Transferring Coreference Resolvers with Posterior Regularization
André F. T. Martins∗†∗
Priberam Labs, Alameda D. Afonso Henriques, 41, 2o , 1000-123 Lisboa, Portugal†
Instituto de Telecomunicações, Instituto Superior Técnico, 1049-001 Lisboa, Portugal
atm@priberam.pt

Abstract
We propose a cross-lingual framework
for learning coreference resolvers forresource-poor target languages, given a resolver in a source language. Our method
uses word-aligned bitext to project information from the source to the target. To
handle task-specific costs, we propose asoftmax-margin variant of posterior regularization, and we use it to achieve robustness to projection errors. We show empirically that this strategy outperforms competitive cross-lingual methods, such asdelexicalized transfer with bilingual wordembeddings, bitext direct projection, andvanilla posterior regularization.

1

Introduction

The goal of coreference resolution is to find thementions in text that refer to the same discourse
entity. While early work focused primarily on English (Soon et al., 2001; Ng and Cardie, 2002),
efforts have been made toward multilingual systems, this being addressed in recent shared tasks(Recasens et al., 2010; Pradhan et al., 2012). However, the lack of annotated data hinders rapid system deployment for new languages. Unsupervised
methods (Haghighi and Klein, 2007; Ng, 2008)
and rule-based approaches (Raghunathan et al.,2010) avoid this data annotation bottleneck, butthey often require complex generative models or
expert linguistic knowledge.
We propose cross-lingual coreference resolution as a way of transferring information froma rich-resource language to build coreference resolvers for languages with scarcer resources; as atestbed, we transfer from English to Spanish andto Brazilian Portuguese. We build upon the recent
successes of cross-lingual learning in NLP, which
proved quite effective in several structured prediction tasks, such as POS tagging (Täckström et al.,2013), named entity recognition (Wang and Manning, 2014), dependency parsing (McDonald etal., 2011), semantic role labeling (Titov and Klementiev, 2012), and fine-grained opinion mining(Almeida et al., 2015). The potential of these techniques, however, has never been fully exploitedin coreference resolution (despite some existing
work, reviewed in §6, but none resulting in an endto-end coreference resolver).
We bridge this gap by proposing a simple
learning-based method with weak supervision,
based on posterior regularization (Ganchev etal., 2010). We adapt this framework to handle
softmax-margin objective functions (Gimpel andSmith, 2010), leading to softmax-margin posterior regularization (§4). This step, while fairly
simple, opens the door for incorporating taskspecific cost functions, which are important tomanage the precision/recall trade-offs in coreference resolution systems. We show that the resulting problem involves optimizing the difference of
two cost-augmented log-partition functions, making a bridge with supervised systems based on latent coreference trees (Fernandes et al., 2012;
Durrett and Klein, 2013), reviewed in §3. Inspired by this idea, we consider a simple penalized variant of posterior regularization that tunes
the Lagrange multipliers directly, bypassing thesaddle-point problem of existing EM and alternating stochastic gradient algorithms (Ganchev et al.,2010; Liang et al., 2009). Experiments (§5) showthat the proposed method outperforms commonlyused cross-lingual approaches, such as delexicalized transfer with bilingual embeddings, direct
projection, and “vanilla” posterior regularization.

2

Architecture and Experimental Setup

Our methodology, outlined as Algorithm 1, is inspired by the recent work of Ganchev and Das(2013) on cross-lingual learning of sequence models. For simplicity, we call the source and tar-Figure 1: Excerpt of a bitext document with automatic coreference annotations (from FAPESP). The English side had its
coreferences resolved by a state-of-the-art system (Durrett and Klein, 2013). The predicted coreference chains {The pulmonary
alveoli, the alveoli, their} and {The pulmonary surfactant} are then projected to the Portuguese side, via word alignments.
Algorithm 1 Cross-Lingual Coreference Resolution via
Softmax-Margin Posterior Regularization
Input: Source coreference system S e , parallel data De andDf , posterior constraints Q.
Output: Target coreference system S f .
1: De↔f ← RUN W ORDA LIGNER(De , Df )b e ← RUN C OREF(S e , De )2: Db f ← P ROJECTA ND F ILTER E NTITIES(De↔f , D
be )
3: D
f
f
b
4: S ← L EARN C OREF W ITH S OFT M ARG PR(D , Q)

get languages English (e) and “foreign” (f ), respectively, and we assume the existence of parallel
documents on the two languages (bitext).
The first two steps (lines 1–2) run a word aligner
and label the source side of the parallel data witha pre-trained English coreference system. Afterwards, the predicted English entities are projectedto the target side of the parallel data (line 3), inducing an automatic (and noisy) training dataset
for the foreign language. Finally, a coreference
system is trained in this dataset with the aid ofsoftmax-margin posterior regularization (line 4).
We next detail all the datasets and tools involvedin our experimental setup. Table 1 provides a summary, along with some statistics.
Parallel Data. As parallel data, we use asentence-aligned trilingual (English-PortugueseSpanish) parallel corpus based on the scientific news Brazilian magazine Revista Pesquisa
FAPESP, collected by Aziz and Specia (2011).1
We preprocessed this dataset as follows. We labeled the English side with the Berkeley Coreference Resolution system v1.0, using the provided
English model (Durrett and Klein, 2013). Then,
we computed word alignments using the Berkeley aligner (Liang et al., 2006), intersected themand filtered out all the alignments whose confi1
We found that other commonly used parallel data (suchas Europarl or the UN corpus) have a predominance of directspeech that is not suitable for our newswire test domain, so
we decided not to use these data.

DatasetEN OntoNotes (train)
EN OntoNotes (dev)EN OntoNotes (test)
ES FAPESP (aligned)
ES AnCora (train)
ES AnCora (dev)
ES AnCora (test)
PT FAPESP (aligned)
PT Summ-It (train)
PT Summ-It (dev)
PT Summ-It (test)# Doc.
2,374
303
322
2,704
875
140
168
2,823
30
7
13

# Sent.
48,762
6,894
8,262
142,633
8,999
1,417
1,704
166,719
469
111
257

# Tok.
1,007,359
136,257
152,728
3,840,936
295,276
46,16753,042
4,538,147
11,771
2,983
6,491

Table 1: Corpus statistics. EN, ES, and PT denote English,
Spanish, and Portuguese, respectively.

dence is below 0.95. After this, we projected English mentions to the target side using the maximal span heuristic of Yarowsky et al. (2001). We
filtered out documents where more than 15% of
the mentions were not aligned. At this point, webf
obtained an automatically annotated corpus D
in the target language. Figure 1 shows a small
excerpt where all mentions were correctly projected. In practice, not all documents are so well
behaved: in the English-Portuguese parallel data,
only 200,175 out of the original 271,122 mentions(about 73.8%) were conserved after the projection
step. In Spanish, this number drops to 69.9%.
Monolingual Data. We also use monolingual
data for validation and comparison with supervised systems. The Berkeley Coreference Resolution system is trained in the English OntoNotes
dataset used in the CoNLL 2011 shared task; thisdataset is also used to train delexicalized models.
For Spanish, we use the AnCora dataset (Recasens and Martı́, 2010) provided in the SemEval
2010 coreference task, which we preprocessed asfollows. We split all MWEs into individual tokens(for consistency with the other corpora). We also
removed the extra gap tokens associated with zeroanaphoric relations, and the anaphoric annotations
associated with relative pronouns (e.g., in “[unacentral de ciclo combinado [que]1 debe empezara funcionar en mayo del 2002]1 ” we removed thenested mention [que]1 ), since these are not annotated in the English dataset.
For Portuguese, we used the Summ-It 3.0 corpus (Collovini et al., 2007), which contains 50
documents annotated with coreferences, from thescience section of the Folha de São Paulo newspaper. This dataset is much smaller than OntoNotes
and AnCora, as shown in Table 1. We split thedata into train, development, and test partitions.
For both Spanish and Portuguese, we obtained
automatic POS tags and dependency parses by using TurboParser (Martins et al., 2013).

3

Coreference Resolution

3.1

Problem Definition and Prior Work

In coreference resolution, we are given a set of
mentions M := {m1 , . . . , mM }, and the goal
is to cluster them into discourse entities, E :={e1 , . . . , eE }, where each ej ⊆ M and ej 6= ∅.
The set
SEE must form a partition of M, i.e., we musthave j=1 ej = M, and ei ∩ ej = ∅ for i 6= j.
A variety of approaches have been proposedto this problem, including entity-centric models(Haghighi and Klein, 2010; Rahman and Ng,
2011; Durrett et al., 2013), pairwise models(Bengtson and Roth, 2008; Versley et al., 2008),
greedy rule-based methods (Raghunathan et al.,2010), and mention-ranking decoders (Denis andBaldridge, 2008; Durrett and Klein, 2013). We
chose to base our coreference resolvers on this lastclass of methods, which permit efficient decoding
by shifting from entity clusters to latent coreference trees. In particular, the inclusion of lexicalized features by Durrett and Klein (2013) yields
nearly state-of-the-art performance with surface
information only. Given that our goal is to prototype resolvers for resource-poor languages, thismodel is a good fit—we next describe it in detail.
3.2

Latent Coreference Tree Models

Let x be a document containing M mentions,sorted from left to right. We associate to the mthmention a random variable ym ∈ {0, 1, . . . , m−1}
to denote its antecedent, where the value ym = 0
means that m is a singleton or starts a new coreference chain. We denote by Y(x) the set of coreference trees that can be formed by linking mentions to their antecedents; we represent each tree
as a vector y := hy1 , . . . , yM i. Note that eachtree y induces a unique clustering E, but that thismap is many-to-one, i.e., different trees may correspond to the same set of entity clusters. We denoteby Y(E) the set of trees that are consistent with agiven clustering E.
We model the probability distribution p(y|x) as
an arc-factored log-linear model:PM> f (x, m, y ) , (1)wpw (y|x) ∝ expmm=1
where w is a weight vector, and each f (x, m, ym )is a local feature vector that depends on the
document x, the mention m, and its candidate antecedent ym .
This model permits acheap computation of the most likely tree yb :=arg maxy∈Y(x) pw (y|x): simply compute the best
antecedent independently for each mention, andcollect them to form a tree. An analogous procedure can be employed to compute the posterior
marginals pw (ym |x) for every mention m.
Gold coreference tree annotations are rarely
available; datasets usually consist of documents
annotated with entity clusters, {hx(n) , E (n) i}N
n=1 .
Durrett and Klein (2013) proposed to learn theprobabilistic model in Eq. 1 by maximizing conditional log-likelihood, treating the coreference trees
as latent variables. They also found advantageous
to incorporate a cost function `(y, Y(E)), measuring the extent to which a prediction y differs fromthe ones that are consistent with the gold entity set
E.2 Putting these pieces together, we arrive at thefollowing loss function to be minimized:
PP0(n) ) ,
L(w) = − N
n=1 logy∈Y(E (n) ) pw (y|x(2)
where p0w is the cost-augmented distribution:
p0w (y|x) ∝ pw (y|x)e`(y,Y(E)) .

(3)

The loss function in Eq. 2 can be seen as a probabilistic analogous of the hinge loss of support
vector machines, and a model trained this way
is called a softmax-margin CRF (Gimpel andSmith, 2010). Note that L(w) is non-convex, corresponding to the difference of two log-partition
functions (both convex on w),
P
0 (w, x(n) ) − log Z(w,(n) ) ;b
L(w) = N
log
Z
x
n=1
(4)
above we denotedP>
Z 0 (w, x) = y∈Y(x) ew f (x,y)+`(y,Y(E)) (5)
P
>
b
Z(w,
x) = y∈Y(E) ew f (x,y) ,(6)2

A precise definition of this cost is provided in §4.3.

P3
where f (x, y) := M
m=1 f (x, m, ym ). Evaluating the gradient of the loss in Eq. 4 requires computing marginals for the candidate antecedents ofeach mention, which can be done in a mentionsynchronous fashion. This enables a simple
stochastic gradient descent algorithm, which was
the procedure taken by Durrett and Klein (2013).
Another way of regarding this framework, expressed through the marginalization in Eq. 2, is to“pretend” that the outputs we care about are theactual coreference trees, but that the datasets are
only “weakly labeled” with the entity clusters. We
build on this point of view in §4.1.

4

Cross-Lingual Coreference Resolution

We now adapt the framework above to learn coreference resolvers in a cross-lingual manner.
4.1

Softmax-Margin Posterior Regularization

In the weakly supervised case, the training data
may only be partially labeled or contain annotation errors. For taking advantage of these data, weneed a procedure that handles uncertainty about
the missing data, and is robust to mislabelings. We
describe next an approach based on posterior regularization (PR) that fulfills these requirements.
For ease of explanation, we introduce corpuslevel counterparts for the variables in §3.2. We
use bold capital letters X := {x(1) , . . . , x(N ) } andY := {y (1) , . . . , y (N ) } to denote the documents
and candidate coreference trees
We
QN in our corpus.
(n) ) thep(y|xdenote by pw (Y|X) :=w
n=1
conditional distribution of trees over the corpus,
induced by a model w, and similarly for the costaugmented distribution p0w (Y|X).
In PR, we define a vector g(X, Y) of corpuslevel constraint features, and a vector b of upperbounds for those features. We consider the familyof distributions over Y (call it Q) that satisfy these
constraints in a posteriori expectation,
Q := {q | Eq [g(X, Y)] ≤ b}.

(7)

To make the analysis simpler, we assume that 0 ≤b ≤ 1, and that for every j, minY gj (X, Y) = 0
and maxY gj (X, Y) = 1, where the min/max
above are over all possible coreference trees Y
that can be build from the documents X in the cor3

Note that the scope of the sum is different in Eqs. 5 and 6:b
Z (w, x) sums over all coreference trees, while Z(w,x)
sums only over those consistent with the gold clusters.
0

pus.4 Under this assumption, the two extreme values of the upper bounds have a precise meaning: if
bj = 0, the jth feature becomes a hard constraint,(i.e., any feasible distribution in Q will vanish outside {Y | gj (X, Y) = 0}), while bj = 1 turns it
into a vacuous feature.
We also make the usual assumption that theconstraint features
decompose over documents,
P(n) , y (n) ); if this were notg(xg(X, Y) := N
n=1
the case, decoding would be much harder, as the
documents would be coupled.
In vanilla PR (Ganchev et al., 2010), one seeks
the model w minimizing the Kullback-Leibler divergence between the set Q and the distribution
pw . Here, we go one step farther to consider the
cost-augmented distribution in Eq. 3. That is, we
minimize KL(Q||p0w ) := minq∈Q KL(qkp0w ).
The next proposition shows that this expression
also corresponds to a difference of two logpartition functions, as in Eq. 4.
Proposition 1. The (regularized) minimization of
the cost-augmented KL divergence is equivalent to
the following saddle-point problem:
minw KL(Qkp0w ) + γ2 kwk2 =(8)minw maxu≥0 F (w, u) − b> u + γ2 kwk2 ,where F (w, u) :=PN0(n) ) − log Z 0 (w, x(n) ) ,u
n=1 log Z (w, x(9)0with Z (w, x) as in Eq. 5, andX>>
Zu0 (w, x) :=ew f (x,y)+`(y,Y(E))−u g(x,y) .
y∈Y(x)(10)
Proof. See Appendix A.
In sum, what Proposition 1 shows is that we
can easily extend the vanilla PR framework ofGanchev et al. (2010) to incorporate a task-specificcost: by Lagrange duality, the resulting optimization problem still amounts to finding a saddle
point of an objective function (Eq. 8), which involves the difference of two log-partition functions (Eq. 9). The difference is that these partition functions now incorporate the cost term`(y, Y(E)). If this cost term has a factorizationcompatible with the features and the constraints,
this comes at no additional computational burden.
4
We can always reduce the problem to this case by scaling
and adding a constant to the constraint feature vectors.

4.2

Penalized Variant

In their discriminative PR formulation for learning
sequence models, Ganchev and Das (2013) optimize an objective similar to Eq. 8 by alternating
stochastic gradient updates with respect to w andu. In their procedure, b was chosen a priori via
linear regression (see their Figure 2).
Here, we propose a different strategy, based on
Proposition 1 and a simple observation: while theconstraint values b have a more intuitive meaning
than the Lagrange multipliers u (since they may
correspond, e.g., to proportions of events observedin the data), choosing these upper bounds is often
no easier than tuning u. In this case, a preferable
strategy is to specify u directly—this leaves thisvariable fixed in Eq. 8, and allows us to get rid ofb. The resulting problem becomesminw F (w, u) + γ2 kwk2 ,(11)which is a penalized variant of PR and no longer asaddle point problem. This variant requires tuning
the Lagrange multipliers uj in the range [0, +∞],
for every constraint. The two extreme cases of
bj = 0 and bj = 1 correspond respectively to
uj = +∞ and uj = 0.5 Note that this grid searchis only appealing for a small number of posterior
constraints at corpus-level (since document-level
constraints would require tuning separate coefficients for each document).
The practical advantages of the penalized variant over the saddle-point formulation are illustrated in Figure 2, which compares the performance of stochastic gradient algorithms for thetwo formulations (there, η2 = 1 − b2 ).
An interesting aspect of this penalized formulation is its resemblance to latent variable models.
Indeed, the objective of Eq. 11 is also a difference of log-partition functions, as the latent-tree
supervised case (cf. Eq. 4). The noticeable difference is that now both partition functions include
extra cost terms, either task-specific (`(y, Y(E))
in Z 0 ) or with soft constraints (u> g(x, y) in Zu0 ).
In particular, if we set a single constrained feature
g1 (x, y) := I(`(y, Y(E)) 6= 0) with weight u1 →+∞, all non-zero-cost summands in Zu0 (w, x)
5This follows from Lagrange duality. If bj = 1, theconstraint is vacuous and by complementary slackness wemust have uj = 0. If bj = 0, this becomes a hard constraint, so for the nth document, any coreference tree y forwhich gj (x(n) , y) 6= 0 must have probability zero—this corresponds to setting uj → +∞ in Eq. 10.

Figure 2: Comparison of saddle-point and penalized PR for
Spanish, using the setup in §5.5. Left: variation of the multiplier u2 over gradient iterations, with strong oscillations ininitial epochs and somewhat slow convergence. Right: impact in the averaged F1 scores (on the dev-set). Contrast withthe more “stable” scores achieved by the penalized method.

bvanish and we get Zu0 (w, x) = Z(w,x), recovering the supervised case (see Eq. 6).
Intuitively, this formulation pushes probability
mass toward structures that respect the constraints
in Eq. 7, while moving away from those that have alarge task-specific cost. A similar idea, but applied
to the generative case, underlies the framework ofconstrastive estimation (Smith and Eisner, 2005).
4.3

Cost Function

Denote by Em the entire coreference
chain of theS
mth mention (so E =m∈M {Em }), and by
Msing := {m ∈ M | Em = {m}} the set of mentions that are projected as singleton in the data (wecall this gold-singleton mentions).
We design a task-specific cost `(by , Y(E)) asin Durrett and Klein (2013) to balance threekinds of mistakes: (i) false anaphora (bym 6=
0 while m ∈ Msing ); (ii) false new (bym =
0 while m ∈/ Msing ); and (iii) wrong link(b
ym 6= 0 but Em 6= Eybm ). Letting IFA (bym , E),IFN (bym , E), and IWL (bym , E) be indicators forthese events, we define aP
weighted Hamming costfunction: `(by , Y(E)) := M
ym , E)+
m=1 (αFA IFA (bαFN IFN (bym , E) + αWL IWL (bym , E)). We set
αFA = 0.0, αFN = 3.0, and αWL = 1.0.6 Since
this cost decomposes as a sum over mentions, thecomputation of cost-augmented marginals (necessary to evaluate the gradient of Eq. 11) can still bedone with mention-ranking decoders.
4.4

Constraint Features

Finally, we describe the constraint features (Eq. 7)
used in our softmax-margin PR formulation.
Constraint #1: Clusters should not split. Let|M| − |E| be the number of anaphoric mentions
6
The only difference with respect to Durrett and Klein(2013) is that they set αFA = 0.1. We set this coefficient
to zero so that all configurations licensed by the constraint
features (to be made precise in §4.4) will have zero cost.

in the projected data. We push these mentions topreserve their anaphoricity (ym 6= 0) and to havetheir antecedent in the projected coreference chain(Em = Eym ). To do so, we force the fraction ofmentions satisfying these properties to be at leastη1 . This can be enforced via a constraint feature
g1 (X, Y) :=(12)
PN PM (n)
(n)
(n)
(n)
− n=1 m=1 I(ym 6= 0 ∧ Em = Eym ),PN(|M(n) | −and an upper bound b1 := −η1 n=1|E (n) |). (These quantities are summed by a constant and rescaled to meet the assumption in §4.1.)
In our experiments, we set η1 = 1.0, turning this
into a hard constraint. This is equivalent to setting
u1 = +∞ in the penalized formulation.
Constraint #2: Most projected singletons
should become non-anaphoric. We define asoft constraint so that a large fraction of the goldsingleton mentions m ∈ Msing satisfy ym = 0.
This can be done via a constraint feature
g2 (X, Y) :=(13)
PN PM (n)(n)(n)
− n=1 m=1 I(ym = 0 ∧ Em = {m}),P(n)and an upper bound b2 := −η2 N
n=1 |Msing |. In
our experiments, we varied η2 in the range [0, 1],either directly or via the dual variable u2 , as described in §4.1. The extreme case η2 = 0 corresponds to a vacuous constraint, while for η2 = 1
this becomes a hard constraint which, combinedwith the previous constraint, recovers bitext direct
projection (see §5.3). The intermediate case makes
this a soft constraint which allows some singletons to be attached to existing entities (therefore
introducing some robustness to non-aligned mentions), but penalizes the number of reattachments.

5

Experiments

We now present experiments using the setup in§2. We compare our coreference resolvers trainedwith softmax-margin PR (§5.5) with three otherweakly-supervised baselines: delexicalized transfer with cross-lingual embeddings (§5.2), bitext
projection (§5.3), and vanilla PR (§5.4). We also
run fully supervised systems (§5.1), to obtain upper bounds for the level of performance we expect
to achieve with the weakly-supervised systems.
An important step in coreference resolution systems is mention prediction. For English, mention
spans were predicted from the noun phrases givenby the Berkeley parser (Petrov and Klein, 2007),the same procedure as Durrett and Klein (2013).
For Spanish and Portuguese, this prediction reliedon the output of the dependency parser, using asimple heuristic: besides pronouns, each maximal
span formed by contiguous descendants of a noun
becomes a candidate mention. This heuristic isquite effective, as shown by Attardi et al. (2010).
5.1

Supervised Systems

Table 2 shows the performance of supervised systems for English, Spanish and Portuguese. All optimize Eq. 4 appended with an extra regularization
term γ2 kwk2 , by running 20 epochs of stochastic
gradient descent (SGD; we set γ = 1.0 and selected the best epoch using the dev-set). All lexicalized systems use the same features as the SUR FACE model of Durrett and Klein (2013), plus features for gender and number.7 We collected a listof pronouns for all languages along with their gender, number, and person information. For English,
we trained on the WSJ portion of the OntoNotes
dataset, and for Spanish and Portuguese we trainedon the monolingual datasets described in §2.
We observe that the Spanish system obtains averaged F1 scores around 44%, a few points below
the English figures.8 In Portuguese, these scores
are significantly lower (in the 37–39% range),
which is explained by the fact that the training
dataset is much smaller (cf. Table 1).
For English, we also report the performance ofdelexicalized systems, i.e., systems where all thelexical features were removed. The second rowof Table 2 shows a drop of 2–2.5 points with respect to the lexicalized system. For the third andfourth rows, the lexical features were replacedby bilingual word embeddings (either EnglishSpanish or English-Portuguese; a detailed description of these embeddings will be provided in §5.2).
Here the drop is small, and for English-Spanish it
looks on par with the lexicalized system.
7

For English, the gender and number of nominal andproper mentions were obtained from the statistics collectedby Bergsma and Lin (2006). For Spanish and Portuguese weused a simple heuristic for nominal mentions, based on thedeterminer preceding the noun (when there is one).
8
We point out that the supervised Spanish system we
present here is strong enough to outperform all participating
systems in the SemEval 2010’s closed regular track. Whentrained on the original Spanish SemEval data (with zero- andrelative pronoun anaphoras) and evaluated in the provided
scorer, it achieves 53.0% averaged F1 in the test partition; forcomparison, TALN-1 (Attardi et al., 2010), the best system atthe shared task, achieved 49.6% averaged F1 .

EN lexicalized
EN delexicalized, no embed.
EN delexicalized, emb. EN-ES
EN delexicalized, emb. EN-PT
ES lexicalized
PT lexicalized

MUC
58.35
56.59
57.55
57.91
48.24
35.60

B3
50.75
48.81
49.83
49.67
40.97
34.47

Dev
CEAFe
52.08
49.95
51.21
51.01
43.59
42.56

Avg.
53.73
51.78
52.86
52.86
44.27
37.54

MUC
59.07
55.96
59.00
58.03
47.03
41.61

B3
49.25
46.94
49.25
48.16
40.68
36.91

Test
CEAFe
48.78
46.19
49.00
48.33
44.09
40.96

Avg.
52.37
49.70
52.42
51.51
43.93
39.83

Table 2: Results for the supervised systems. We show also the performance of delexicalized English systems, with and withoutcross-lingual embeddings. Shown are MUC (Vilain et al., 1995), B3 (Bagga and Baldwin, 1998), and CEAFe (Luo, 2005), as
well their averaged F1 scores, all computed using the reference implementation of the CoNLL scorer (Pradhan et al., 2014).

ES simple baseline
ES baseline #1 (delex. transfer)
ES baseline #2 (bitext dir. proj.)
ES baseline #3 (vanilla PR)
ES softmax-margin PR
PT simple baseline
PT baseline #1 (delex. transfer)
PT baseline #2 (bitext dir. proj.)
PT baseline #3 (vanilla PR)
PT softmax-margin PR

MUC
25.73
33.04
39.42
41.29
42.34
26.04
22.51
30.43
30.97
33.43

B3
24.73
27.47
30.04
33.68
35.53
26.67
23.27
27.37
27.82
31.00

Dev
CEAFe
27.89
32.71
38.25
38.56
39.95
33.19
33.27
36.47
35.14
38.82

Avg.
26.12
31.07
35.90
37.84
39.27
28.63
26.35
31.42
31.31
34.42

MUC
26.06
34.35
37.21
39.34
41.22
22.72
31.11
31.93
38.39
38.18

B3
26.12
28.69
29.72
32.95
35.30
23.91
27.36
27.97
33.34
34.05

Test
CEAFe
29.87
34.42
35.97
38.23
39.94
27.35
32.78
35.40
38.73
39.47

Avg.
27.35
32.49
34.30
36.84
38.82
24.66
30.42
31.77
36.82
37.23

Table 3: Results for all the cross-lingual systems. Bold indicates the overall highest scores. As a lower bound, we show a simple
deterministic baseline that, for pronominal mentions, selects the closest non-pronominal antecedent, and, for non-pronominal
mentions, selects the closest non-pronominal mention that is a superstring of the current mention.

5.2

Baseline #1: Delexicalized Transfer With
Cross-Lingual Embeddings

We now turn to the cross-lingual systems. Delexicalized transfer is a popular strategy in NLP (Zeman and Resnik, 2008; McDonald et al., 2011),
recently strengthened with cross-lingual word representations (Täckström et al., 2012). The procedure works as follows: a delexicalized model forthe source language is trained by eliminating all
the language-specific features (such as lexical features); then, this model is used directly in the target language. We report here the performance of
this baseline on coreference resolution for Spanish and Portuguese, using the delexicalized models
trained on the English data as mentioned in §5.1.
To achieve a unified feature representation, we
mapped all language-specific POS tags to universal tags (Petrov et al., 2012). All lexical features
were replaced either by cross-lingual word embeddings (for words that are not pronouns); or bya universal representation containing the gender,
number, and person information of the pronoun.
To obtain the cross-lingual word embeddings, we
ran the method described by Hermann and Blunsom (2014) for the English-Spanish and EnglishPortuguese pairs, using the parallel sentences in§2. When used as features, these 128-dimensional
continuous representations were scaled by a factorof 0.5 (selected on the dev-set), using the proce-dure of Turian et al. (2010).
The second and seventh rows in Table 3 show
the performance of this baseline, which is rather
disappointing. For Spanish, we observe a large
drop in performance when going from supervised
training to delexicalized transfer (about 11–13%
in averaged F1 ). For Portuguese, where the supervised system is not so accurate, the difference isless sharp (about 9–11%). These drops are mainly
due to the fact that this method does not take into
account the intricacies of each language—e.g.,possessive forms have different agreement rules inEnglish and in Romance languages;9 those, on theother hand, have clitic pronouns that are absent inEnglish. Feature weights that promote certain English agreement relations may then harm performance more than they help.
5.3

Baseline #2: Bitext Direct Projection

Another popular strategy for cross-lingual learning is bitext direct projection, which consists inprojecting annotations through parallel data inthe source and target languages (Yarowsky et al.,
2001; Hwa et al., 2005). This is essentially thesame as Algorithm 1, except that line 4 is replacedby simple supervised learning, via a minimization
9

For example, in Figure 1, their agrees in number withthe possessor (the alveoli), but the corresponding sua agrees
in number and gender with the thing possessed (função).

of the loss function in Eq. 4 with `2 -regularization.
This procedure has the disadvantage of being very
sensitive to annotation errors, as we shall see. For
Portuguese, this baseline is a near-reproduction of
Souza and Orăsan (2011)’s work, discussed in §6.
The third and eighth rows in Table 3 showthat this baseline is stronger than the delexicalizedbaseline, but still 6–8 points away from the supervised systems. This gap is due to a mix of two
factors: prediction errors in the English side of
the bitext, and missing alignments. Indeed, when
automatic alignments are used, false negatives for
coreferent pairs of mentions are common, due towords that have not been aligned with sufficiently
high confidence. The direct projection method is
not robust to these annotation errors.
5.4

Baseline #3: Vanilla PR

Our last baseline is a vanilla PR approach; thisis an adaptation of the procedure carried out by
Ganchev and Das (2013) to our coreference resolution problem. The motivation is to increase therobustness of bitext projection to annotation errors, which we do by applying the soft constraints
in §4.4. We seek a saddle-point of the PR objective by running 20 epochs of SGD, alternating wupdates and u-updates. The best results in the devset were obtained with η1 = 1.0 and η2 = 0.9.
By looking at the fourth and ninth rows of Table 3, we observe that vanilla PR manages to reduce the gap to supervised systems, obtaining consistent gains over the bitext projection baseline(with the exception of the Portuguese dev-set).
This confirms the ability of PR methods to handle
annotation mistakes in a robust manner.
5.5

Our Proposal: Softmax-Margin PR

Finally, the fifth and last rows in Table 3 show theperformance of our systems trained with softmaxmargin PR, as described in §4.1. We optimized theloss function in Eq. 11 with γ = 1.0 by running 20
epochs of SGD, setting u1 = +∞ and u2 = 1.0(cf. §4.4)—the last value was tuned in the dev-set.
As shown in Figure 2, this penalized variant wasmore effective than the saddle point formulation.
From Table 3, we observe that softmax-margin
PR consistently beats all the baselines, narrowing the gap with respect to supervised systems toabout 5 points for Spanish, and 2–3 points for Portuguese. Gains over the vanilla PR procedure (thestrongest baseline) lie in the range 0.5–3%. Thesegains come from the ability of softmax-margin PR

to handle task-specific cost functions, enabling abetter management of precision/recall tradeoffs.
5.6

Error Analysis

We carried out some error analysis, focused on
the Spanish development dataset, to better understand where the improvements of softmax-margin
PR come from. The main conclusions carry out tothe Portuguese case, with a few exceptions, mostly
due to different human annotation criteria.
Table 4 shows the precision and recall scoresfor mention prediction and the different coreference evaluation metrics. Note that all systems predict the same candidate mentions; however a final
post-processing discards all mentions that ended
up in singleton entities, for compliance with theofficial scorer. Therefore, the mention prediction
score reflects how well a system does in predicting
if a mention is anaphoric or not. The first thing tonote is that the PR methods, due to their ability
to create new links during training (via constraint#2) tend to predict fewer singletons than the direct
projection method. Indeed, we observe that soft
max-margin PR achieves 47.1% mention prediction recall, which is more than 5% above the direct projection method, and 10% above the delexicalized transfer method. Note also that, whilethe vanilla PR method achieves higher recall than
the two other baselines, it is still almost 5% below the system trained with soft-max margin PR.
This is because vanilla PR does not benefit fromthe cost function in §4.3—such cost is able to penalize false non-anaphoric mentions and encourage larger clusters, allowing softmax-margin PR
to achieve a better precision-recall trade-off. From
Table 4, we can see that this improvement in mention recall consistently translates into higher recall
for the MUC, B3 and CEAFe coreference metrics.
Further analysis revealed that a major source oferror for the delexicalized baseline is its inability to handle pronominal mentions robustly acrosslanguages—as hinted in footnote 9. In practice,
we found the delexicalized systems to be quite
conservative with possessive pronouns: for the
Spanish dataset, where the vast majority of possessive pronouns are anaphoric, the delexicalized
model incorrectly predicts 53.3% of these pronouns as non-anaphoric. The direct projection
model is slightly less conservative, missing 30.1%of the possessives (arguably due to its inability torecover missing links in the projected data, dur-

delex.
dir. proj.
vanilla PR
our PR

Mention
MUC
B3
CEAFe
37.1 / 62.2 25.6 / 46.5 19.6 / 45.7 27.9 / 39.5
41.7 / 77.5 29.3 / 60.4 19.2 / 69.5 31.8 / 47.9
42.2 / 78.0 30.9 / 62.3 23.2 / 61.7 31.9 / 48.8
47.1 / 74.1 33.7 / 57.1 26.0 / 56.1 34.9 / 46.7

Table 4: Recall/precision scores for mention prediction,
MUC, B3 and CEAFe , all computed in the Spanish dev set.

ing training). By comparison, the vanilla and softmax margin PR models only miss 4.9% and 3.4%of the possessives, respectively. In Portuguese,where many possessives are not annotated in thegold data, we observe a similar but much less pronounced trend.

6

Related Work

While multilingual coreference resolution has
been the subject of recent SemEval and CoNLL
shared tasks, no submitted system attempted
cross-lingual training. As shown by Recasens andHovy (2010), language-specific issues pose a challenge, due to phenomena as pronoun dropping andgrammatical gender that are absent in English but
exist in other languages. We have discussed someof these issues in the scope of the present work.
Harabagiu and Maiorano (2000) and Postolache
et al. (2006) projected English corpora to Romanian to bootstrap human annotation, either manually or via automatic alignments. Rahman and Ng(2012) applied translation-based projection at test
time (but require an external translation service).
Hardmeier et al. (2013) addressed the related taskof cross-lingual pronoun prediction. While allthese approaches help alleviate the corpus annotation bottleneck, none resulted in a full coreference
resolver, which our work accomplished.
The work most related with ours is Souza andOrăsan (2011), who also used parallel data totransfer an English coreference resolver to Portuguese, but could not beat a simple baseline thatclusters together mentions with the same head.
Their approach is similar to our bitext direct projection baseline, except that they used Reconcile(Stoyanov et al., 2010) instead of the Berkeley
Coreference System, and a smaller version of the
FAPESP corpus. We have shown that our softmaxmargin PR procedure is superior to this approach.
Discriminative PR has been proposed by
Ganchev et al. (2010). The same idea underlies
the generalized expectation criterion (Mann and
McCallum, 2010; Wang and Manning, 2014). An
SGD algorithm for solving the resulting saddle

point problem has been proposed by Liang et al.
(2009), and used by Ganchev and Das (2013) forcross-lingual learning of sequence models. We extended this framework in two aspects: by incorporating a task-specific cost in the objective function,and by formulating a penalized variant of PR.

7

Conclusions

We presented a framework for cross-lingual transfer of coreference resolvers. Our method uses
word-aligned bitext to project information fromthe source to the target language.
Robustness to projection errors was achieved via a
PR framework, which we generalized to handle
task-specific costs, yielding softmax-margin PR.
We also proposed a penalized formulation thatis effective for a small number of corpus-based
constraints. Empirical gains were shown overthree popular cross-lingual methods: delexicalized
transfer, bitext direct projection, and vanilla PR.

Acknowledgments
I would like to thank the reviewers for theirhelpful comments, José Guilherme Camargo de
Souza for pointing to existing datasets, and Mariana Almeida for valuable feedback. This work
was partially supported by the EU/FEDER programme, QREN/POR Lisboa (Portugal), underthe Intelligo project (contract 2012/24803), andby the FCT grants UID/EEA/50008/2013 and
PTDC/EEI-SII/2312/2012.

A

Proof of Proposition 1

Let us fix w and see how to evaluate KL(Q||p0w ) =minq∈Q KL(qkp0w ). We have:P
KL(qkp0w ) = −H(q) − Y q(Y) log p0w (Y|X)
P= −H(q) + n log Z 0 (w, x(n) ) −P>
Y q(Y)(w f (X, Y) + `(Y)),PN(n)
where `(Y) :=)) and f (X, Y) :=n=1 `(y, Y(E
PN
(n)
(n)
, y ). Introducing Lagrange multipliers u for
n=1 f (xthe posterior constraints, we get the Lagrangian function:P
L(q, u) = −H(q) + n log Z 0 (w, x(n) ) − b> uP
− Y q(Y)(w>f (X, Y)+`(Y)−u>g(X, Y)).
By standard variational arguments (namely, Fenchel duality
between the the log-partition function and the negative entropy; see e.g. Martins et al. (2010)), we have that the optimalq ∗ that minimizes the Lagrangian is>q ∗ (Y) =>ew f (X,Y)+`(Y)−u g(X,Y)
.
QN
0
(n) )
n=1 Zu (w, x

Plugging this in the Lagrangian yields Eq. 8.

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