University of Maryland

Making Phonological
Decisions
William J. Idsardi
University of Maryland
idsardi@umd.edu
Mayfest 2006
1

Resnick
2

3 topics
Finding vowel categories/features
Finding vowel harmony
Finding word boundaries
3

What is
phonology
for
Swingley
4

Long-term Memory
Audition
Articulation
5

Long-term Memory
Lex Phon
Surface
Audition
Phonetics
Articulation
6

Using Statistics
Magic!
Data summarization and compression
(not exemplars)
Decision making under uncertainty
(not fuzziness)
Measures of confidence
Statistics over induced representations
(2nd order, ...)
7

Terminology
Knowledge OF Language
= Decisions about Grammar
Knowledge ABOUT Language
= Statistics supporting KOL
8

Finding phonemes
9

Minimal pair conundrum
No reliable minimal pair judgements
until ~ 18 mos.
“Minimal pairs are a parlour game”
(François Dell)
What are children doing from 12-18 mos.
10

Recursive
binary
divisions.
Dresher
11

Classical Manchu Representations
These percepts are not representations. The learner has not yet
identified any contrasts in the vowel system.
Assume contrastive features are determined in order:
[i
]
/V/
[´]
[u]
[U]
[ç]
[a]
12

Classical Manchu Vowels
Contrastive Values:
[low]
[i
]
/ˆ/
[u]
[U]
[low]
[´]
/A/
[a]
[ç]
13

Classical Manchu Vowels
Contrastive Values:
[low]
[i
]
/ˆ/
[u]
[U]
[low]
[´]
/A/
[a]
[ç]
13

Classical Manchu Vowels
Contrastive Values:
[low] >[coronal]
[i
]
/I/
[coronal]
[u]
/U/
[U]
[low]
[´]
/A/
[a]
[ç]
14

Classical Manchu Vowels
Contrastive Values:
[low] >[coronal]
[i
]
/I/
[coronal]
[u]
/U/
[U]
[low]
[´]
/A/
[a]
[ç]
14

Classical Manchu Vowels
Contrastive Values:
[low] >[coronal]
/i/
[coronal]
[u]
/U/
[U]
[low]
[´]
/A/
[a]
[ç]
15

Classical Manchu Vowels
Contrastive Values:
[low] >[coronal]
/i/
[coronal]
[u]
/U/
[U]
[low]
[´]
/A/
[a]
[ç]
15

Classical Manchu Vowels
Contrastive Values:
[low] > [coronal] > [labial]
/i/
[coronal]
[u]
/U/
[U]
[low]
/A/
[´]
[labial]
/O/
[ç]
[a]
16

Classical Manchu Vowels
Contrastive Values:
[low] > [coronal] > [labial]
/i/
[coronal]
[u]
/U/
[U]
[low]
/A/
[´]
[labial]
/O/
[ç]
[a]
16

Classical Manchu Vowels
Contrastive Values:
[low] > [coronal] > [labial]
/i/
[coronal]
[u]
/U/
[U]
[low]
/A/
[´]
[labial]
/O/
[ç]
[a]
17

Classical Manchu Vowels
Contrastive Values:
[low] > [coronal] > [labial]
/i/
[coronal]
[u]
/U/
[U]
[low]
/A/
[´]
[a]
[labial]
/ç/
18

Classical Manchu Vowels
Contrastive Values:
[low] > [coronal] > [labial]
/i/
[coronal]
[u]
/U/
[U]
[low]
/A/
[´]
[a]
[labial]
/ç/
[low]
18

Classical Manchu Vowels
Contrastive Values:
[low] > [coronal] > [labial > [ATR]
/i/
[coronal]
[ATR]
/u/
/U/
[low]
/´/
/a/
[labial]
/ç/
[low]
19

Classical Manchu Vowels
Contrastive Values:
[low] > [coronal] > [labial > [ATR]
/i/
[coronal]
[ATR]
/u/
/U/
[low]
/´/
/a/
[labial]
/ç/
[low]
19

Classical Manchu Vowels
Contrastive Values:
[low] > [coronal] > [labial > [ATR]
/i/
[coronal]
[ATR]
/u/
/U/
[low]
/´/
/a/
[labial]
/ç/
[low]
20

Classical Manchu Vowels
Contrastive Values:
[low] > [coronal] > [labial > [ATR]
/i/
[coronal]
[ATR]
/u/
/U/
[low]
/´/
/a/
[labial]
/ç/
[low]
20

Classical Manchu Vowels
Contrastive Values:
[low] > [coronal] > [labial > [ATR]
/i/
[coronal]
[ATR]
/u/
/U/
[low]
/´/
/a/
[labial]
/ç/
ç/
[low]
21

Classical Manchu Vowels
Contrastive Values:
[low] > [coronal] > [labial > [ATR]
/i/
[coronal]
/u/ [u]
/U/
/´/ [labial]
/a/
/ç/
[low]
22

Classical Manchu Vowels
Contrastive Values:
[low] > [coronal] > [labial > [ATR]
/i/
[coronal]
/u/ [u]
[ATR]
[ATR]
/´/ [labial]
[low]
/ç/
[low]
[low]
/a/
/U/
22

Classical Manchu Vowels
Contrastive Values:
[low] > [coronal] > [labial > [ATR]
/i/
[coronal]
[ATR]
[low]
[low]
/´/
/a/
/u/
[ATR]
[labial]
/ç/
[low]
/U/
23

If bimodal
then active.
Maye
24

100
75
50
25
0
100
-150
-137.5
-125
-112.5
-100
-87.5
-75
-62.5
-50
-37.5
-25
-12.5
0
12.5
25
37.5
50
62.5
75
87.5
100
112.5
125
-150 -100 -50 0 50 100 150
137.5
150
b
p
75
50
25
b
p
ph
0
-150 -100 -50 0 50 100 150
Lisker & Abramson (1964, 1970)
25

100 100
75 75
50 50
25 25
b
p
0
0
-150
-150
-137.5
-137.5 -125
-125
-112.5
-112.5
-100
-100
-87.5
-87.5
-75
-75
-62.5
-62.5
-50
-50
-37.5
-37.5
-25
-25
-12.5
-12.5
00
12.5 12.5
25 25
37.5 37.5
50 50
62.5 62.5
75 75
87.5 87.5
100 100
112.5 112.5
125 125
137.5 137.5
150
150
-150 -100 -50 0 50 100 150
100 100
75 75
50 50
25 25
b
p
ph
0
0
-150 -100 -50 0 50 100 150
Lisker & Abramson (1964, 1970)
25

100 100
75 75
50 50
25 25
b
p
0
0
-150
-150
-137.5
-137.5 -125
-125
-112.5
-112.5
-100
-100
-87.5
-87.5
-75
-75
-62.5
-62.5
-50
-50
-37.5
-37.5
-25
-25
-12.5
-12.5
00
12.5 12.5
25 25
37.5 37.5
50 50
62.5 62.5
75 75
87.5 87.5
100 100
112.5 112.5
125 125
137.5 137.5
150
150
-150 -100 -50 0 50 100 150
100 100
75 75
50 50
25 25
b
p
ph
0
0
-150 -100 -50 0 50 100 150
Lisker & Abramson (1964, 1970)
25

100 100
75 75
50 50
25 25
good discrimination
b
p
0
0
-150
-150
-137.5
-137.5 -125
-125
-112.5
-112.5
-100
-100
-87.5
-87.5
-75
-75
-62.5
-62.5
-50
-50
-37.5
-37.5
-25
-25
-12.5
-12.5
00
12.5 12.5
25 25
37.5 37.5
50 50
62.5 62.5
75 75
87.5 87.5
100 100
112.5 112.5
125 125
137.5 137.5
150
150
-150 -100 -50 0 50 100 150
100 100
75 75
50 50
25 25
good discrimination
b
p
ph
0
0
-150 -100 -50 0 50 100 150
Lisker & Abramson (1964, 1970)
25

100 100
75 75
50 50
poor discrimination
good discrimination
b
p
25 25
0
0
-150
-150
-137.5
-137.5 -125
-125
-112.5
-112.5
-100
-100
-87.5
-87.5
-75
-75
-62.5
-62.5
-50
-50
-37.5
-37.5
-25
-25
-12.5
-12.5
00
12.5 12.5
25 25
37.5 37.5
50 50
62.5 62.5
75 75
87.5 87.5
100 100
112.5 112.5
125 125
137.5 137.5
150
150
-150 -100 -50 0 50 100 150
100 100
75 75
50 50
25 25
good discrimination
good discrimination
b
p
ph
0
0
-150 -100 -50 0 50 100 150
Lisker & Abramson (1964, 1970)
25

Familiarized to
Unimodal vs. Bimodal Distributions
occurrence
per block of
familiarization
16
12
8
Not always for
phonological
non-contrast
4
0
1 2 3 4 5 6 7 8
Token Number
/da/
/ta/
26

Greek Vowels
F1 x F2 space for Greek vowel tokens
k-means clustering
criteria for stopping (over-fitting penalty)
procedure finds four vowels
(approximately i, e, a, o+u)
27

Bimodality is not
always so clear.
Swingley
28

Learning from the
Primordial soup
Elizabeth Allyn Smith
Kathleen Currie Hall
29

Greek Vowels
F1 x F2 space for Greek vowel tokens
k-means clustering
criteria for stopping (over-fitting penalty)
procedure finds four vowels
(approximately i, e, a, o+u)
30

English: Peterson and Barney
3000
F2
2000
1000
front
back
200 400 600 800 1000 1200
F1
high ------------low
31

Combine approaches
Normalize
Recursive binary division algorithm
Make Ø/[F] divisions
Using compactness of clustering on [F] as
criteria
32

Normalization
Don’t use F1 and F2
Use F1/F3 and F2/F3
Corrects for male/female/child differences
On-line rather than statistical normalization
33

Raw data ANOVA
F0
300
200
100
m f
F1
1300
1000
700
400
100
m f
F2
3000
2000
1000
mf
F3
4000
3000
2000
f
m
a
c
a
c
a
c
a
c
main effects (gender, age) p < 0.001 for all
interaction (gender*age) p < 0.01 for F0, F2
34

Ratio with F3 ANOVA
F1/F3
0.40
0.30
0.20
0.10
a
c
mf
F2/F3
0.9
0.7
0.5
0.3
0.1
a
c
m f
no main effects (p > 0.24)
marginal interaction for F2/F3 (p = 0.0919)
35

A little improvement
0.9
F2
3000
2000
F2/F3
0.8
0.7
0.6
0.5
0.4
1000
0.3
0.2
200 400 600 800 1000 1200
F1
.10 .20 .30 .40
F1/F3
36

Best split for front
0.9
How compact
F2/F3
0.8
0.7
0.6
0.5
0.4
0.3
0.2
Text
.10 .20 .30 .40
F1/F3
front ✔
back
37

Trapping the problem
Number of contrasts is bounded:
From below by phonology (too few)
From above by phonetics (too many)
Actual answer is trapped in-between
38

Look for
phonological
activity.
Dresher
39

Context
sensitive
contrasts.
Maye
40

Frequent
frames
Mintz
41

Two different contrastive hierarchies:
a. [high] > [labial]
b. [labial] > [high]
[–high]
[+high]
[–labial]
[+labial]
/a/ [–labial] [+labial]
[–high]
[+high]
/u/
/i/
/u/
/a/
/i/
We might expect that the two vowel systems will pattern differently. For
example, system (a) might show alternations or neutralization between /i/
and /u/; in system (b) /i/ might be more closely related to /a/.
42

Diagnosing vowel harmony
CHILDES transcripts (need sane orthography)
Turkish
need a comparison non-VH (e.g. Polish)
(Auto)correlation between adjacent vowels
Compare same and different vowels
within- and between- utterances
43

CHILDES Turkish
50,000
37,500
25,000
47,340
1:2.27
Chi-square test: p < 0.0001
Fisher’s exact test: p < 0.0001
20,869
12,500
1:5.29
9,119
0
within utterance
same vowel
1,723
across utterances
different vowels
44

Not done
Cue for vowel harmony not the same as rule
for vowel harmony
Cue: more “same” vowels within utterances
Rules: [front] harmony
! ! ! [round] harmony when [high]
45

Finding other rules
Find other active features
Tohono O’odham palatalization:
t, d, s → tʃ, dʒ, ʃ / _ i, u, ɨ
[coronal] → [laminal] / _ [high]
correlation between [laminal] and [high]
So [laminal], [high] are active
Arbitrary correlations
46

Finding words
47

Transitional
probabilities!
Saffran
48

“UG, statistics or both”
Look between
stresses!
Yang
49

Virtuous circularity
“We find that the best
heuristics make use of
structural information
obtained by parsing
input sentences during
the course of learning”
Sakas
50

Bayes!
Johnson
51

Bayes’s Rule
p(A&B) = p(A|B) * p(B)
p(A&B) = p(B|A) * p(A)
p(A|B) * p(B) = p(B|A) * p(A)
p(A|B) = p(B|A) * p(A) / p(B)
52

Bayesian phonology
p(UR|SR) = p(SR|UR) * p(UR) / p(SR)
p(UR|SR) p(SR|UR): analysis by synthesis
p(UR): UG as Bayesian priors
Poeppel
53

Finding words from
vowel harmony
p(#|XY) = p(XY|#) * p(#) / p(XY)
Estimate p(XY|#) from p(XY|Utterance)
Put some prior expectations on p(#)
Get p(XY) from data
54

a ï o u e i ö ü
a ï o u e i ö ü
Some info in there
% # % no #
% # % no #
100
75
50
25
100
75
50
25
0
0
ï
o
55

I’m next!
(after lunch)
Hudson Kam
56

Discussion
57

Cohorts and neighbors
Features
Analysis by synthesis
Multi-resolution
3 passes
58

Detail
Multi-resolution
Both coarse and fine info
Exemplar: k-nearest neighbors
coarseness in retrieval
Substatistics
fineness calculated in coarse addresses
59