INTERSPEECH 2017
August 20–24, 2017, Stockholm, Sweden

DNN-SPACE: DNN-HMM-based Generative Model of Voice F0 Contours
for Statistical Phrase/Accent Command Estimation
Nobukatsu Hojo1 , Yasuhito Ohsugi2 , Yusuke Ijima1 , Hirokazu Kameoka3
1

NTT Media Intelligence Laboratories, NTT Corporation, Japan
2
The University of Tokyo, Japan
3
NTT Communication Science Laboratories, NTT Corporation, Japanhojo.nobukatsu@lab.ntt.co.jp

Abstract

this approach is that a phrase/accent command pair sequence
is modeled as an output sequence of a path-restricted hidden
Markov model (HMM) so that estimating the state transition
amounts to estimating the phrase/accent commands. There are
two benefits for this statistical reformulation: one is to derive
an efficient parameter inference algorithm utilizing powerfulstatistical methods, and the other is to obtain an automaticallytrainable version of the Fujisaki model. Owing to these benefits, some SPACE-based applications have already been proposed such as F0 generation for text-to-speech synthesis [18]or F0 prediction for electrolaryngeal speech enhancement [19].
Therefore, if we could improve the parameter estimation accuracy of the SPACE method, we expect that it will also be able
to improve the basic performance of such SPACE-based applications.
An important approach to improve Fujisaki model parameter estimation is leveraging auxiliary linguistic information [20, 21, 22, 23]. Since the phrase/accent commands areclosely associated with the linguistic information such as breathgroup or accent nucleus, it is expected that the command estimation accuracy can be improved by using them as auxiliary information for inferences. In a previous study, Hirose et al. [21]proposed to use linguistic information to obtain a first approximation of the location of the commands which is then adjusted
by an iterative analysis-by-synthesis process. Torres et al. [22]also proposed to use genetic algorithms to estimate Fujisaki
model parameters considering linguistic aspects. It is expectedthat the parameter estimation accuracy of the SPACE method
will also improve by utilizing the linguistic information.
Motivated in a way similar to these previous studies, weaimed to improve the parameter estimation accuracy of the
SPACE method by extending the statistical model so that it
would incorporate a linguistic information model. More specifically, we constructed a deep neural network (DNN) that maps
the linguistic feature vectors to the state posterior probabilitiesof the HMM. We formulated a generative model of the F0 contours by combining the DNN with the SPACE model in sucha way that a parameter estimation algorithm could be derived
on the basis of a DNN-HMM [24] framework and an auxiliary
function method. We call this proposed method “DNN-SPACE”
in this paper. The key of the formulation is to incorporate a linguistic information model to the conventional SPACE method
without changing its basic parameter optimization algorithms.
The rest of this paper is organized as follows. Section 2
briefly reviews the original Fujisaki model and a discrete-time
stochastic counterpart to the Fujisaki model (SPACE). Section
3 formulates the proposed method (DNN-SPACE) to extend
SPACE to integrate the linguistic information models. Section
4 presents experimental evaluations obtained for the proposed
method. Section 5 concludes the paper with a summary of key
points and a mention of future work.

This paper proposes a method to extract prosodic features from a speech signal by leveraging auxiliary linguistic
information. A prosodic feature extractor called the statisticalphrase/accent command estimation (SPACE) has recently been
proposed. This extractor is based on a statistical model formulated as a stochastic counterpart of the Fujisaki model, a wellfounded mathematical model representing the control mechanism of vocal fold vibration. The key idea of this approachis that a phrase/accent command pair sequence is modeled as
an output sequence of a path-restricted hidden Markov model(HMM) so that estimating the state transition amounts to estimating the phrase/accent commands. Since the phrase and accent commands are related to linguistic information, we may
expect to improve the command estimation accuracy by using
them as auxiliary information for the inference. To model the
relationship between the phrase/accent commands and linguistic information, we construct a deep neural network (DNN) thatmaps the linguistic feature vectors to the state posterior probabilities of the HMM. Thus, given a pitch contour and linguistic
information, we can estimate phrase/accent commands via state
decoding. We call this method “DNN-SPACE.” Experimental
results revealed that using linguistic information was effectivein improving the command estimation accuracy.
Index Terms: the Fujisaki model, SPACE, linguistic information, DNN

1. Introduction
The fundamental frequency (F0 ) contours in speech containvarious types of non-linguistic information such as the speaker’s
identity, emotions and intentions. Modeling the F0 contoursof speech utterances can thus be potentially useful for many
speech applications, including speech recognition, speakerrecognition, speech synthesis and dialog systems.
The Fujisaki model [1, 2] is a well-founded mathematicalmodel that describes an F0 contour as the sum of two contributions. This model approximates actual F0 contours of speech
fairly well when the model parameters are appropriately chosen, and its validity has been demonstrated for many typologically diverse languages [1, 3, 4, 5, 6, 7, 8, 9]. Since prosodic
features in speech are predominantly characterized by the levels
and timings of the phrase and accent components, one important
challenge is to solve the inverse problem of estimating the Fujisaki model parameters automatically from a raw F0 contour.
For estimating the Fujisaki model parameters from a raw
F0 contour, several methods have been developed [2, 10, 11, 12,
13, 14, 15]. Among these methods, the statistical phrase/accentcommand estimation (SPACE) [16, 17, 15] method is noteworthy because it is based on a statistical model formulated as astochastic counterpart of the Fujisaki model. The key idea of

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http://dx.doi.org/10.21437/Interspeech.2017-719

Here, we briefly review the conventional probabilistic pitch
contour model based on the discrete-time version of the Fujisaki
model [16, 17, 15].
In the original Fujisaki model, phrase commands and accent commands are assumed to respectively consist of Diracdeltas and rectangular pulses. In addition, they are not allowed to overlap each other. To incorporate these requirements,
we find it convenient to model the up [k] and ua [k] pair, i.e.,o[k] = (up [k], ua [k])⊤ , using a path-restricted HMM. In previous studies [16, 17, 15], the authors assumed that {o[k]}K
k=1
is a sequence of outputs generated from an HMM with the specific topology illustrated in Fig. 1.
In state r0 , µp [k] and µa [k] are both constrained to be zero.
In state p1 , referred to as the “phrase state”, µp [k] can take a
non-zero value, Cp [k], whereas µa [k] is still restricted to zero.
At the phrase state, no self transitions are allowed. In state r1 ,µp [k] and µa [k] become zero again. This path constraint restricts µp [k] to consisting of isolated deltas. State r1 leads tostates a1 , · · · , aN , referred to as “accent states”. At each accent(a)state, µa [k] can take a different non-zero value Cn , whereasµp [k] is forced to be zero. A direct state transition from an accent state to a different state without passing through state r1 is
not allowed. This path constraint restricts µa [k] to consistingof rectangular pulses. The output distribution of each state is
assumed to be the Gaussian distribution
o[k] ∼ N (csk , Γsk ),(6)
where sk indicates the state variable. Namely, the mean vector µ[k] = (µp [k], µa [k])⊤ = csk and the covariance matrix
Σ[k] = Γsk is considered to evolve in time as a result of thestate transition s1 , · · · , sK . The definition of the above HMM
can be summarized as follows:

Figure 1: Command function modeling with an HMM.

2. Generative model of speech F0 contours
2.1. Original Fujisaki model
The Fujisaki model [1, 2] assumes an F0 contour on a logarithmic scale, y(t), where t is time, is the superposition of threecomponents: a phrase component yp (t), an accent componentya (t), and a base component yb :y(t) = yp (t) + ya (t) + yb .
(1)
The phrase component yp (t) consists of the major-scale pitch
variations over the duration of the prosodic units, and the accent component ya (t) consists of the smallerscale pitch variations in accented syllables. These two components are modeled
as the outputs of second-order critically damped filters, one being excited with a command function up (t) consisting of Diracdeltas (phrase commands), and the other with ua (t) consistingof rectangular pulses (accent commands):
xp (t) = Gp (t) ∗ up (t),{α2 te−αt (t ≥ 0),
Gp (t) =0(t < 0)(2)xa (t) = Ga (t) ∗ ua (t),{β 2 te−βt (t ≥ 0)
Ga (t) =0(t < 0)(4)

output sequence : o[k] = (up [k], ua [k])T
state set S = {r0 , p0 , r1 , a0 , · · · , aN −1 }state sequence : s = {sk }koutput distribution : p(o[k]|sk = i) = N (ci [k], Σi )T
(i ∈ r0 , r1 )(0, 0)(p),ci [k] = (C [k], 0)T (i ∈ p0 )(0, C (a) )T(i ∈ an )
n
[ 2
]
vp,i
0
Σi =
.
2
0 va,i(3)(5)

state transition probability : ϕî,i = p(sk = i|sk−1 = î)where ∗ denotes convolution over time. The baseline component yb is a constant value related to the lower bound of the
speaker’s F0 , below which no regular vocal fold vibration canbe maintained. α and β are natural angular frequencies of
the two second-order systems, which are known to be almost
constant within an utterance as well as across utterances for aparticular speaker. It has been shown that α = 3 rad/s andβ = 20 rad/s can be used as default values.
It is interesting to note that the phrase and accent commands, which we will henceforth refer to as the Fujisaki model
parameters, can be interpreted as quantities related to linguistic
information. In the Japanese language, a phrase command andan accent command typically occur at the beginning of eachbreath group and over the range of accent nucleus in each accentual phrase, respectively.
2.2. Probabilistic formulation of F0(SPACE)

Given the state sequence s = {sk }K
k=1 , the above HMM
generates the up [k] and ua [k] pair. Taking into consideration(2) and (4), we then fed up [k] and ua [k] through the different
critically damped filters Gp [k] and Ga [k] to generate the phrase
and accent components yp [k] and ya [k]:xp [k] = Gp [k] ∗ up [k],(7)xa [k] = Ga [k] ∗ ua [k](8)where ∗ denotes convolution over k. An F0 contour is thengiven byy[k] = xp [k] + xa [k] + xb ,(9)where xb denotes the baseline value.

3. Proposed model (DNN-SPACE)

contour model

As discussed in sec. 2.1, phrase and accent commands areclosely associated with linguistic information such as breath

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HMM

θ

s

o

maximize the posterior probability p(o, s, θ|y, w, λ) with respect to o, s and θ. In a similar way that Sato et al. did fortheir proposed parameter optimization algorithm [25], for our
method we derived an iterative algorithm to search the maximum posterior probability:λwô = arg max p(o, ŝ, θ̂|y, w, λ),

(12)

o

y

Fujisaki model

Linguistic information
model (DNN)ŝ = arg max p(ô, s, θ̂|y, w, λ),

(13)

s

θ̂ = arg max p(ô, ŝ, θ|y, w, λ).

(14)

θ

Figure 2: Graphical representation of proposed model.

It should be noted from the decomposition
p(y, o, w, s, θ|λ) =p(y|o)p(o|s, θ)p(w|s, λ)p(s|θ)p(θ)(15)
that the objective function of (12) and (14) is independent fromw and λ. This means the updates of (12) and (14) can be derived in the same way as Sato et al. described [25] by using theauxiliary function method. As for the update of (13), the objective function is in the same form as that of DNN-HMM [24].
Therefore, a Viterbi algorithm-based update algorithm can bederived.

groups or accent nucleus. Thus, we may expect to improve thecommand estimation accuracy by leveraging auxiliary linguistic information. To incorporate the linguistic information modelto the conventional SPACE method, we constructed a DNN thatmaps the linguistic feature vectors to the state posterior probabilities of the HMM. We formulated the generative model ofthe F0 contours by combining the DNN with the SPACE modelin such a way that a parameter estimation algorithm could bederived on the basis of the DNN-HMM [24] framework and an
auxiliary function method. The key to our formulation is incorporating a linguistic information model to the conventional
SPACE method without changing its basic parameter optimization algorithms.
Given the linguistic information sequence w = {w[k]}, weconstructed a DNN that maps w[k] to the posterior probabilityof the HMM state sk . For simplicity, the DNN was trained todiscriminate the three sets of HMM states shown below given
the linguistic feature w[k].
• Phrase state ({p0 })• Accent states ({a0 , · · · , aN })• The other states ({r0 , r1 })All the accent states share the same posterior probability given
the linguistic information. In the work we report in this paper, we assumed that the DNN can be trained with speech corpora that include linguistic annotations and manually annotatedphrase/accent command functions. Accordingly, we formulated
a generative model of the F0 contours by combining the DNN
with the SPACE method on the basis of the DNN-HMM [24]framework. More specifically, we assumed the generative probability p(w|s, λ) was time-independent and transformed by applying Bayes’ theorem:∏p(w|s, λ) =p(w[k]|sk , λ)(10)

4. Experiments
4.1. Experimental conditions
To evaluate the parameter estimation accuracy of the proposed
method, we conducted an experiment using the ATR Japanese
speech database B-set [26]. This database consists of 503 phonetically balanced sentences. We selected speech samples of
one male speaker (MHT). The ground truth data of the Fujisaki
model parameters had been manually annotated by an expert in
the speech prosody field. In these ground truth data, the baseline
values were all set at log 60 Hz. We compared the performanceof the proposed method with that of two conventional Fujisaki
model parameter extractors that do not utilize linguistic information; Narusawa’s method [11] and the SPACE method [17].
We used 450 sentences for training the DNN and then tested theparameter estimation accuracy on the remaining 53 sentences.
We used the DNN with two hidden layers with 256 units,a fully-connected network and a sigmoid activation function.
As linguistic feature w, we used 495 dimensional vectors thatare used as the linguistic feature vectors for DNN-based speechsynthesis. The vectors include information such as phonemes
and accent types [27]. The weights of the DNN were initialized randomly, then optimized to minimize the cross entropy between the target and predicted value, using the Adam [28]-based
back-propagation algorithm. The parameters for the Adam algorithm were set as α = 0.0001, β1 = 0.9, β2 = 0.999, andϵ = 1e − 8. We used 22 sentences as the development set.
We obtained V/UV segments by simple energy thresholding. The constant parameters were fixed at t0 = 8ms, α =3.0 rad/s, β = 20.0 rad/s, vp2 [k] = 0.22 , va2 [k] = 0.12 ,vb2 = 0.0012 and vn2 [k] = 1015 for unvoiced regions andvn2 [k] = 0.22 for voiced regions. The parameter xb was set
at the minimum log F0 value in the voiced regions. The initialvalues for the proposed method were set at those obtained witha conventional method [17] that does not utilize linguistic information. The parameter estimation algorithm was run for 20
iterations.
We evaluated the accuracy of the parameter estimation on
the basis of two criteria: log F0 RMSE (root mean sequared
error) and detection rates. Our aim was to confirm whether the
proposed model can achieve higher parameter estimation accu-k=∏ p(sk |w[k], λ)p(w[k])kp(sk ).

(11)

Here, λ denotes the parameters of the DNN. We used the relative frequency for p(sk ) and assumed p(w[k]) as a constant.
The formulation for the generative process of the other parameters ({y, o, s, θ}) is the same as that described in sec. 2.2. Figure 2 shows the graphical representation of the proposed model.
There are two benefits for this formulation. First, by utilizing the linguistic feature w[k] as an input vector of the DNN, we
can assume there was no specific distribution for p(w[k]|sk , λ).
Therefore, we can use the proposed DNN-SPACE method
framework to leverage auxiliary information other than linguistic information, such as spectral features or image features. Second, the basic parameter estimation algorithms are not changed
from those for the conventional SPACE method. The parameter estimation algorithm for the proposed method is derived to1076

Table 1: Detection rates and log F0 RMSE (S=0.3s)

Observed F0

102

(5)
Magnitude(4)
Magnitude(3)
Magnitude(2)
Magnitude(1)
F0 [Hz]Estimated F0

1
0.5
0
1
0.5
0
1
0.5
0
1
0.5
0
0

PhraseNarusawa [11]SPACE [17]
DNN-SPACE (proposed)

AccentDetection rates
0.666
0.700
0.717

log F0 RMSE
0.11600.05400.06364.2. Experimental results

1

PhraseAccentPhraseAccentPhraseAccent2
3Time [s]Table 1 shows the results obtained with our quantitative evaluation with S = 0.3 s. The “Narusawa” and “SPACE” rows
shows the detection rate and log F0 RMSE of the command sequences obtained with the conventional method which does not
utilize linguistic information. The “DNN-SPACE” row shows
the command sequence obtained with the proposed method using linguistic information. We can see that the detection rate of
the proposed method is improved compared to the conventional
methods. We can conclude from the result that leveraging auxiliary linguistic information for parameter estimation improves
the command estimation accuracy. While the log F0 RMSE of
the proposed method was improved compared to Narusawa’s
method, it was slightly worse than the SPACE method. These
results show that improvement in command detection accuracy
by utilizing the linguistic information does not always lead tomore accurate F0 contour estimation. This is because the Fujisaki model has the nature that even though a set of command
functions that ignores the relationship with the linguistic information, it can approximate a given observed F0 contour.
Figure 3 shows the parameter estimation results along withthe ground truth data. We can also confirm that the proposedmodel is able to estimate parameters more accurately than theprevious models. For example, while the conventional Narusawa and SPACE methods had insertion errors of phrase commands around t = 3.0, our proposed method eliminated them.
This is because our method can utilize linguistic information inwhich there is no phrase boundary around t = 3.0.

4

Figure 3: Example of command detection. (1) An observed
F0 contour in voiced regions (solid line) and the estimated F0
contours by the proposed method (dotted line). The estimatedphrase and accent commands. (2) Narusawa’s method [11].
(3) SPACE [17]. (4) DNN-SPACE (the proposed method). (5)Grand truth (manually labeled by an expert).
racy. The detection rate was used to evaluate the accuracy ofthe parameter estimates, which was calculated in the following way: we performed matching between the estimated andground truth command sequences on a command-by-commandbasis by using dynamic programming algorithm. If the timedifference between the estimated and ground truth phrase commands was shorter than S seconds, the estimated phrase command was considered “matched” and the local distance was set
at zero. Otherwise the local distance was set at 1. As forthe accent commands, we took the average of the time difference between the onsets of the estimated and ground truth accent commands and the time difference between the offsets ofthe estimated and ground truth accent commands. In the sameway, when the average time difference was shorter than S seconds, the estimated accent command was considered matched.
The magnitudes of the phrase and accent commands were nottaken into account in our evaluation. This is because the magnitude estimation was very sensitive to the baseline F0 value,
which was set differently in the proposed method and in manual annotation. Let NE and NA be the total number of commands in the estimated and ground truth command sequences,
NM be the number of the matched commands between thetwo sequences, and NEsum , NAsum and NMsum be the sum of
NE , NA , NM for all 53 sentences. We defined the insertion error rate EI as (NEsum − NMsum )/NAsum , the deletion error rate
ED as (NAsum − NMsum )/NAsum , and the detection rate D as
1 − EI − ED .

5. Conclusion
In this paper, we described a method we propose to extract
prosodic features from a speech signal by leveraging auxiliary
linguistic information. The DNN-SPACE method we propose
was extended from the conventional SPACE method to model
the relationship between phrase/accent commands and linguistic information. We evaluated the method’s parameter estimation accuracy and revealed that using linguistic information was
effective in improving the command estimation accuracy. Our
future work will include incorporating sequence model such as
RNN instead of DNN to model the time dependence of command functions and further improve the parameter estimation
accuracy.

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