Modified Distortion Matrices
for Phrase-Based SMT
Arianna Bisazza & Marcello Federico – FBK (Italy)
PSMT decoding overview
E' necessario incoraggiare tale mobilità garantendo la sicurezza dei percorsi professionali
2
A. Bisazza & M. Federico – Modified Distortion Matrices for PSMT
PSMT decoding overview
E' necessario incoraggiare tale mobilità garantendo la sicurezza dei percorsi professionali
Freedom of movement must be encouraged
LM scores
3
LM scores
A. Bisazza & M. Federico – Modified Distortion Matrices for PSMT
PSMT decoding overview
E' necessario incoraggiare tale mobilità garantendo la sicurezza dei percorsi professionali
Freedom of movement must be encouraged while ensuring that career paths …
LM scores
4
LM scores
LM scores
LM scores
A. Bisazza & M. Federico – Modified Distortion Matrices for PSMT
PSMT decoding overview
E' necessario incoraggiare tale mobilità garantendo la sicurezza dei percorsi professionali
Freedom of movement must be encouraged while ensuring that career paths …
LM scores
5
LM scores
LM scores
LM scores
A. Bisazza & M. Federico – Modified Distortion Matrices for PSMT
Reordering
Models
Many solutions have been proposed
with different reo. classes, features,
train modes etc.
Tillman 04, Zens & Ney 06
AlOnaizan & Papineni 06
Galley & Manning 08
Green & al.10, Feng & al.10
…
E' necessario incoraggiare tale mobilità garantendo la sicurezza dei percorsi professionali
6
A. Bisazza & M. Federico – Modified Distortion Matrices for PSMT
Reordering
Models
Many solutions have been proposed
with different reo. classes, features,
train modes etc.
Tillman04,
Zens&Ney06
Tillman
04, Zens
& Ney 06
AlOnaizan
& Papineni06
AlOnaizan
& Papineni
06
Galley
& Manning08
Galley
& Manning
08
Green
&al.10,Feng
Feng& &al.10
Green
& al.10,
al.10
……
E' necessario incoraggiare tale mobilità garantendo la sicurezza dei percorsi professionali
No matter what reordering model is used,
permutation search space must be limited!
 The power of all reordering models is
bound to the reordering constraints in use
7
A. Bisazza & M. Federico – Modified Distortion Matrices for PSMT
E' necessario incoraggiare tale mobilità garantendo la sicurezza dei percorsi professionali
8
A. Bisazza & M. Federico – Modified Distortion Matrices for PSMT
E' necessario incoraggiare tale mobilità garantendo la sicurezza dei percorsi professionali
Reordering Constraints
#perm.=11!≈40,000,000
9
A. Bisazza & M. Federico – Modified Distortion Matrices for PSMT
E' necessario incoraggiare tale mobilità garantendo la sicurezza dei percorsi professionali
Reordering Constraints
#perm.=11!≈40,000,000
D(x,y)=|y-x-1|
w0 w1
<s> 0 1
w0
0
w1 2
w2 3 2
w3 4 3
w4 5 4
w5 6 5
w6 7 6
w7 8 7
w8 9 8
w9 10 9
w10 11 10
w2
2
1
0
2
3
4
5
6
7
8
9
w3
3
2
1
0
2
3
4
5
6
7
8
w4
4
3
2
1
0
2
3
4
5
6
7
w5
5
4
3
2
1
0
2
3
4
5
6
w6
6
5
4
3
2
1
0
2
3
4
5
w7
7
6
5
4
3
2
1
0
2
3
4
w8
8
7
6
5
4
3
2
1
0
2
3
w9
9
8
7
6
5
4
3
2
1
0
2
Source-to-Source distortion
10
A. Bisazza & M. Federico – Modified Distortion Matrices for PSMT
w10
10
9
8
7
6
5
4
3
2
1
0
E' necessario incoraggiare tale mobilità garantendo la sicurezza dei percorsi professionali
DL: distortion limit
Reordering Constraints
#perm.=11!≈40,000,000
D(x,y)=|y-x-1|
DL=3  #perm.≈7,000
w0 w1
<s> 0 1
w0
0
w1 2
w2 3 2
w3 4 3
w4 5 4
w5 6 5
w6 7 6
w7 8 7
w8 9 8
w9 10 9
w10 11 10
w2
2
1
0
2
3
4
5
6
7
8
9
w3
3
2
1
0
2
3
4
5
6
7
8
w4
4
3
2
1
0
2
3
4
5
6
7
w5
5
4
3
2
1
0
2
3
4
5
6
w6
6
5
4
3
2
1
0
2
3
4
5
w7
7
6
5
4
3
2
1
0
2
3
4
w8
8
7
6
5
4
3
2
1
0
2
3
w9
9
8
7
6
5
4
3
2
1
0
2
Source-to-Source distortion
11
A. Bisazza & M. Federico – Modified Distortion Matrices for PSMT
w10
10
9
8
7
6
5
4
3
2
1
0
w0 w1 w2 w 3 w4 w5 w6 w7 w8 w9 w
<s> 0 1 2 3 4 5 6 7 8 9 10
w0
0 1 2 3 4 5 6 7 8 9
w1 2
0 1 2 3 4 5 6 7 8
w2 3 2
0 1 2 3 4 5 6 7
w3 4 3 2
0 1 2 3 4 5 6
w4 5 4 3 2
0 1 2 3 4 5
w5 6 5 4 3 2
0 1 2 3 4
w6 7 6 5 4 3 2
0 1 2 3
w7 8 7 6 5 4 3 2
0 1 2
w8 9 8 7 6 5 4 3 2
0 1
w9 10 9 8 7 6 5 4 3 2
0
w10 11 10 9 8 7 6 5 4 3 2
10
The problem with DL…
Arabic-English
EN
AR
EN
AR
12
A. Bisazza & M. Federico – Modified Distortion Matrices for PSMT
w0 w1 w2 w 3 w4 w5 w6 w7 w8 w9 w
<s> 0 1 2 3 4 5 6 7 8 9 10
w0
0 1 2 3 4 5 6 7 8 9
w1 2
0 1 2 3 4 5 6 7 8
w2 3 2
0 1 2 3 4 5 6 7
w3 4 3 2
0 1 2 3 4 5 6
w4 5 4 3 2
0 1 2 3 4 5
w5 6 5 4 3 2
0 1 2 3 4
w6 7 6 5 4 3 2
0 1 2 3
w7 8 7 6 5 4 3 2
0 1 2
w8 9 8 7 6 5 4 3 2
0 1
w9 10 9 8 7 6 5 4 3 2
0
w10 11 10 9 8 7 6 5 4 3 2
10
The problem with DL…
German-English
EN
EN
DE
DE
13
A. Bisazza & M. Federico – Modified Distortion Matrices for PSMT
#perm.=11! ≈40,000,000
D(x,y)=|y-x-1|
DL=3  #perm.≈7,000
Current solution:
increase the DLimit
w0 w1
<s> 0 1
w0
0
w1 2
w2 3 2
w3 4 3
w4 5 4
w5 6 5
w6 7 6
w7 8 7
w8 9 8
w9 10 9
w10 11 10
w2
2
1
0
2
3
4
5
6
7
8
9
w3
3
2
1
0
2
3
4
5
6
7
8
w4
4
3
2
1
0
2
3
4
5
6
7
w5
5
4
3
2
1
0
2
3
4
5
6
w6
6
5
4
3
2
1
0
2
3
4
5
w7
7
6
5
4
3
2
1
0
2
3
4
w8
8
7
6
5
4
3
2
1
0
2
3
w9
9
8
7
6
5
4
3
2
1
0
2
Source-to-Source distortion
14
A. Bisazza & M. Federico – Modified Distortion Matrices for PSMT
w10
10
9
8
7
6
5
4
3
2
1
0
#perm.=11! ≈40,000,000
D(x,y)=|y-x-1|
DL=3  #perm.≈7,000
DL=7  #perm.≈7,000,000
Generally leads to
worse translations!
Current solution:
increase the DLimit
w0 w1
<s> 0 1
w0
0
w1 2
w2 3 2
w3 4 3
w4 5 4
w5 6 5
w6 7 6
w7 8 7
w8 9 8
w9 10 9
w10 11 10
w2
2
1
0
2
3
4
5
6
7
8
9
w3
3
2
1
0
2
3
4
5
6
7
8
w4
4
3
2
1
0
2
3
4
5
6
7
w5
5
4
3
2
1
0
2
3
4
5
6
w6
6
5
4
3
2
1
0
2
3
4
5
w7
7
6
5
4
3
2
1
0
2
3
4
w8
8
7
6
5
4
3
2
1
0
2
3
w9
9
8
7
6
5
4
3
2
1
0
2
Source-to-Source distortion
15
A. Bisazza & M. Federico – Modified Distortion Matrices for PSMT
w10
10
9
8
7
6
5
4
3
2
1
0
Our solution:
#perm.=11! ≈40,000,000
D(x,y)=|y-x-1|
DL=3  #perm.≈7,000
DL=7  #perm.≈7,000,000
w0 w1
<s> 0 1
w0
0
w1 2
w2 3 2
w3 4 3
w4 5 4
w5 6 5
w6 7 6
w7 8 7
w8 9 8
w9 10 9
w10 11 10
w2
2
1
0
2
3
4
5
6
7
8
9
w3
3
2
1
0
2
3
4
5
6
7
8
w4
4
3
2
1
0
2
3
4
5
6
7
w5
5
4
3
2
1
0
2
3
4
5
6
w6
6
5
4
3
2
1
0
2
3
4
5
w7
7
6
5
4
3
2
1
0
2
3
4
w8
8
7
6
5
4
3
2
1
0
2
3
w9
9
8
7
6
5
4
3
2
1
0
2
Source-to-Source distortion
16
A. Bisazza & M. Federico – Modified Distortion Matrices for PSMT
w10
10
9
8
7
6
5
4
3
2
1
0
#perm.=11! ≈40,000,000
D(x,y)=|y-x-1|
DL=3  #perm.≈7,000
DL=7  #perm.≈7,000,000
DL=3 & modif(D)
 #perm.≈20,000
Simplifies the task of
reordering models!
Our solution:
modify distortion
for each test sentence
w0 w1
<s> 0 1
w0
0
w1 2
w2 3 2
w3 4 3
w4 5 4
w5 6 5
w6 7 6
w7 8 7
w8 9 8
w9 10 9
w10 11 10
w2
2
1
0
2
3
4
5
6
7
8
9
w3
3
2
1
0
2
3
4
5
6
2
8
w4
4
3
2
1
0
2
3
4
5
2
7
w5
5
4
3
2
1
0
2
3
4
5
6
w6
6
5
4
3
2
1
0
2
3
4
5
w7
7
6
0
0
3
2
1
0
2
3
4
w8
8
7
0
0
4
3
2
1
0
2
3
w9
9
8
7
6
5
4
3
2
1
0
2
Source-to-Source distortion
17
A. Bisazza & M. Federico – Modified Distortion Matrices for PSMT
w10
10
9
8
7
6
5
0
3
2
1
0
Rest of the talk:
How to modify the distortion matrix?
What effect on translation quality?
What effect on baseline runtimes?
18
A. Bisazza & M. Federico – Modified Distortion Matrices for PSMT
Chunk-based
fuzzy reordering rules
Shallow syntax chunking:
•
cheaper and easier than deep parsing
•
constrains reorderings in a softer way
Fuzzy (non-determinisic) reordering rules:
•
generate N permutations for each matching sequence
•
final reordering decision is taken during translation,
guided by all SMT models (reoM, LM...)
Few rules for language pair, to only capture long reordering
19
A. Bisazza & M. Federico – Modified Distortion Matrices for PSMT
Chunk-based
fuzzy reordering rules
w-
$Ark
and took part
CC1
20
VC2
Arabic-English
“Move verb chunk (and following chunk)
to the right by 1 to N chunks”
fy AltZAhrp E$rAt AlmslHyn
in the march
PC3
mn AlktA}b
.
dozens of militants from the Brigades
NC4
PC5
A. Bisazza & M. Federico – Modified Distortion Matrices for PSMT
Pct6
Chunk-based
fuzzy reordering rules
w-
$Ark
and took part
CC1
CC1
CC1
CC1
21
VC2
PC3
PC3
PC3
Arabic-English
“Move verb chunk (and following chunk)
to the right by 1 to N chunks”
fy AltZAhrp E$rAt AlmslHyn
in the march
PC3
VC2
NC4
NC4
mn AlktA}b
.
dozens of militants from the Brigades
NC4
PC5
Pct6
NC4
VC2
PC5
PC5
PC5
VC2
Pct6
Pct6
Pct6
A. Bisazza & M. Federico – Modified Distortion Matrices for PSMT
Chunk-based
fuzzy reordering rules
w-
$Ark
and took part
CC1
CC1
CC1
CC1
CC1
CC1
22
VC2
PC3
PC3
PC3
NC4
NC4
Arabic-English
“Move verb chunk (and following chunk)
to the right by 1 to N chunks”
fy AltZAhrp E$rAt AlmslHyn
in the march
mn AlktA}b
.
dozens of militants from the Brigades
PC3
VC2
NC4
NC4
VC2
PC5
NC4
PC5
Pct6
NC4
VC2
PC5
PC5
PC5
VC2
Pct6
Pct6
Pct6
PC5
PC3
Pct6
Pct6
PC3
VC2
A. Bisazza & M. Federico – Modified Distortion Matrices for PSMT
Chunk-based
fuzzy reordering rules
Reordered
source LM
Reordering selection
w-
$Ark
and took part
CC1
CC1
CC1
CC1
CC1
CC1
23
VC2
PC3
PC3
PC3
NC4
NC4
fy AltZAhrp E$rAt AlmslHyn
in the march
mn AlktA}b
.
dozens of militants from the Brigades
PC3
VC2
NC4
NC4
VC2
PC5
NC4
PC5
Pct6
NC4
VC2
PC5
PC5
PC5
VC2
Pct6
Pct6
Pct6
PC5
PC3
Pct6
Pct6
PC3
VC2
A. Bisazza & M. Federico – Modified Distortion Matrices for PSMT
0.7
0.1
0.1
0.4
0.9
Chunk-based
fuzzy reordering rules
Reordered
source LM
Reordering selection
w-
$Ark
and took part
CC1
CC1
VC2
PC3
fy AltZAhrp E$rAt AlmslHyn
in the march
mn AlktA}b
.
dozens of militants from the Brigades
PC3
VC2
NC4
PC5
Pct6
NC4
PC5
Pct6
0.7
Pct6
0.1
0.1
0.4
0.9
Reorderings to encode in the distortion matrix
CC1
24
NC4
PC5
VC2
PC3
A. Bisazza & M. Federico – Modified Distortion Matrices for PSMT
CC1 VC2
Modifying the
distortion matrix
CC1
VC2
PC3
NC4
PC5
Pct6
CC1
PC3
VC2
w0 w1
<s> 0 1
w0
0
w1 2
w2 3 2
w3 4 3
w4 5 4
w5 6 5
w6 7 6
w7 8 7
w8 9 8
PC3
w2
2
1
0
2
3
4
5
6
7
NC4
w3
3
2
1
0
2
3
4
5
6
NC4
w4
4
3
2
1
0
2
3
4
5
w5
5
4
3
2
1
0
2
3
4
PC5
w6
6
5
4
3
2
1
0
2
3
w7
7
6
5
4
3
2
1
0
Pct6
w8
8
7
6
5
4
3
2
1
0
2
PC5
Pct6
Reorderings to encode in the distortion matrix
CC1
25
NC4
PC5
VC2
PC3
A. Bisazza & M. Federico – Modified Distortion Matrices for PSMT
Pct6
CC1 VC2
Modifying the
distortion matrix
CC1
VC2
PC3
NC4
PC5
Pct6
CC1
PC3
VC2
w0 w1
<s> 0 1
w0
0
w1 2
w2 3 2
w3 4 3
w4 5 4
w5 6 5
w6 7 6
w7 8 7
w8 9 8
PC3
w2
2
0
0
2
3
4
5
6
7
NC4
w3
3
0
1
0
2
3
4
5
6
NC4
w4
4
3
2
1
0
2
3
4
5
w5
5
4
3
2
1
0
2
3
4
PC5
w6
6
5
4
3
2
1
0
2
3
w7
7
6
5
4
3
2
1
0
Pct6
w8
8
7
6
5
4
3
2
1
0
2
PC5
Pct6
Reorderings to encode in the distortion matrix
CC1
26
NC4
PC5
VC2
PC3
A. Bisazza & M. Federico – Modified Distortion Matrices for PSMT
Pct6
CC1 VC2
Modifying the
distortion matrix
CC1
VC2
PC3
NC4
PC5
Pct6
CC1
PC3
VC2
w0 w1
<s> 0 1
w0
0
w1 2
w2 3 2
w3 4 2
w4 5 4
w5 6 5
w6 7 6
w7 8 7
w8 9 8
PC3
w2
2
0
0
2
3
4
5
6
7
NC4
w3
3
0
1
0
2
3
4
5
6
NC4
w4
4
3
2
1
0
2
3
4
5
w5
5
4
3
2
1
0
2
3
4
PC5
w6
6
5
4
3
2
1
0
2
3
w7
7
6
5
4
3
2
1
0
Pct6
w8
8
7
6
5
4
3
2
1
0
2
PC5
Pct6
Reorderings to encode in the distortion matrix
CC1
27
NC4
PC5
VC2
PC3
A. Bisazza & M. Federico – Modified Distortion Matrices for PSMT
Pct6
CC1 VC2
Modifying the
distortion matrix
CC1
VC2
PC3
NC4
PC5
Pct6
CC1
PC3
VC2
w0 w1
<s> 0 1
w0
0
w1 2
w2 3 2
w3 4 2
w4 5 4
w5 6 5
w6 7 6
w7 8 7
w8 9 8
PC3
w2
2
0
0
2
3
4
5
6
7
NC4
w3
3
0
1
0
2
3
4
5
6
NC4
w4
4
3
0
1
0
2
3
4
5
w5
5
4
0
2
1
0
2
3
4
PC5
w6
6
5
4
3
2
1
0
2
3
w7
7
6
5
4
3
2
1
0
Pct6
w8
8
7
6
5
4
3
2
1
0
2
PC5
Pct6
Reorderings to encode in the distortion matrix
CC1
28
NC4
PC5
VC2
PC3
A. Bisazza & M. Federico – Modified Distortion Matrices for PSMT
Pct6
CC1 VC2
Modifying the
distortion matrix
CC1
VC2
PC3
NC4
PC5
Pct6
CC1
PC3
VC2
w0 w1
<s> 0 1
w0
0
w1 2
w2 3 2
w3 4 2
w4 5 4
w5 6 5
w6 7 6
w7 8 7
w8 9 8
PC3
w2
2
0
0
2
3
4
5
6
7
NC4
w3
3
0
1
0
2
3
4
5
6
NC4
w4
4
0
0
1
0
2
3
4
5
w5
5
0
0
2
1
0
2
3
4
PC5
w6
6
5
4
3
2
1
0
2
3
w7
7
6
5
4
3
2
1
0
Pct6
w8
8
7
6
5
4
3
2
1
0
2
PC5
Pct6
Reorderings to encode in the distortion matrix
CC1
29
NC4
PC5
VC2
PC3
A. Bisazza & M. Federico – Modified Distortion Matrices for PSMT
Pct6
CC1 VC2
Modifying the
distortion matrix
CC1
VC2
PC3
NC4
PC5
Pct6
CC1
PC3
VC2
w0 w1
<s> 0 1
w0
0
w1 2
w2 3 2
w3 4 2
w4 5 4
w5 6 5
w6 7 2
w7 8 2
w8 9 8
PC3
w2
2
0
0
2
3
4
5
6
7
NC4
w3
3
0
1
0
2
3
4
5
6
NC4
w4
4
0
0
1
0
2
3
4
5
w5
5
0
0
2
1
0
2
3
4
PC5
w6
6
5
4
3
2
1
0
2
3
w7
7
6
5
4
3
2
1
0
Pct6
w8
8
7
6
5
4
3
2
1
0
2
PC5
Pct6
Reorderings to encode in the distortion matrix
CC1
30
NC4
PC5
VC2
PC3
A. Bisazza & M. Federico – Modified Distortion Matrices for PSMT
Pct6
CC1 VC2
Modifying the
distortion matrix
CC1
VC2
PC3
NC4
PC5
Pct6
CC1
PC3
VC2
w0 w1
<s> 0 1
w0
0
w1 2
w2 3 2
w3 4 2
w4 5 4
w5 6 5
w6 7 2
w7 8 2
w8 9 8
PC3
w2
2
0
0
2
3
4
5
6
7
NC4
w3
3
0
1
0
2
3
4
5
6
NC4
w4
4
0
0
1
0
2
3
4
5
w5
5
0
0
2
1
0
2
3
4
PC5
w6
6
5
4
3
2
1
0
2
3
w7
7
6
5
4
3
2
1
0
Pct6
w8
8
7
6
0
0
3
2
1
0
2
PC5
Pct6
Reorderings to encode in the distortion matrix
CC1
31
NC4
PC5
VC2
PC3
A. Bisazza & M. Federico – Modified Distortion Matrices for PSMT
Pct6
CC1 VC2
Modifying the
distortion matrix
CC1
VC2
PC3
NC4
PC5
Pct6
CC1
PC3
VC2
w0 w1
<s> 0 1
w0
0
w1 2
w2 3 2
w3 4 2
w4 5 4
w5 6 5
w6 7 2
w7 8 2
w8 9 8
PC3
w2
2
0
0
2
3
4
5
6
7
NC4
w3
3
0
1
0
2
3
4
5
6
NC4
w4
4
0
0
1
0
2
3
4
5
w5
5
0
0
2
1
0
2
3
4
PC5
w6
6
5
4
3
2
1
0
2
3
w7
7
6
5
4
3
2
1
0
Pct6
w8
8
7
6
0
0
3
2
1
0
2
PC5
Pct6
Reorderings to encode in the distortion matrix
CC1
32
NC4
PC5
VC2
PC3
A. Bisazza & M. Federico – Modified Distortion Matrices for PSMT
Pct6
Experiments
• Tasks: NIST-MT09 for Ar-En, WMT10 for De-En
• Systems based on Moses, include state-of-the-art
hierarchical lexicalized reordering models
[Tillmann 04; Koehn & al 05; Galley & Manning 08]
• Baseline Distortion Limits: 5 in Ar-En, 10 in De-En
• Evaluation by:
- BLEU for lexical match & local order
- KRS for global order
33
A. Bisazza & M. Federico – Modified Distortion Matrices for PSMT
Arabic-English:
BLEU modif‐DL5 50.9 +0.9 BLEU
+0.6 KRS
(signif.)
50.7 50.5 50.3 50.1 49.9 Translation Time
plain‐DL5 plain‐DL8 49.7 83.0 Translation Quality
83.5 84.0 KRS 84.5 85.0 ms/word 389 400 350 Test set: eval09-NW
Distortion modified with 3-best
reorderings per rule-matching sequence
300 250 200 plain‐DL5 35
273 263 plain‐DL8 A. Bisazza & M. Federico – Modified Distortion Matrices for PSMT
modif‐DL5 German-English:
BLEU modif‐DL4 +0.4 BLEU
+0.7 KRS
(signif.)
20.6 20.4 20.2 Translation Quality
plain‐DL10 Translation Time
20.0 plain‐DL20 19.8 plain‐DL4 19.6 66.0 67.0 68.0 69.0 KRS 70.0 71.0 350 292 300 Test set: newstest10
Distortion modified with 3-best
reorderings per rule-matching sequence
369 ms/word 250 200 158 163 150 100 plain‐DL4 plain‐DL10 plain‐DL20 modif‐DL4 37
A. Bisazza & M. Federico – Modified Distortion Matrices for PSMT
Conclusions
• Modified distortion allows for finer & linguistically motivated
definition of search space
• We achieve better translation & faster decoding in language
pairs where long reordering concentrates on few patterns
• Our method is complementary to reordering modeling
• For now, few reordering rules are needed to modify distortion
• We are currently working on a fully data-driven approach to
replace the rules
38
A. Bisazza & M. Federico – Modified Distortion Matrices for PSMT
w0 w1
<s> 0 1
w0
0
w1 2
w2 3 T
w3 4 H
w4 5 A
w5 6 N
w6 7 K
w7 8 S
w8 9 8
w9 10 9
w10 11 10
39
w2
2
1
0
2
T
4
5
6
7
8
9
w3
3
2
1
0
T
3
4
5
6
7
8
w4
4
3
2
1
0
E
2
3
4
5
6
7
w5
5
4
3
2
1
N
2
3
4
5
6
w6
6
5
4
3
2
T
0
F
2
3
4
5
w7
7
6
5
4
3
I
1
O
2
3
4
w8
8
7
6
5
Y
O
U
R
0
w9 w10
9 10
8 9
7 8
6 7
5 6
N !
3 4
2 3
1 2
0 1
2
0
3 2
A. Bisazza & M. Federico – Modified Distortion Matrices for PSMT
w0 w1
<s> 0 1
w0
0
w1 2
w2 3 T
w3 4 H
w4 5 A
w5 6 N
w6 7 K
w7 8 S
w8 9 8
w9 10 9
w10 11 10
40
w2
2
1
0
2
T
4
5
6
7
8
9
w3
3
2
1
0
T
3
4
5
6
7
8
w4
4
3
2
1
0
E
2
3
4
5
6
7
w5
5
4
3
2
1
N
2
3
4
5
6
w6
6
5
4
3
2
T
0
F
2
3
4
5
w7
7
6
5
4
3
I
1
O
2
3
4
w8
8
7
6
5
Y
O
U
R
0
w9 w10
9 10
8 9
7 8
6 7
5 6
N !
3 4
2 3
1 2
0 1
2
0
3 2
A. Bisazza & M. Federico – Modified Distortion Matrices for PSMT