The statistical analysis of acoustic correlates of speech rhythm
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Transcript of The statistical analysis of acoustic correlates of speech rhythm
The statistical analysis of acoustic correlates of speech rhythm
Denise Duarte*Universidade Federal de Goiásand Universidade de São Paulo
Antonio Galves Universidade de São Paulo
Nancy L. GarciaUniversidade Estadual de Campinas
Ricardo Maronna*Universidad de La Plata
http://www.ime.usp.br/~tycho* : authors who presented the paper
1. Introduction
Data description: two corpora
“20 sentences”: 20 sentences spoken three times by two female native speakers of BP and EP ( segmented by Flaviane R. Fernandes and Janaisa M. Viscardi)
“RNM”: 20 sentences of each of : English, Polish, Dutch, French, Spanish, Catalan, Italian, Japanese 5 sentences uttered by each of 4 female speakers
Purposes
Apply the RNM approach to the enlarged data set. Present alternative descriptive statistical measures Analize the effect of dropping the last vocalic
interval of each sentence. Introduce a probalility model for duration, which
allows for improved descriptions and hypothesis testing
Use this model to give statistical support to the rhythmic class hypothesis
The RNM statistics
For each sentence of the corpus the following are computed:
DC, DV= standard deviation for vocalic and consonantal intervals
%V= proportion of time spent on vocalic intervals
Values are averaged for each speaker
%V, DC and DV for the ten languages
2.51 5.14 414.64 5.35 40.14.23 5.33 42.33.78 4.39 43.63.32 4.74 43.84.00 4.81 45.23.68 4.52 45.64.02 3.56 53.1
EP 4.33 5.57 45.3BP 4.01 4.53 49.1
Languages V C VPolishEnglishDutchFrenchSpanishItalian CatalanJapanese
%V vs. DC for the ten languages
%V and DC for individual speakers
0.35 0.40 0.45 0.50 0.55%V
0.03
0.04
0.05
0.06
0.07
C
ca
ca
ca
cadu
du
du
du
en
en
en
en
es
es
eses
frfr
frfr
it
it
it
it
ja
ja
jaja
po
popo
po
EP1
EP2
BP2 BP1
DV vs. DC for the ten languages
2.5 3.0 3.5 4.0 4.5V
3.6
4.1
4.6
5.1
5.6
C
Polish
EnglishDutch
French
SpanishItalian
Catalan
Japanese
EP
BP
3. Alternative analysis
3.1 Dropping the last vocalic interval
The last vocalic interval is an important source of variability.
It was obserded that in BP and EP there is a stretching in final vocalic intervals.
New data set: omitting the last vocalic interval for each language, and also the subsequent consonantal interval, if one exists.
The data without the last vocalic interval
40 42 44 46 48 50 52 54%V
3.6
4.1
4.6
5.1
C
jap
bp
cat
itaspa
fre
dut
ep
pol
eng
Location of BP and EP speakers in the %V vs. DC Plane – complete sentences
The effect of the last vocalic interval in BP and EP- individual values
40 42 44 46 48 50 52 54%V
4.0
4.5
5.0
5.5
C
ep:wlv
bp
bp:wlv
dclv
BPsp1
BPsp1-wlv
BPsp2
BPsp2-wlv
EPsp2
EPsp2-wlv
EPsp1
EPsp1-wlv
ep
3.2 Robust statistics
“Robust”= insensive to extreme valuesSimplest robust measure of location: replace the
mean by the median.To find the median of a set of numbers: sort them
and pick the one in the middleSimplest robust measure of dispersion: replace the
standard deviation by the median absolute deviation(MAD).
evenisnif
nmwithxx
oddisnifn
mwithxxmedian
mm
m
2)(
21
2
1
)(
)1()(
)(
)()( xmedxmedxMAD i
Robust statistics
40 42 44 46 48 50 52 54PVmed
3.0
3.5
4.0
4.5
5.0
5.5
DC
mad
eng
pol
dut
f re
esp
ita cat
jap
bp
ep
4. A probability model for duration
Former analysis is descriptive Finding a parametric family of probability distributions that fits the data closely would have two advantages:
May yield a better description of data Allows us to make inference, i. e., to extend
results from the “sample” (the data set) to the “population” ( the set of all potential setences)
4.1 Histograms show similar asymmetrical shapes
-0.050 0.005 0.060 0.115 0.170 0.225 0.280 0.335 0.390 0.445time
0
10
20
30
40
Histogram: consonantal intervals- Dutch
0.000 0.025 0.050 0.075 0.100 0.125 0.150 0.175 0.200 0.225 0.250 0.275time
0
5
10
15
20
25
30
Histogram: Consonantal intervals - Italian
Several distributions tried: Log-normal, Weibull, exponential, Gamma
The Gamma was the best fit :quantile-quantile (QQplot)- Given a data set and a theoretical, plot the quantiles of the
latter vs those of the empirical distribution
Gamma distribution
It has two parameters: a and , b controlling shape and size, respectively:
small a: high asymmetry; a = 1 gives the the exponential distribution;
Large a approximates the normal. The parameters are related to the mean m and
standard deviation s by=m ab
s2=ab2
Estimated Gamma parameters vocalic intervals
Estimated Gamma parameters consonantal intervals
Mean values for vocalic and consonantal intervals
0.1070 0.073100.1000 0.075800.1020 0.07110
EP 0.1000 0.078000.0950 0.073600.0970 0.074300.0970 0.077100.0890 0.07440
BP 0.0950 0.085800.0780 0.08780
MeanLang Consonantal VocalicEnglishDutchPolish
FrenchSpanishItalianCatalan
Japanese
5. Hypothesis testing
In view of the close relationship between a and b , we may use one of the two, or one function of
both, to represent relevant features.Based on the RNM results, we choose the model
standard deviation :=1/2
Standard deviation of Gamma for the ten languages – complete sentences
0.035 0.040 0.045 0.050 0.055stdC
Jap Fre Cat Esp Ita
BP
Dut Pol
EP
Eng
Rhythmic class hypothesis
We represent the rhythmic class hypothesis by the following statistical model:
1.The syllabic languages ( Italian, Spanish, French, Catalan , BP) have the same standard deviation, say, s
1.
2.The accentual ones (Polish, Dutch, English, EP) share another, say, s
2
3. s1, s
2and the standard deviation for Japanese
s3 are different .
Results
To test the model, we first tested (1) and (2) by means of the Likelihood Ratio Test, which yielded a p-value of 0.91, which means that the equality of s's within rhythmic classes is highly compatible with the data ( a small p-value indicates rejection).
Then we tested the null hypothesis that some of s1 ,
s2, s3 are equal, which was rejected with a p-value
of 0.0012, thus giving statistical evidence that the three are different.
Acknowledgments
We want to thank Franck Ramus, Marina Nespor and Jacques Mehler, who generously made their unpublished data avalaible to us.
We also thank Janaisa Viscardi and Flaviane Fernandes for the segmentation of the acoustic
data
The “20 sentences” corpus
The following sentences of the corpus 20 sentences were considered in the statistical analysis. The choice was based on the quality of acoustic signal and to avoid dubious cases of labeling.
1. A moderniza₤₧o foi satisfatória. 5. A falta de moderniza₤₧o ₫ catastrófica.6. O trabalho da pesquisadora foi publicado.8. O governador aceitou a moderniza₤₧o.9. A falta de autoridade foi alarmante.11. A catalogadora compreendeu o trabalho da pesquisadora.12. A professora discutiu a gramaticalidade.15. A procura da gramaticalidade ₫ o nosso objetivo.16. A pesquisadora perdeu autoridade.18. A autoridade cabe ao governador.20. A gramaticalidade das frases foi conseguida.
Grants supporting the research
FAPESP grant n. 98/3382-0 (Projeto Temático Rhythmic patterns, parameter setting and language change ) PRONEX grant 66.2177/1996-6 (Núcleo de Excel₨ncia Critical phenomena in probability and stochastic processes)
CNPq grant 465928/2000-5 (Probabilistic tools for pattern identification applied to linguistics)
Related papers and referencesAbercrombie, D. (1967). Elements of general phonetics. Chicago: Aldine.
Grabe, E. and Low, E., L. (2000) Acoustic correlates in rhythmic class. Paper presented at the 7th conference on laboratory phonology, Nijmegen.
Lloyd, J. (1940) Speech signal in telephony. London.
Mehler, J., Jusczyk, P., Dehane-Lambertz, G., Bertoncini, N. And Amiel-Tison, C. (1988) A percursor of language acquisition in young infants. Cognition 29: 143-178.
Nazzi, T., Bertoncini, N. and Mehler, J. ( 1998) Language discrimination by newborns towads an understanding of the role of the rhythm. Journal of experimental psychology: human perception and perfomance 24 (3): 756-766.
Nespor, M. (1990) On the rhythm parameter in phonology. Logical issues in language acquisition, Iggy Roca , 157-175.
Ramus, F. And Mehler, J. ( 1999). Language acquisition with suprasegmental cues: a study based on speecch resynthesis. JASA 105: 512-521.
Ramus, F., Nespor, M. and Mehler (1999) Correlates of linguistic rhythm in speech. Cognition 73: 265-292.
Frota, S. and Vigário, M.(2001) On the correlates of rhythm distinctions: the European/ Brazilian Portuguese case. To be published in Probus.
Appendix: the meaning of a p-valueConsider the situation of testing a statistical hypothesis: To
fix ideas, suppose that we have samples from two populations, and we want to test the hypothesis that both have the same (unknown) mean. Of course, even if the hypothesis is true, the two sample means will be different, due to sampling variability.
To test the hypothesis, we compute a number T from our data (the so-called “test statistics”) which measures the discrepancy between the data and the hypothesis. In our example T will depend on the differences between the sample means. If T is very large, we have a statistical evidence against the hypothesis. What is a rational definition of “large”?
Suppose our data yields T=3.5; and that we compute
the probability p that, if the hypothesis is true, we obtain a value of T greater than 3.5. This the so-called “p-value” of the test. If, say, p= 0.002, this means that, if the means are equal, we would be observing an exceptionally large value ( since a
larger one is observed only with probability 0.2%); Thus we would have grounds to reject the
hypothesis.