Modeling a class posterior probability of context dependent phonemes in a speech recognition system
What is disclosed is a system and method for modelling a class posterior probability of context dependent phonemes in a speech recognition system. A representation network is trained by projecting a N-dimensional feature vector into G intermediate layers of nodes. At least some features are associated with a class label vector. A last intermediate layer Z G of the representation network is discretized to obtain a discretized layer {circumflex over (Z)}. Feature vector Q is obtained by randomly selecting V features from discretized layer {circumflex over (Z)}. Q is repeatedly hashed to obtain a vector Q f where Q f is an output of the f th hashing. An equivalent scalar representation is determined for each Q f . In a manner more fully disclosed herein, a posterior probability P f is determined for each (x, b) pair based on the equivalent scalar representation of each respective Q f . The obtained posterior probabilities are used to improve classification accuracy in a speech recognition system.
1. A computer implemented method for modeling a class posterior probability of context dependent phonemes in a Hidden Markov Model based speech recognition system, the computer implemented method comprising:
receiving a N-dimensional feature vector x 1 , x 2 , . . . , x N with a respective M-dimensional class label vector b 1 , b 2 , . . . , b M , where (x,b) represents the x th feature and its label;
assigning a feature to each node of an input layer of a representation network comprising an input layer of N nodes and G≥2 intermediate layers of nodes with each intermediate layer having N g nodes, where g ∈(1, G), all edges of all nodes of the input layer being connected to all nodes of a first intermediate layer, all edges of all nodes of each intermediate layer being connected to all nodes of a next successive intermediate layer;
computing, for all nodes of each intermediate layer, discriminative features based on features of nodes in a preceding layer;
discretizing features of last intermediate layer Z G into E-intervals to obtain a discretized layer {circumflex over (Z)}, where E≥2;
generating a feature vector Q=(q 1 , q 2 , . . . , q V ) by randomly selecting V ∈(1, N G ) features from discretized layer {circumflex over (Z)};
for f=1 to F, hashing Q into Q f =(q 1 f , q 2 f , . . . , q V f ), where Q f is obtained from the f th hashing, where F≥2;
determining an equivalent scalar representation for each Q f ;
for f=1 to F, determining a posterior probability P f for each (x, b) pair based on the determined respective equivalent scalar representation;
use the posterior probabilities to improve classification accuracy in the Hidden Markov Model based speech recognition system; and
use the Hidden Markov Model based speech recognition system to recognize speech.
2. The computer implemented method of claim 1 , wherein computing the discriminative feature for the i th node of the g th intermediate layer comprises:
a
i
g
=
∑
j
=
1
N
g
-
1
w
i
,
j
g
*
Z
j
g
-
1
+
d
i
g
Z
i
g
=
1
-
exp
(
a
i
g
)
1
+
exp
(
a
i
g
)
where w i,j g is a weight applied to edges connecting the i th node of the g th intermediate layer to the j th edge of all nodes of a preceding layer, and d i g is a bias term.
3. The computer implemented method of claim 1 , wherein the hashing comprises:
h
(
Q
)
=
∑
k
=
1
V
q
k
*
E
k
-
1
.
4. The computer implemented method of claim 1 , further comprising:
for f=1 to F, set all locations in an array U f [E V ][M] equal to 0; and
for f=1 to F, set array location U f [r f (x)][b] equal to 1, for each (x, b) pair.
5. The computer implemented method of claim 4 , wherein the scalar representation of Q f for a given f comprises:
r
f
(
x
)
=
∑
k
=
1
V
q
k
f
*
E
k
-
1
where q k f ; represents the k th feature of Q f .
6. The computer implemented method of claim 5 , wherein determining the posterior probability P f for a given (x, b) pair comprises:
P
f
(
x
,
b
)
=
U
f
[
r
f
(
x
)
]
[
b
]
∑
d
=
1
M
U
f
[
r
f
(
x
)
]
[
b
]
.
7. The computer implemented method of claim 1 , wherein the representation network is configured dynamically based on a dimensionality of the received feature vector.
8. The computer implemented method of claim 1 , further comprising communicating the determined posterior probabilities to any of: a display device, a storage device, and a remote device over a network.
9. A Hidden Markov Model based speech recognition system comprising:
a representation network having an input layer of N nodes and G≥2 intermediate layers of nodes, each intermediate layer having N g nodes, where g ∈(1, G), all edges of all nodes of the input layer being connected to all nodes of a first intermediate layer, all edges of all nodes of each intermediate layer being connected to all nodes of a next successive intermediate layer; and
at least one processor executing machine readable program instructions which configure the processor to:
receive a N-dimensional feature vector x 1 , x 2 , . . . , x N with a respective M-dimensional class label vector b 1 , b 2 , . . . , b M , where (x, b) represents the X th feature and its label;
initialize the representation network by assigning a feature to each node of the input layer;
train the representation network by computing, for all nodes of each intermediate layer, discriminative features based on features of nodes in a preceding layer;
compute a posterior probability P f for each (x, b) pair comprising:
discretize features of last intermediate layer Z G into E-intervals to obtain a discretized layer {circumflex over (Z)}, where E≥2;
generate a feature vector Q=(q 1 , q 2 , . . . , q V ) by randomly selecting V ∈(1, N G ) features from discretized layer {circumflex over (Z)};
for f=1 to F, hash Q into Q f =(q 1 f , q 2 f , . . . , q V f ), where Q f is obtained from the f th hashing, where F≥2;
determine an equivalent scalar representation for each Q f ; and
for f=1 to F, determine a posterior probability P f for each (x, b) pair based on the respective equivalent scalar representation;
use the posterior probabilities to improve classification accuracy of context dependent phonemes in the Hidden Markov Model based speech recognition system; and
use the Hidden Markov Model based speech recognition system to recognize speech.
10. The speech recognition system of claim 9 , wherein the discriminative feature computed for the i th node of the g th intermediate layer comprises:
a
i
g
=
∑
j
=
1
N
g
-
1
w
i
,
j
g
*
Z
j
g
-
1
+
d
i
g
Z
i
g
=
1
-
exp
(
a
i
g
)
1
+
exp
(
a
i
g
)
where w i,j g is a weight applied to edges connecting the i th node of the g th intermediate layer to the j th edge of all nodes of a preceding layer, and d i g is a bias term.
11. The speech recognition system of claim 9 , wherein hashing comprises:
h
(
Q
)
=
∑
k
=
1
V
q
k
*
E
k
-
1
.
12. The speech recognition system of claim 9 , wherein the processor is further configured to:
for f=1 to F, set all locations in an array U f [E V ][M] equal to 0; and
for f=1 to F, set array location U f [r f (x)][b] equal to 1, for each (x, b) pair.
13. The speech recognition system of claim 12 , wherein the scalar representation of Q f for a given f comprises:
r
f
(
x
)
=
∑
k
=
1
V
q
k
f
*
E
k
-
1
where q k f represents the k th feature of Q f .
14. The speech recognition system of claim 13 , wherein the posterior probability for a given (x, b) pair comprises:
P
f
(
x
,
b
)
=
U
f
[
r
f
(
x
)
]
[
b
]
∑
d
=
1
M
U
f
[
r
f
(
x
)
]
[
b
]
.
15. The speech recognition system of claim 9 , wherein the representation network is configured dynamically based on a dimensionality of the received feature vector.
16. The speech recognition system of claim 9 , wherein the processor is further configured to communicate the determined posterior probabilities to any of: a display device, a storage device, and a remote device over a network.
17. A method for modeling a class posterior probability of context dependent phonemes corresponding to a M-dimensional vector using a representation network with an input layer of N nodes and G≥2 intermediate layers of nodes with each intermediate layer having N g nodes, where g ∈(1, G), all edges of all nodes of the input layer being connected to all nodes of a first intermediate layer, all edges of all nodes of each intermediate layer being connected to all nodes of a next successive intermediate layer, the method comprising:
receiving a N-dimensional feature vector x 1 , x 2 , . . . , x N with a respective M-dimensional class label vector b 1 , b 2 , . . . , b M , where (x,b) represents the x th feature and its label;
assigning a feature to each node of the input layer of the representation network;
computing, for all nodes of each intermediate layer, discriminative features based on features of nodes in a preceding layer;
discretizing features of last intermediate layer Z G into E-intervals to obtain a discretized layer {circumflex over (Z)}, where E≥2;
generating a feature vector Q=(q 1 , q 2 , . . . , q V ) by randomly selecting V ∈(1, N G ) features from discretized layer {circumflex over (Z)};
for f=1 to F, hashing Q into Q f =(q 1 f , q 2 f , . . . , q V f ), where Q f is obtained from the f th hashing, where F≥2;
determining an equivalent scalar representation for each Q f ;
for f=1 to F, determining a posterior probability P f for each (x, b) pair based on the determined respective equivalent scalar representation;
modeling a class posterior probability of a M-dimensional vector y 1 , y 2 , . . . , y M ;
using the modeled class posterior probabilities to improve classification accuracy of context dependent phonemes in a speech recognition system; and
using the speech recognition system to recognize speech.
18. The method of claim 17 , wherein computing the discriminative feature for the i th node of the g th intermediate layer comprises:
a
i
g
=
∑
j
=
1
N
g
-
1
w
i
,
j
g
*
Z
j
g
-
1
+
d
i
g
Z
i
g
=
1
-
exp
(
a
i
g
)
1
+
exp
(
a
i
g
)
where w i,j g is a weight applied to edges connecting the i th node of the g th intermediate layer to the j th edge of all nodes of a preceding layer, and d i g is a bias term.
19. The method of claim 17 , wherein hashing comprises:
h
(
Q
)
=
∑
k
=
1
V
q
k
*
E
k
-
1
.
20. The method of claim 17 , further comprising:
for f=1 to F, set all locations in an array U f [E V ][M] equal to 0; and
for f=1 to F, set array location U f [r f (x)][b] equal to 1, for each (x, b) pair.
21. The method of claim 20 , wherein the scalar representation of Q f for a given f comprises:
r
f
(
x
)
=
∑
k
=
1
V
q
k
f
*
E
k
-
1
where q k f represents the k th feature of Q f .
22. The method of claim 21 , wherein determining posterior probability P f for a given (x, b) pair comprises:
P
f
(
x
,
b
)
=
U
f
[
r
f
(
x
)
]
[
b
]
∑
d
=
1
M
U
f
[
r
f
(
x
)
]
[
b
]
.
23. The method of claim 17 , wherein the representation network is configured dynamically based on a dimensionality of the received feature vector.
24. The method of claim 17 , further comprising communicating the determined posterior probabilities to any of: a display device, a storage device, and a remote device over a network.
25. A system for modeling a class posterior probability of context dependent phonemes corresponding to a M-dimensional vector, the system comprising:
a representation network having an input layer of N nodes and G≥2 intermediate layers of nodes, each intermediate layer having N g nodes, where g ∈(1, G), all edges of all nodes of the input layer being connected to all nodes of a first intermediate layer, all edges of all nodes of each intermediate layer being connected to all nodes of a next successive intermediate layer; and
at least one processor executing machine readable program instructions which configure the processor to:
receive a N-dimensional feature vector x 1 , x 2 , . . . , x N with a respective M-dimensional class label vector b 1 , b 2 , . . . , b M , where (x, b) represents the x th feature and its label;
initialize the representation network by assigning a feature to each node of the input layer;
train the representation network by computing, for all nodes of each intermediate layer, discriminative features based on features of nodes in a preceding layer;
compute a posterior probability P f for each (x, b) pair comprising:
discretize features of last intermediate layer Z G into E-intervals to obtain a discretized layer {circumflex over (Z)}, where E≥2;
generate a feature vector Q=(q 1 , q 2 , . . . , q V ) by randomly selecting V ∈(1, N G ) features from discretized layer {circumflex over (Z)};
for f=1 to F, hash Q into Q f =(q 1 f , q 2 f , . . . , q V f ), where Q f is obtained from the f th hashing, where F≥2;
determine an equivalent scalar representation for each Q f ; and
for f=1 to F, determine a posterior probability P f for each (x, b) pair based on the respective equivalent scalar representation;
model a class posterior probability of a M-dimensional vector y 1 , y 2 , . . . , y M ;
use the modeled class posterior probabilities to improve classification accuracy of context dependent phonemes in a speech recognition system; and
use the speech recognition system to recognize speech.
26. The system of claim 25 , wherein the discriminative feature computed for the i th node of the g th intermediate layer comprises:
a
i
g
=
∑
j
=
1
N
g
-
1
w
i
,
j
g
*
Z
j
g
-
1
+
d
i
g
Z
i
g
=
1
-
exp
(
a
i
g
)
1
+
exp
(
a
i
g
)
where w i,j g is a weight applied to edges connecting the i th node of the g th intermediate layer to the j th edge of all nodes of a preceding layer, and d i g is a bias term.
27. The system of claim 25 , wherein hashing comprises:
h
(
Q
)
=
∑
k
=
1
V
q
k
*
E
k
-
1
.
28. The system of claim 25 , wherein the processor is further configured to:
for f=1 to F, set all locations in an array U f [E V ][M] equal to 0; and
for f=1 to F, set array location U f [r f (x)][b] equal to 1, for each (x, b) pair.
29. The system of claim 28 , wherein the scalar representation of Q f for a given f comprises:
r
f
(
x
)
=
∑
k
=
1
V
q
k
f
*
E
k
-
1
where q k f represents the k th feature of Q f .
30. The system of claim 29 , wherein the posterior probability for a given (x, b) pair comprises:
P
f
(
x
,
b
)
=
U
f
[
r
f
(
x
)
]
[
b
]
∑
d
=
1
M
U
f
[
r
f
(
x
)
]
[
b
]
.
31. The system of claim 25 , wherein the representation network is configured dynamically based on a dimensionality of the received feature vector.
32. The system of claim 25 , wherein the processor is further configured to communicate the determined posterior probabilities to any of: a display device, a storage device, and a remote device over a network.