<s>
In	O
signal	O
processing	O
,	O
Feature	O
space	O
Maximum	O
Likelihood	O
Linear	O
Regression	O
(	O
fMLLR	B-General_Concept
)	O
is	O
a	O
global	O
feature	O
transform	O
that	O
are	O
typically	O
applied	O
in	O
a	O
speaker	O
adaptive	O
way	O
,	O
where	O
fMLLR	B-General_Concept
transforms	O
acoustic	O
features	O
to	O
speaker	O
adapted	O
features	O
by	O
a	O
multiplication	O
operation	O
with	O
a	O
transformation	O
matrix	O
.	O
</s>
<s>
In	O
some	O
literature	O
,	O
fMLLR	B-General_Concept
is	O
also	O
known	O
as	O
the	O
Constrained	O
Maximum	O
Likelihood	O
Linear	O
Regression	O
(	O
cMLLR	O
)	O
.	O
</s>
<s>
fMLLR	B-General_Concept
transformations	O
are	O
trained	O
in	O
a	O
maximum	O
likelihood	O
sense	O
on	O
adaptation	O
data	O
.	O
</s>
<s>
These	O
transformations	O
may	O
be	O
estimated	O
in	O
many	O
ways	O
,	O
but	O
only	O
maximum	O
likelihood	O
(	O
ML	O
)	O
estimation	O
is	O
considered	O
in	O
fMLLR	B-General_Concept
.	O
</s>
<s>
The	O
fMLLR	B-General_Concept
transformation	O
is	O
trained	O
on	O
a	O
particular	O
set	O
of	O
adaptation	O
data	O
,	O
such	O
that	O
it	O
maximizes	O
the	O
likelihood	O
of	O
that	O
adaptation	O
data	O
given	O
a	O
current	O
model-set	O
.	O
</s>
<s>
This	O
technique	O
is	O
a	O
widely	O
used	O
approach	O
for	O
speaker	O
adaptation	O
in	O
HMM-based	O
speech	B-Application
recognition	I-Application
.	O
</s>
<s>
Later	O
research	O
also	O
shows	O
that	O
fMLLR	B-General_Concept
is	O
an	O
excellent	O
acoustic	O
feature	O
for	O
DNN/HMM	O
hybrid	O
speech	B-Application
recognition	I-Application
models	O
.	O
</s>
<s>
The	O
advantage	O
of	O
fMLLR	B-General_Concept
includes	O
the	O
following	O
:	O
</s>
<s>
the	O
adaptation	O
process	O
can	O
be	O
performed	O
within	O
a	O
pre-processing	O
phase	O
,	O
and	O
is	O
independent	O
of	O
the	O
ASR	B-Application
training	O
and	O
decoding	O
process	O
.	O
</s>
<s>
this	O
type	O
of	O
adapted	O
feature	O
can	O
be	O
applied	O
to	O
deep	O
neural	O
networks	O
(	O
DNN	O
)	O
to	O
replace	O
traditionally	O
used	O
mel-spectrogram	B-Algorithm
in	O
end-to-end	O
speech	B-Application
recognition	I-Application
models	O
.	O
</s>
<s>
fMLLR	B-General_Concept
's	O
speaker	O
adaptation	O
process	O
leads	O
to	O
a	O
significant	O
performance	O
boost	O
for	O
ASR	B-Application
models	O
,	O
hence	O
outperforming	O
other	O
transform	O
or	O
features	O
like	O
MFCCs	B-Algorithm
(	O
Mel-Frequency	B-Algorithm
Cepstral	I-Algorithm
Coefficients	I-Algorithm
)	O
and	O
FBANKs	O
(	O
Filter	O
bank	O
)	O
coefficients	O
.	O
</s>
<s>
fMLLR	B-General_Concept
features	O
can	O
be	O
efficiently	O
realized	O
with	O
speech	O
toolkits	O
like	O
Kaldi	B-General_Concept
.	O
</s>
<s>
Major	O
problem	O
and	O
disadvantage	O
of	O
fMLLR	B-General_Concept
:	O
</s>
<s>
when	O
the	O
amount	O
of	O
adaptation	O
data	O
is	O
limited	O
,	O
the	O
transformation	O
matrices	O
tends	O
to	O
easily	O
overfit	B-Error_Name
the	O
given	O
data	O
.	O
</s>
<s>
Feature	O
transform	O
of	O
fMLLR	B-General_Concept
can	O
be	O
easily	O
computed	O
with	O
the	O
open	O
source	O
speech	O
tool	O
Kaldi	B-General_Concept
,	O
the	O
Kaldi	B-General_Concept
script	O
uses	O
the	O
standard	O
estimation	O
scheme	O
described	O
in	O
Appendix	O
B	O
of	O
the	O
original	O
paper	O
,	O
in	O
particular	O
the	O
section	O
Appendix	O
B.1	O
"	O
Direct	O
method	O
over	O
rows	O
"	O
.	O
</s>
<s>
In	O
the	O
Kaldi	B-General_Concept
formulation	O
,	O
fMLLR	B-General_Concept
is	O
an	O
affine	O
feature	O
transform	O
of	O
the	O
form	O
→	O
,	O
which	O
can	O
be	O
written	O
in	O
the	O
form	O
→	O
W	O
,	O
where	O
=	O
is	O
the	O
acoustic	O
feature	O
with	O
a	O
1	O
appended	O
.	O
</s>
<s>
For	O
a	O
thorough	O
review	O
that	O
explains	O
fMLLR	B-General_Concept
and	O
the	O
commonly	O
used	O
estimation	O
techniques	O
,	O
see	O
the	O
original	O
paper	O
"	O
Maximum	O
likelihood	O
linear	O
transformations	O
for	O
HMM-based	O
speech	B-Application
recognition	I-Application
"	O
.	O
</s>
<s>
Note	O
that	O
the	O
Kaldi	B-General_Concept
script	O
that	O
performs	O
the	O
feature	O
transforms	O
of	O
fMLLR	B-General_Concept
differs	O
with	O
by	O
using	O
a	O
column	O
of	O
the	O
inverse	O
in	O
place	O
of	O
the	O
cofactor	O
row	O
.	O
</s>
<s>
Experiment	O
result	O
shows	O
that	O
by	O
using	O
the	O
fMLLR	B-General_Concept
feature	O
in	O
speech	B-Application
recognition	I-Application
,	O
constant	O
improvement	O
is	O
gained	O
over	O
other	O
acoustic	O
features	O
on	O
various	O
commonly	O
used	O
benchmark	O
datasets	O
(	O
TIMIT	B-Application
,	O
,	O
etc	O
)	O
.	O
</s>
<s>
In	O
particular	O
,	O
fMLLR	B-General_Concept
features	O
outperform	O
MFCCs	B-Algorithm
and	O
FBANKs	O
coefficients	O
,	O
which	O
is	O
mainly	O
due	O
to	O
the	O
speaker	O
adaptation	O
process	O
that	O
fMLLR	B-General_Concept
performs	O
.	O
</s>
<s>
In	O
,	O
phoneme	O
error	O
rate	O
(	O
PER	O
,	O
%	O
)	O
is	O
reported	O
for	O
the	O
test	O
set	O
of	O
TIMIT	B-Application
with	O
various	O
neural	O
architectures	O
:	O
</s>
<s>
As	O
expected	O
,	O
fMLLR	B-General_Concept
features	O
outperform	O
MFCCs	B-Algorithm
and	O
FBANKs	O
coefficients	O
despite	O
the	O
use	O
of	O
different	O
model	O
architecture	O
.	O
</s>
<s>
Where	O
MLP	B-Algorithm
(	O
multi-layer	B-Algorithm
perceptron	I-Algorithm
)	O
serves	O
as	O
a	O
simple	O
baseline	O
,	O
on	O
the	O
other	O
hand	O
RNN	B-Algorithm
,	O
LSTM	B-Algorithm
,	O
and	O
GRU	B-Algorithm
are	O
all	O
well	O
known	O
recurrent	O
models	O
.	O
</s>
<s>
The	O
Li-GRU	O
architecture	O
is	O
based	O
on	O
a	O
single	O
gate	O
and	O
thus	O
saves	O
33%	O
of	O
the	O
computations	O
over	O
a	O
standard	O
GRU	B-Algorithm
model	O
,	O
Li-GRU	O
thus	O
effectively	O
address	O
the	O
gradient	O
vanishing	O
problem	O
of	O
recurrent	O
models	O
.	O
</s>
<s>
As	O
a	O
result	O
,	O
the	O
best	O
performance	O
is	O
obtained	O
with	O
the	O
Li-GRU	O
model	O
on	O
fMLLR	B-General_Concept
features	O
.	O
</s>
<s>
fMLLR	B-General_Concept
can	O
be	O
extracted	O
as	O
reported	O
in	O
the	O
s5	O
recipe	O
of	O
Kaldi	B-General_Concept
.	O
</s>
<s>
Kaldi	B-General_Concept
scripts	O
can	O
certainly	O
extract	O
fMLLR	B-General_Concept
features	O
on	O
different	O
dataset	O
,	O
below	O
are	O
the	O
basic	O
example	O
steps	O
to	O
extract	O
fMLLR	B-General_Concept
features	O
from	O
the	O
open	O
source	O
speech	O
corpora	O
.	O
</s>
<s>
These	O
instruction	O
are	O
based	O
on	O
the	O
codes	O
provided	O
in	O
this	O
,	O
which	O
contains	O
Kaldi	B-General_Concept
recipes	O
on	O
the	O
LibriSpeech	O
corpora	O
to	O
execute	O
the	O
fMLLR	B-General_Concept
feature	O
extraction	O
process	O
,	O
replace	O
the	O
files	O
under	O
$	O
KALDI_ROOT/egs/librispeech/s5/	O
with	O
the	O
files	O
in	O
the	O
repository	O
.	O
</s>
<s>
Install	O
Kaldi	B-General_Concept
.	O
</s>
<s>
Run	O
the	O
Kaldi	B-General_Concept
recipe	O
run.sh	O
for	O
LibriSpeech	O
at	O
least	O
until	O
Stage	O
13	O
(	O
included	O
)	O
,	O
for	O
simplicity	O
you	O
can	O
used	O
the	O
modified	O
.	O
</s>
<s>
Compute	O
the	O
fMLLR	B-General_Concept
features	O
by	O
running	O
the	O
following	O
script	O
,	O
the	O
script	O
can	O
also	O
be	O
downloaded	O
:	O
</s>
<s>
Apply	O
CMVN	B-General_Concept
and	O
dump	O
the	O
fMLLR	B-General_Concept
features	O
to	O
new	O
.ark	O
files	O
,	O
the	O
script	O
can	O
also	O
be	O
downloaded	O
:	O
</s>
<s>
Use	O
the	O
Python	O
script	O
to	O
convert	O
Kaldi	B-General_Concept
generated	O
.ark	O
features	O
to	O
.npy	O
for	O
your	O
own	O
dataloader	O
,	O
an	O
example	O
is	O
provided	O
:	O
</s>
