class of optimization techniques called dual decomposition (Komodakis, Paragios, and Tziritas 2007; Rush et al. 2010; Martins et al. 2011a). We derive a modular, extensible, parallelizable approach in which semantic constraints map not just to declarative components in the algorithm, but also to procedural ones, in the form of “workers.” Although dual decomposition algorithms only solve a relaxation of the original problem, we make our approach exact by wrapping the algorithm in a branch-and-bound search procedure.³⁹

We experimentally find that our algorithm achieves accuracy comparable to the results presented in Table 8, while respecting all imposed linguistic constraints. In comparison with beam search, which violates many of these constraints, the presented exact decoder is slower, but it decodes nine times faster than CPLEX, a state-of-the-art, proprietary, general-purpose exact ILP solver.⁴⁰

Here, we take a declarative approach to modeling argument identification using an ILP and relate our formulation to prior work in shallow semantic parsing. We show how knowledge specified in a linguistic resource (FrameNet in our case) can be used to derive the constraints in our ILP. Finally, we draw connections of our specification to graphical models, a popular formalism in artificial intelligence and machine learning, and describe how the constraints can be treated as factors in a factor graph.

Pairwise “Exclusions.” For many target classes, there are pairs of roles forbidden to appear together in the analysis of a single target token. Consider the following two sentences:

• (1) 

  resembles.

• (2) 

  resemble each other.

Pairwise “Requirements.” The sentence in Example (1) illustrates another kind of constraint. The target resemble cannot have only one of Entity_1 and Entity_2 as roles in text. For example,

• (3) 

  * resembles.

There are several LP and ILP solvers available, and a great deal of effort has been spent by the optimization community to devise efficient generic solvers. An example is CPLEX, a state-of-the-art solver for mixed integer programming that we use as a baseline to solve the ILP in Equation (11) as well as its LP relaxation in Equation (17). Like many of the best implementations, CPLEX is proprietary.

Although enforcing the four different sets of constraints is intuitive from a general linguistic perspective, we ground their use in definitive linguistic information present in the FrameNet lexicon. From the annotated data in the FrameNet 1.5 release, we gathered that only 3.6% of the time is a role instantiated multiple times by different spans in a sentence. This justifies the uniqueness constraint enforced by Equation (12). Use of such a constraint is also consistent with prior work in frame-semantic parsing (Johansson and Nugues 2007). Similarly, we found that in the annotations, no arguments overlapped with each other for a given target. Hence, the overlap constraints in Equation (14) are also justified.

Our third and fourth sets of constraints, presented in Equations (15) and (16), come from FrameNet, too. Examples (1) and (2) are instances where the target resemble evokes the Similarity frame, which is defined in FrameNet as:

For this frame, the lexicon lists several roles other than the three we have already observed, such as Dimension (the dimension along which the entities are similar), Differentiating_fact (a fact that reveals how the concerned entities are similar or different), and so forth. Along with the roles, FrameNet also declares the “excludes” and “requires” relationships noted in our discussion in Section 7.1.1. The case of the Similarity frame is not unique; in Figure 1, the frame Collaboration, evoked by the target partners, also has two roles Partner_1 and Partner_2 that share the “requires” relationship. In fact, out of 877 frames in FrameNet 1.5, 204 frames have at least a pair of roles for which the “excludes” relationship holds, and 54 list at least a pair of roles that share the “requires” relationship.

The LP in Equation (17) can be represented as a maximum a posteriori inference problem in an undirected graphical model. In the factor graph, each component (z_r,s) of the vector z corresponds to a binary variable, and each instantiation of a constraint in Equations (12), (14), (15), and (16) corresponds to a factor. Smith and Eisner (2008) and Martins et al. (2010) used such a representation to impose constraints in a dependency parsing problem; the latter discussed the equivalence of linear programs and factor graphs for representing discrete optimization problems. All of our constraints take standard factor forms we can describe using the terminology of Smith and Eisner and Martins et al. The uniqueness constraint in Equation (12) corresponds to an Xor factor, while the overlap constraint in Equation (14) corresponds to an AtMostOne factor. The constraints in Equation (15) enforcing the “excludes” relationship can be represented with an Or factor. Finally, each “requires” constraints in Equation (16) is equivalent to an XorWithOutput factor.

In the following section, we describe how we arrive at solutions for the LP in Equation (17) using dual decomposition, and how we adapt it to efficiently recover the exact solution of the ILP (Equation (11)), without the need of an off-the-shelf ILP solver.

Dual decomposition methods address complex optimization problems in the dual, by dividing them into simple worker problems (subproblems), which are repeatedly solved until a consensus is reached. The simplest technique relies on the subgradient algorithm (Komodakis, Paragios, and Tziritas 2007; Rush et al. 2010); as an alternative, Martins et al. (2011a, 2011b) proposed an augmented Lagrangian technique, which is more suitable when there are many small components —commonly the case in declarative constrained problems, like the one at hand. Here, we present a brief overview of the latter, which is called AD³.

Like in the subgradient method, the λ-updates can be regarded as price adjustments, which will affect the next round of z_m-updates. The only difference with respect to the subgradient method (Rush et al. 2010) is that each subproblem involved in a z_m-update also has a quadratic penalty that penalizes deviations from the previous average voting; it is this term that accelerates consensus and therefore convergence. Martins et al. (2011b) also provide stopping criteria for the iterative updates using primal and dual residuals that measure convergence; we refer the reader to that paper for details.

A key attraction of this algorithm is that all the components of the declarative specification remain intact in the procedural form. Each worker corresponds exactly to one constraint in the ILP, which corresponds to one linguistic constraint. There is no need to work out when, during the procedure, each constraint might have an effect, as in beam search.

In a different application, Martins et al. (2011b, Section 4) showed how to solve each z_m-subproblem associated with the Xor, XorWithOutput and Or factors in runtime O(|i(m)| log |i(m)|). The only subproblem that remains is that of the AtMostOne factor; a solution with the same runtime is given in Appendix B.

It is worth recalling that AD³, like other dual decomposition algorithms, solves a relaxation of the actual problem. Although we have observed that the relaxation is often tight (cf. Section 7.3), this is not always the case. Specifically, a fractional solution may be obtained, which is not interpretable as an argument, and therefore it is desirable to have a strategy to recover the exact solution. Two observations are noteworthy. First, the optimal value of the relaxed problem (Equation (17)) provides an upper bound to the original problem (Equation (11)). This is because Equation (11) has the additional integer constraint on the variables. In particular, any feasible dual point provides an upper bound to the original problem's optimal value. Second, during execution of the AD³ algorithm, we always keep track of a sequence of feasible dual points. Therefore, each iteration constructs tighter and tighter upper bounds. With this machinery, we have all that is necessary for implementing a branch-and-bound search that finds the exact solution of the ILP. The procedure works recursively as follows:

• 1. 

  Initialize L = −∞ (our best value so far).

• 2. 

  Run Algorithm 2. If the solution u* is integer, return u* and set L to the objective value. If along the execution we obtain an upper bound less than L, then Algorithm 2 can be safely stopped and return “infeasible”—this is the bound part. Otherwise (if u* is fractional) go to step 3.

• 3. 

  Find the “most fractional” component of u* (call it and branch: constrain u_j = 0 and go to step 2, eventually obtaining an integer solution or infeasibility; and then constrain u_j = 1 and do the same, obtaining . Return the that yields the largest objective value.

We present experiments only on argument identification in this section, as our goal is to exhibit the importance of incorporating the various linguistic constraints during our inference procedure. We present results on the full text annotations of FrameNet 1.5, and do not experiment on the SemEval 2007 benchmark, as we have already established our constraint-agnostic models as state-of-the-art. The model weights ψ used in the scoring function c were learned as in Section 6.1 (i.e., by training a logistic regression model to maximize conditional log-likelihood). The AD³ parameter ρ was initialized to 0.1, and we followed Martins et al. (2011b) in dynamically adjusting it to keep a balance between the primal and dual residuals.

We compare the following algorithms to demonstrate the efficacy of our collective argument identification approach:⁴³

• 1. 

  Naive: This strategy selects the best span for each role r according to the score function c(r,s), independently of all other roles—the decoding rule formalized in Equation (7) of Section 6.1. It ignores all constraints except “uniqueness.”

• 2. 

  Beam: This strategy employs greedy beam search to eliminate overlaps between predicted arguments, as described in Algorithm 1. Note that it does not try to respect the “excludes” and “requires” constraints between pairs of roles. The default size of the beam in Section 1 was a safe 10,000; this resulted in extremely slow decoding times. For time comparison, we tried beam sizes of 100 and 2 (the latter being the smallest size that achieves the same F₁ score on the FrameNet 1.5 dev set).

• 3. 

  CPLEX, LP: This uses CPLEX to solve the relaxed LP in Equation (17). To handle fractional z, for each role r, we choose the best span s* such that s* = , breaking ties arbitrarily.

• 4. 

  CPLEX, exact: This tackles the actual ILP (Equation (11)) with CPLEX.

• 5. 

  AD³, LP: The relaxed problem is solved using AD³. We choose a span for each role as in strategy 3.

• 6. 

  AD³, exact: This couples AD³ with branch-and-bound search to get the exact integer solution.

Table 9 shows performance of these decoding strategies on the test set. We report precision, recall, and F₁ scores. As with experiments in previous sections, we use the evaluation script from SemEval 2007 shared task. Because these scores do not penalize constraint violations, we also report the number of overlap, “excludes,” and “requires” constraints that were violated in the test set. Finally, we tabulate each setting's decoding time in seconds on the whole test set averaged over five runs.⁴⁴ The naive model is very fast but suffers degradation in precision and violates one constraint roughly per nine targets. The decoding strategy of Section 6.1 used a default beam size of 10,000, which is extremely slow; a faster version of beam size 100 results in the same precision and recall values, but is 15 times faster on our test set. Beam size 2 results in slightly worse precision and recall values, but is even faster. All of these, however, result in many constraint violations. Strategies involving CPLEX and AD³ perform similarly to each other and to beam search on precision and recall, but eliminate most or all of the constraint violations. With respect to precision and recall, exact AD³ and beam search with a width of 10,000 were found to be statistically indistinguishable (p > 0.01). The decoding strategy with beam size 2 is 11–16 times faster than the CPLEX strategies, but is only twice as fast as AD³, and results in significantly more constraint violations. The exact algorithms are slower than the LP versions, but compared with CPLEX, AD³ is significantly faster and has a narrower gap between its exact and LP versions. We found that relaxation was tight 99.8% of the time on the test examples.

The example in Figure 1 is taken from our test set, and shows an instance where two roles, Partner_1 and Partner_2, share the “requires” relationship; for this example, the beam search decoder misses the Partner_2 role, which is a violation, while our AD³ decoder identifies both arguments correctly. Note that beam search makes plenty of linguistic violations. We found that beam search, when violating many “requires” constraints, often finds one role in the pair, which increases its recall. AD³ is sometimes more conservative in such cases, predicting neither role. Figure 6 shows such an example where beam search finds one role (Partner_1) while AD³ is more conservative and predicts no roles. Figure 7 shows another example contrasting the output of beam search and AD³ where the former predicts two roles sharing an “excludes” relationship; AD³ does not violate this constraint and tries to predict a more consistent argument set. Overall, we found it interesting that imposing the constraints did not have much effect on standard measures of accuracy.

Table 9 only shows results with gold frames. We ran the exact version of AD³ with automatic frames as well. When the semi-supervised graph objective UJSF-ℓ_1,2 is used for frame identification, the performance with AD³ is only a bit worse in comparison with beam search (row 11 in Table 8) when frame and argument identification are evaluated together. We get a precision of 72.92, a recall of 65.22 and an F₁ score of 68.86 (partial frame matching). Again, all linguistic constraints are respected, unlike beam search.

We have presented an approach to rich frame-semantic parsing, based on a combination of knowledge from FrameNet, two probabilistic models trained on full text annotations released along with the FrameNet lexicon, and expedient heuristics. The frame identification model uses latent variables in order to generalize to predicates unseen in either the FrameNet lexicon or training data, and our results show that, quite often, this model chooses a frame closely related to the gold-standard annotation. We also presented an extension of this model that uses graph-based semi-supervised learning to better generalize to new predicates; this achieves significant improvements over the fully supervised approach. Our argument identification model, trained using maximum conditional log-likelihood, unifies the traditionally separate steps of detecting and labeling arguments. Our system achieves improvements over the previous state of the art on the SemEval 2007 benchmark data set at each stage of processing and collectively. We also report stronger results on the more recent, larger FrameNet 1.5 release.

We applied the AD³ algorithm to collective prediction of a target's arguments, incorporating declarative linguistic knowledge as constraints. It outperforms the naive local decoding scheme that is oblivious to the constraints. Furthermore, it is significantly faster than a decoder employing a state-of-the-art proprietary solver; it is only twice as slow as beam search (our chosen decoding method for comparison with the state of the art), which is inexact and does not respect all linguistic constraints. This method is easily amenable to the inclusion of additional constraints.

From our results, we observed that in comparison to the SemEval 2007 data set, frame-semantic parsing performance significantly increases when we use the FrameNet 1.5 release; this suggests that the increase in the number of full text annotations and the size of the FrameNet lexicon is beneficial. We believe that with more annotations in the future (say, in the range of the number of PropBank annotations), our frame-semantic parser can reach even better accuracy, making it more useful for NLP applications that require semantic analysis.

There are several open problems to be addressed. Firstly, we could further improve the coverage of the frame-semantic parser by improving our semi-supervised learning approach; two possibilities are custom metric learning approaches (Dhillon, Talukdar, and Crammer 2010) that suit the frame identification problem in graph-based SSL, and sparse word representations (Turian, Ratinov, and Bengio 2010) as features in frame identification. The argument identification model might also benefit from semi-supervised learning. Further feature engineering and improved preprocessing, including tokenization into lexical units, improved syntactic parsing, and the use of external knowledge bases, is expected to improve the system's accuracy. Finally, the FrameNet lexicon does not contain exhaustive semantic knowledge. Automatic frame and role induction is an exciting direction of future research that could further enhance our methods of automatic frame-semantic parsing. The parser described in this article is available for download at http://www.ark.cs.cmu.edu/SEMAFOR.

We describe here the filtering rules that Johansson and Nugues (2007) used for identifying frame evoking targets in their SemEval 2007 shared task paper. They built a filtering component based on heuristics that removed words that appear in certain contexts, and kept the remaining ones.⁴⁵ These are:

• have was retained only if had an object,

• be was retained only if it was preceded by there,

• will was removed in its modal sense,

• of course and in particular were removed,

• the prepositions above, against, at, below, beside, by, in, on, over, and under were removed unless their head was marked as locative,

• after and before were removed unless their head was marked as temporal,

• into, to, and through were removed unless their head was marked as direction,

• as, for, so, and with were always removed,

• because the only sense of the word of was the frame Partitive, it was removed unless it was preceded by only, member, one, most, many, some, few, part, majority, minority, proportion, half, third, quarter, all, or none, or it was followed by all, group, them, or us,

• all targets marked as support verbs for some other target were removed.

The proof of this procedure's correctness follows from the proof in Appendix B of Martins et al. (2011b).

We thank Collin Baker, Katrin Erk, Richard Johansson, and Nils Reiter for software, data, evaluation scripts, and methodological details. We thank the reviewers of this and the earlier papers, Alan Black, Ric Crabbe, Michael Ellsworth, Rebecca Hwa, Dan Klein, Russell Lee-Goldman, Slav Petrov, Dan Roth, Josef Ruppenhofer, Amarnag Subramanya, Partha Talukdar, and members of the ARK group for helpful comments. This work was supported by DARPA grant NBCH-1080004, NSF grants IIS-0836431 and IIS-0915187, Qatar National Research Foundation grant NPRP 08-485-1-083, Google's support of the Worldly Knowledge Project at CMU, computational resources provided by Yahoo, and TeraGrid resources provided by the Pittsburgh Supercomputing Center under grant TG-DBS110003.