INTERSPEECH 2014

Structured Soft Margin Confidence Weighted Learning forGrapheme-to-Phoneme Conversion
Keigo Kubo, Sakriani Sakti, Graham Neubig, Tomoki Toda, Satoshi Nakamura
Graduate School of Information Science,
Nara Institute of Science and Technology (NAIST), Japankeigo-k@is.naist.jp, ssakti@is.naist.jp, neubig@is.naist.jp,
tomoki@is.naist.jp, s-nakamura@is.naist.jp

Abstracttasks.
However, there is still room for improvement in structured
NAROW. It updates the parameters by sequentially using N best hypotheses predicted with the current parameters. Thus,
the parameters that appear in early hypotheses are overfitted
compared with those in later hypotheses. In addition, it updates the second order statistics independently of the amountof the margin error, which means that the score difference between a correct class and a hypothesis is insufficient. This leads
to an increase the second order statistics even during the update of relatively unimportant hypotheses. This narrows the
movement of a feature weights unnecessarily. We can hypothesize that the latter problem in structured NAROW can be solved
by using multi-class Confidence Weighted Learning (CW) [17],which also uses second order statistics, instead of the structured
NAROW. However, multi-class CW tends to overfit the current
data due to non-permission of margin error, unlike structured
NAROW. In addition, it does not resolve the former problem
stated above.
In this paper, we propose a novel method called structured
Soft Margin Confidence Weighted Learning (SMCW), which
extends multi-class CW to structured learning. The learning
method newly introduces two ideas, which the multi-class CW
does not have, to solve the above problems: (1) regularization
inspired by soft margin support vector machines, allowing us
margin error, and (2) update using N -best hypotheses simultaneously and interdependently. We evaluate the effectivenessof structured SMCW on a g2p conversion task compared withthe joint sequence model, structured learning based on MIRA,
structured AROW, and structured NAROW.

In recent years, structured online discriminative learning methods using second order statistics have been shown to outperform conventional generative and discriminative models in thegrapheme-to-phoneme (g2p) conversion task. However, thesemethods update the parameters by sequentially using N -best
hypotheses predicted with the current parameters. Thus, theparameters appearing in early hypotheses are overfitted compared with those in later hypotheses. In this paper, we propose anovel method called structured soft margin confidence weighted
learning, which extends multi-class confidence weighted learning to structured learning. The proposed method extends multiclass CW in two ways, allowing for improved robustness to
overfitting: (1) regularization inspired by soft margin support
vector machines, allowing for margin error, and (2) update using N -best hypotheses simultaneously and interdependently. Inan evaluation experiment on the g2p conversion task, the proposed method improved over all other approaches in terms ofphoneme error rate with a significant difference.
Index Terms: g2p conversion, out-of-vocabulary word, online discriminative training, structured learning, confidence
weighted algorithm

1. Introduction
The speech recognition and text-to-speech fields are increasingly proceeding to open-domain and the multilingual tasks [1].
In such fields, out-of-vocabulary (OOV) words which lack pronunciations are a major bottleneck [2, 3]. In order to solve the
OOV problem, grapheme-to-phoneme (g2p) conversion, which
predicts the pronunciation for OOV words, is an extremely important component. G2p conversion has been handled using
rule-based approaches [4] and statistical approaches based on
methods such as neural networks [5], decision trees [6], maximum entropy [7], generative joint sequence models [8, 9], andonline discriminative learning [10, 11].
We have proposed structured online discriminative learning methods using second order statistics for g2p conversion,
where second order statistics represent the confidence in thecurrent value of a feature weight. The learning methods are
methods that extend Adaptive Regularization of Weight Vectors(AROW) [12] and Narrow AROW (NAROW) [13] to structured
learning, and are called as structured AROW [14] and structured NAROW [15] respectively. Especially, the performance ofstructured NAROW outperformed the performance of the conventional joint sequence model and online discriminative learning based on the Margin Infused Relaxed Algorithm (MIRA)[16] in our previous experiment with various g2p conversion

Copyright © 2014 ISCA

2. G2p Conversion
2.1. Formalization
We define g2p conversion as a process of converting a graphemesequence x into a phoneme sequence y. Given a correct
phoneme sequence y for a grapheme sequence x, we formalize g2p conversion asŷ = arg max wT Φ(x, y),(1)ywhere w indicates the classifier’s weight vector and Φ(x, y) indicates a feature vector which consists of arbitrary values suchas frequencies of joint n-gram features [11] on x and y. In
Eq.(1), ŷ can be efficiently obtained using dynamic programming. Structured learning can be employed to obtain a w thatallows for accurate prediction of the correct phoneme sequencein this framework.

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14- 18 September 2014, Singapore

the probability that the correct answer’s score is greater than orequal to the hypothesis’s score using a weight vector ŵ generated from N (w, Σ) (namely, the probability that ŵT oin ispositive or 0) is greater than η, while minimizing the movementof parameters in w and Σ with the KL divergence criterion.
By converting a normal distribution that regards the difference in the scores of the correct answer and a hypothesisŵT oin as a random variable and having a mean 0 and a variance oTin Σoin to a standard normal distribution, the constraint
in Eq.(5) can be rewritten as√(6)
wT oin ≥ ϕη oTin Σoin ,2.2. Existing Structured Learning: Structured NAROW
Structured NAROW assumes that the weight vector follows amultivariate normal distribution N (w, Σ) which has a mean w
and a variance-covariance matrix Σ. Σ, roughly speaking, is alearning rate for w. Its inverse Σ−1 is a second order information matrix representing the confidence of each feature weight.
By introducing Σ, structured NAROW avoids excessively moving the weights of the important features that have frequently
been updated. This property reduces the overfitting problem
over noisy data.
Given N -best hypotheses for a current data point (xi , yi )and current weights wi , structured NAROW solves the following optimization problems using the hypotheses sequentially tofind an optimized w and Σ in N (w, Σ),arg minw

i∑
t=1

ztT w +wT Σ−1
i w
,
2

(2)

oT
in Σoin
,
2rin

(3)

arg min DKL (N (wi , Σ)||N (wi , Σi )) +Σ

where ϕη is an output value by the inverse function of the cumulative distribution of the standard normal distribution at probability η, which is equivalent to the margin over a hypothesis.
The √optimization problem can not be minimized by the squareroot oTin Σoin , which is a concave function. Therefore, multiclass CW, in accordance with the CW proposed by Dredze et al.
[18], approximated the above constraint as
wT oin ≥ ϕη oTin Σoin .

where zt denotes a subgradient of a loss function in ∂ℓt (wt )on the t-th update, and oin is defined as Φ(xi , yi ) − Φ(xi , ŷn )which is the difference vector between the feature vector of thecorrect yi and the feature vector of the n-th hypothesis ŷn .
DKL (N (wi , Σ)||N (wi , Σi )) is the Kullback-Leibler (KL)divergence. The setting of the rin in structured NAROW is
rin = bvvinin−1 when bvin > 1 and rin = +∞ otherwise,
where vin is oT
in Σi oin > 0, and b > 0 is a new hyperparameter to adjust the generalization of learning. This setting
is derived based on the minimization of the mistake bound forthe structured NAROW and suppresses the excessive rise of theconfidence of each feature weight in order to take advantage ofthe subsequent learning.
In the structured NAROW, the loss function ℓ is defined asℓt (wt ) = max(0, vt dt − wtT ot ),When the above constraint is not satisfied, a margin error occurs. Because Σ is included in the inequality for margin error,
an update of second order statistics in the multi-class CW depends on the amount of the margin error, in contrast to structured NAROW.
In multi-class CW, updating parameters by solving Eq.(5)using the hypotheses sequentially like structured NAROW iscalled Sequential Update, and updating parameters by solving
Eq.(5) using the hypotheses in parallel and independently andthen averaging the results is called Parallel Update. From aprevious report [17], the performance of Sequential Update andParallel Update depends on the task. However, as describedabove, Sequential Update tends to overfit parameters appearing
in early hypotheses compared with those in later hypotheses.
Also, Parallel Update tends to avoid overfitting the current data,
but does not guarantee sufficient discriminative ability over thecurrent data due to the averaging. In addition, because multiclass CW does not allow us margin error, it tends to overfit thecurrent data.

(4)

where vt and ot are vin and oin on the t-th update respectively.
Also dt = d(yt , ŷt ) indicates the loss value incurred by incorrectly classifying yt as ŷt on the t-th update. We define dt as
the number of phoneme errors for the g2p conversion task. As a
subgradient zt of the above loss function, we choose −ot whenmargin error ℓt (wt ) > 0 and 0 otherwise.
As described above, structured NAROW updates the parameters by sequentially using N -best hypotheses. Also, from
Eq.(3), it updates the second order statistics independently of
the amount of margin error.

4. Structured SMCW
Multi-class CW can be applied to structured learning problems
straightforwardly, although structured learning problems needdecoding to obtain a complete feature vector. Thus, we propose structured SMCW, which inherits its basic concept frommulti-class CW. In addition, structured SMCW introduces aslack variable to allow us to violate the margin for a hypothesis and updates parameters using N -best hypotheses simultaneously and interdependently, to achieve robustness to overfitting.
Given N -best hypotheses for a current data point (xi , yi )with current weights wi , structured SMCW solves the following optimization problem using all the hypotheses simultaneously to find an optimized w and Σ,

3. Multi-Class CW
Multi-class CW also assumes that a weight vector follows amultivariate normal distribution as with structured NAROW.
Given N -best hypotheses for a current data point (xi , yi ) withcurrent weights wi , multi-class CW solves the following optimization problem using the hypotheses sequentially or in parallel to find an optimized w and Σ,
arg minarg min − log det Σ + 12 Tr(Σ−1
i Σ)
w,Σ

DKL (N (w, Σ)||N (wi , Σi ))w,Σ

s.t. Prŵ∼N (ŵ,Σ) [ŵT oin ≥ 0] ≥ η,

(7)

s.t.
(5)

∑ 2
C
+ 21 (wi − w)T Σ−1i (wi − w) + 2
n ξn
din
T
T
1
w oin ≥ ( oT Σo + rin )oin Σoin − ξn ;
in
in

(8)
∀n,

where w0 = 0, Σ0 = I, and the first, second, and third terms
correspond to terms are related to w and Σ in the KullbackLeibler divergence of the cost term in Eq.(5) (for the detail of

where η ∈ (0.5, 1] is a hyperparameter controlling the margin.
The optimization problem in Eq.(5) finds w and Σ such that1264

the derivation for KL divergencemultivariate normal∑between2
distributions, refer to [19]). C2ξisaregularization termnnemployed in L2 soft margin SVM, where ξn is a slack variable
for the n-th hypothesis to allow us margin error, and C > 0
is a hyperparameter controlling the generalization for learning.
1in
Also, ϕη in Multi-class CW is replaced with oTdΣo
+ rin
,
in
in
where din is a loss value equivalent to the number of phoneme
errors in g2p conversion and rin is the same as that in structured
NAROW. By this setting, when C in a regularization term and b
included in rin are +∞ and 0 respectively, this learning method
can be regarded as MIRA. Also, rin plays a role to suppress theexcessive rise of the confidence of each feature weight as withstructured NAROW.
To solve the above constrained optimization problem, wefirstly obtain the dual problem by using Lagrange multipliers as

Table 1: Datasets used in the g2p conversion experiment;
dataset name (Dataset), the number of grapheme and phoneme
symbols (g/p), vocabulary sizes of training data (Train), development data (Dev), and test data (Test) and the number of trials
of cross-validation (K-fold).
DatasetNETtalk
BrulexCELEXEnglishCMUdict− log det Σ + 12 Tr(Σ−1
i Σ)

L=

α

where αn ≥ 0 is a Lagrange multiplier for the n-th hypothesis.
We regard Σi as a diagonal matrix having Σip as diagonal elements, where p represents an index of the feature. By partiallydifferentiating with w, Σp , and ξn respectively and setting themto 0, we get∑
w = wi + Σi (αn oin ),
(10)

15000

1

27/39

100886

5941

12000

2

1 T
α Q̂α s.t. αn ≥ 0; ∀n,2Q̂nm = oTin Σi oim +

(11)
(12)

(16)

∑ vinp (1 + 4α̂T vip )

,

(17)

∑
δnm
vinp vimp
+2
.
C
(1
+
2α̂T vip )2p(18)(1 + 2α̂T vip )2

Because all elements in Q̂ are non-negative, in the range of
αn ≥ 0 for all n, the function maximized in Eq.(16) is a concave function and the quadratic programming problem guarantees that it has only one local optimal solution, which is theglobal optimal solution. The quadratic programming problem
can be solved by the interior point methods [20].
From the function in Eq.(16), the greater C1 , the smaller
the optimal αn for all n. Thus, a greater C1 implies better generalization for learning. Also, due to non-diagonal elements
in Q̂, when a hypothesis is similar to many other hypotheseswith respect to features and the variance of its shared features ishigh, αn of the hypothesis does not become unnecessarily high.
Namely, αn for all n are determined by interdependences of
all the hypotheses. This avoids overfitting while guaranteeing
discriminative ability over the current data.
To improve the accuracy of the approximation in thesecond-order Taylor series expansion of the first term, we would
like to select α̂n close to the optimal αn for all n. We do so by
first setting arbitrary initial values of α̂n for all n. The second
step solves the above quadratic programming problem with current α̂n . The third step sets α̂n to the optimal αn obtained in
the second step. By repeating the second step and the third step,an α̂n that improves the approximation can be found. However,the computation costs is expensive because it is necessary to recalculate for ĉ and Q̂ in Eq.(16) for new α̂n . Thus, in this paper,
we select a better α̂n close to the optimal αn for all n as below,
and do not repeat the update of α̂n . We first consider an α̂n thatcan satisfy the constraint for the n-th hypothesis in Eq.(8) by1
itself, as a better α̂n . If wiT oin ≥ din + rinoTin Σi oin holds,
such an α̂n is 0 in terms of the minimization of KL divergence.
If it does not hold, such an α̂n can be derived as below by substituting Eq.(10) and Eq.(12) into the constraint in Eq.(8) and(13)

s.t. αn ≥ 0; ∀n,where the n-th element in vector ĉ and the element on the n-th
row and the m-th column in matrix Q̂ arecn = −wiT oin + din ,δnm
Qnm = oT,in Σi oim +
C

5000

p

ip

+

39995

ĉn = −wiT oin + din +where α and vip are defined as (α1 , · · · , αN )T and1
Σip o2iN p )T re(vi1p , · · · , viN p )T = ( r1i1 Σip o2i1p , · · · , riN
spectively. From Eq.(10) and Eq.(11), Lagrange multipliers α
indicate the learning rate for each hypothesis.
By substituting Eq.(10), Eq.(11), and Eq.(12) to Eq.(9), we
get the following dual problem for Eq.(8),∑∑arg max 12 p log(1 + 2αT vip ) + 12 p 1+2α1T v
αT vipT
1 T
p 1+2αT vip + α c − 2 α Qα26/53

K-fold105where the n-th element in vector ĉ and the element on the n-th
row and the m-th column in matrix Q̂ aren∑

Vocabulary size
Dev
Test
1000
1000
1373
2747

arg max αT ĉ −

in

α

26/50
40/39

Train
17595
23353

and extracting terms related to α, we get the following quadratic
programming problem,

∑ 2
C
(9)
+ 12 (wi − w)T Σ−1i (wi − w) + 2
n ξn
∑
T
T
1
+ n αn (−w oin + din + r oin Σoin − ξn ),

Σip
Σp =
,
1 + 2αT vip
αn
ξn =
,
C

g/p

(14)
(15)

where δnm is 1 when n = m, and 0 otherwise. It is difficult
to find an optimal α due to the first, second, and third terms
in Eq.(13). However, we note that the increment of the second
term and the decrement of the third term by a change in α cancel each other out, and vice versa. Thus, the second and thirdterms can be ignored for finding an optimal α without any approximation1 . For the remaining first term, we apply a secondorder Taylor series expansion at α̂ = (α̂1 , · · · , α̂N )T . By applying the second-order Taylor series expansion to the first term
1 It can be confirmed with applying the arbitrary order Taylor series
expansion to the two terms and then extracting terms related to α or
drawing a graph for the two terms on the change of an αn .

1265

Table 2: Evaluation result of each method for phoneme error rate (PER) and word error rate (WER) in the g2p conversion task. Values
on NETtalk and Brulex in this table are obtained by averaging results on each cross-validation.
Dataset Measure Joint MIRA SAROW SNAROW SSMCW
NETtalk PER(%) 7.71 6.70
6.75
6.53
6.37
WER(%) 31.6 28.18 28.66
27.97
27.34
Brulex PER(%) 1.26 1.03
1.09
0.99
0.99
WER(%) 6.57 5.24
5.59
5.14
5.11
CELEX PER(%) 2.62 2.39
2.51
2.30
2.24
English WER(%) 12.15 11.07 11.81
11.17
10.71
CMUdict PER(%) 6.77 6.19
6.15
6.11
6.09
WER(%) 28.55 26.35 26.48
26.46
26.28
T
using the fact that oTin Σi oin ≥ oin Σoin from Eq.(11),wiT oin + αn oTin Σi oin − din +≥implemented in slearp8 as baseline g2p conversion tools.
MIRA, SAROW, SNAROW, and structured SMCW (SSMCW),
which is our proposed approach and implemented in slearp, employed context features, chain features, and joint n-gram features in accordance with [11]. The transition feature introducedin [11] was not used, as it was found to decrease performancein the NETtalk task. For alignment used in MIRA, SAROW,SNAROW and SSMCW, we used the unconstrained many-tomany alignment method of [21] as implemented in mpaligner9 .
For the context window size, joint n-gram size, hyperparameter r for SAROW, hyperparameter b for SNAROW, and N -best
hypotheses for training, we refer to our previous work [14] and[15], except hyperparameter b and C for SSMCW. 0.0075, 0.01,
and 0.0125 for b and 10, 100, and 1000 for C were tried as thehyperparameters for SSMCW. The training iterations and thehyperparameters for each method are uniquely determined byphoneme error rate on the development data.
Table 2 shows the evaluation result on the g2p conversion
task. The best performance and performances that have no significant difference according to Paired Bootstrap Resampling[22] at a level of 0.05 over the best performance are written
in bold. From Table 2, for NETtalk and CELEX, SSMCW
improved over all other approaches with a significant difference in terms of both PER and WER. The error rate reductions (ERR) for PER in NETtalk and CELEX were 17.4% and14.5% over Joint, 4.9% and 6.3% over MIRA, 5.6% and 10.8%
over SAROW, 2.5% over 2.6% SNAROW. Also, in Brulex and
CMUdict, SSMCW obtains top-class performances comparedwith other approach. The result implies that our proposed
method significantly contribute to the prediction performance.

αn
C

1 T
1 T
oin Σi oin ≥oin Σoin .
rin
rin

(19)

Note that we consider α̂n that can satisfy the constraint after
an updating with α̂m = 0 for all m with m ̸= n, and thusw = wi + αn Σi oin for the substitution by Eq.(10). Then, we
get a lower bound for such an α̂n by obtaining αn that satisfies
the inequality of the left part and the middle part for the above
as
αn ≥

1
oT
−wiT oin + din + rin
in Σi oin1oT
in Σi oin + C

.

(20)

We secondly consider the value of N for N -best hypotheses.
The greater the value of N , the smaller the optimal αn for all nwill become. Thus, we define α̂n for all n as0
if wiT oin



1
oT
≥ din + rin
in Σi oin
(21)
oT
Σ
o

i
in
T
in

−w
o
+d
+
in
in
i
rin

1
otherwise.
NoT Σ o + 1
in

i in

C

5. Experiment and Result
We evaluated our structured SMCW on the g2p conversion task.
Table 1 shows g2p conversion task datasets employed in theexperiment. The development data is employed to determine
the optimal number of training iterations and parameters foreach method. For the datasets in Table 1, NETtalk (English)
and Brulex (French) were obtained from the Pascal Letterto-Phoneme Conversion Challenge2 . CMUdict (English) and
CELEX (English) were also obtained from their corresponding
Web pages34 . We attempted to faithfully follow the convention
in [9] in terms of data exclusion and data split, except extracting
development data from training data5 .
We employed the joint sequence model (Joint) implemented in Sequitur6 , MIRA implemented in DirecTL+7 , structured AROW (SAROW), and structured NAROW (SNAROW)

6. Conclusion
We proposed structured SMCW, enhancing multi-class CWwith regularization inspired by soft margin support vector machine and update using N -best hypotheses simultaneously andinterdependently. We evaluated the proposed approach on g2p
conversion tasks with our proposed approach significantly improving over all other approaches, obtaining 2.5%-17.4% ERR
for PER in NETtalk and CELEX.

7. Acknowledgments

2 http://pascallin.ecs.soton.ac.uk/Challenges/PRONALSYL/Datasets
3 http://www.speech.cs.cmu.edu/cgi-bin/cmudict

Part of this work was supported by JSPS KAKENHI Grant
Number 24240032 and by the Commissioned Research of National Institute of Information and Communications Technology(NICT), Japan.

4 http://www.ldc.upenn.edu/Catalog/

catalogEntry.jsp?catalogId=LDC96L14
5 Dev and Test in NETtalk and other datasets are selected from thedataset at regular intervals in order, to be different for each fold. We
termed this cross-validation in accordance with [9].
6 http://sequitur.info/
7 http://code.google.com/p/directl-p/

8 http://sourceforge.jp/projects/slearp/
9 http://sourceforge.jp/projects/mpaligner/1266

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