Penalized maximum likelihood estimation methods, the baum welch algorithm and diagonal balancing of symmetric matrices for the training of acoustic models in speech recognition

• US 6,374,216 B1
• Filed: 09/27/1999
• Issued: 04/16/2002
• Est. Priority Date: 09/27/1999
• Status: Expired due to Fees

• Current Assignee: International Business Machines Corporation
• Original Assignee: International Business Machines Corporation
• Inventors: Micchelli, Charles A., Olsen, Peder A.
• Primary Examiner(s): Dorvil, Richemond
• Assistant Examiner(s): Nolan, Daniel A.
• Application Number:
  US09/404,995
• Time in Patent Office: 932 Days
• Field of Search: 704/251-256, 704/236-240
• US Class Current: 704/236
• CPC Class Codes: G10L 15/063 Training

Abstract

A nonparametric family of density functions formed by histogram estimators for modeling acoustic vectors are used in automatic recognition of speech. A Gaussian kernel is set forth in the density estimator. When the densities are found for all the basic sounds in a training stage, an acoustic vector is assigned to a phoneme label corresponding to the highest likelihood for the basis of the decoding of acoustic vectors into text.

Claims

1. A computer implemented method for machine recognition of speech, comprising the steps of:

inputting acoustic data;

forming a nonparametric density estimator $f_n<br><br>\left(x\right)=\underset{\mathrm{<br><br>}\in <br><br>Z_n}{\sum <br><br>}<br><br>c_i<br><br>k<br><br>\left(x,x^i\right),x\in <br><br>R^d,\mathrm{where}<br><br>\text{\hspace{1em}<br><br>}<br><br>Z_n=\left\{1,2,\mathrm{\dots <br><br>}<br><br>\text{\hspace{1em}<br><br>},n\right\},k<br><br>\left(x,y\right)$

 

is some specified positive kernel function, $c_i\ge <br><br>0,\mathrm{<br><br>}\in <br><br>Z_n,\underset{i=1}{\overset{n}{\sum <br><br>}}<br><br>\text{\hspace{1em}<br><br>}<br><br>c_i=1$

 

are parameters to be chosen, and {xⁱ}<sub>iε

Zn</sub> is a given set of training data;

setting a kernel for the estimator;

selecting a statistical criterion to be optimized to find values for parameters defining the nonparametric density estimator; and

iteratively computing the density estimator for finding a maximum likelihood estimation of acoustic data.

2. The computer implemented method for machine recognition of speech as recited in claim 1, wherein the statistical criterion to be optimized is selected from a penalized maximum likelihood criteria or a maximum likelihood criteria.

3. The computer implemented method for machine recognition of speech as recited in claim 2, wherein the maximum likelihood criteria is selected.

4. The computer implemented method for machine recognition of speech as recited in claim 3, wherein a process of degree raising of polynomials is used for global maximization.

5. The computer implemented method for machine recognition of speech as recited in claim 3, wherein the step of iteratively computing employs a process of diagonal balancing of matrices to maximize the likelihood.

6. The computer implemented method for machine recognition of speech as recited in claim 5, wherein a form of the iteratively computing is ĉ

=c/nA^T((Ac)<sup>−

1</sup>), where c=(c₁, c₂, . . . , c_n), c_i≧

0, $\underset{i=1}{\overset{n}{\sum <br><br>}}<br><br>\text{\hspace{1em}<br><br>}<br><br>c_i=1$

is an initial choice for the parameters, ĉ

is the updated parameter choice, and K={k(xⁱ,x^j)}<sub>i,jε

Zn</sub>, A=cK, where c is chosen such that Ae=e for e=(1, 1, . . . ,1).

7. The computer implemented method for machine recognition of speech as recited in claim 2, wherein the penalized maximum likelihood criteria is selected.

8. The computer implemented method for machine recognition of speech as recited in claim 7, wherein the step of iteratively computing employs a process of diagonal balancing of matrices to maximize the penalized likelihood.

9. The computer implemented method for machine recognition of speech as recited in claim 8, wherein the step of iteratively computing the density estimator uses an update of parameters given as a unique vector vε

intSⁿ(b) satisfying v·

Kv=K((Kc)<sup>−

1</sup>)·

c−

γ

v·

b, where b_i=∫

_R^dk(x,xⁱ)dx, b=(b₁, b₂, . . . ,b_n), Sⁿ(b)={c;

cε

R^d, b^Tc=1} and γ

=n−

v^TKv.

10. The computer implemented method for machine recognition of speech as recited in claim 9, wherein the update parameter is given as $v=\frac{c·}{}$

K

((Kc)-1-σ



 



e)n-σ



 



cT

Kc,

where σ

>

0 is a parameter chosen to yield a best possible performance.

11. The computer implemented method for machine recognition of speech as recited in claim 1, wherein the kernel is a Gaussian kernel.

12. The computer implemented method for machine recognition of speech as recited in claim 1, wherein the kernel is given by the formula $k$

(x,y)=1(1+





x-y





2)2,

x,yε

R^d, where k(x,y), x,yε

R^d is a reproducing kernel for a Hilbert space of functions on R^d.

13. The computer implemented method for machine recognition of speech as recited in claim 1, wherein $c=\frac{e}{n}$

 



and

 



k

(x,y)=1h

k

(x-yh).

14. The computer implemented method for machine recognition of speech as recited in claim 1, further comprising the step of assigning the maximum likelihood estimation to a phoneme label.

15. The computer implemented method for machine recognition of speech as recited in claim 1, wherein the non-parametric density estimator has the form $f_n$

(x)=1nhd

∑



∈

Zn

k

(x-xih),

xε

R^d, where Z_n={1, . . . ,n}, k is some specified function, and {xⁱ;

iε

Z_n} is a set of observations in R^d of some unknown random variable.