Browse Prior Art Database

Nonlinear Adaptation Mapping Based on Conditional Expectations

IP.com Disclosure Number: IPCOM000114206D
Original Publication Date: 1994-Nov-01
Included in the Prior Art Database: 2005-Mar-27
Document File: 4 page(s) / 87K

Publishing Venue

IBM

Related People

Nadas, A: AUTHOR [+3]

Abstract

Reference speech X and new speech Y aligned to a fenemic phone are used to estimate the conditional expectation T(x)=E(Y vbar X=x). The nonlinear mapping T: X rarrow Y is obtained from a joint mixture model (X,Y,I) where the mixture index I is the (leafeme, position-within-leafeme) pair. the new talker is trained on the pooled Y and T(X) data.

This text was extracted from an ASCII text file.
This is the abbreviated version, containing approximately 52% of the total text.

Nonlinear Adaptation Mapping Based on Conditional Expectations

      Reference speech X and new speech Y aligned to a fenemic phone
are used to estimate the conditional expectation T(x)=E(Y vbar X=x).
The nonlinear mapping T: X rarrow Y is obtained from a joint mixture
model (X,Y,I) where the mixture index I is the (leafeme,
position-within-leafeme) pair.  the new talker is trained on the
pooled Y and T(X) data.

Our aim is to find an adaptive transformation
for making reference speech look like some new speech.  Previous
methods for this have been linear or piecewise linear; we develop a
natural nonlinear map.

      Let I with values i epsilon lbrace 1,2,...,k rbrace denote the
random class index corresponding to a small subword unit.  Denote by
X a reference vector and by Y a new spectral vector.  Assume further
that the joint distribution of these vectors given I=i is 2d
dimensional multivariate gaussian with density g(x,y vbar eta sub i,
Sigma sub i) and with mean vector
and covariance matrix

Let p sub i denote the 'prior' (i.e., marginal) probability of the
classes.  Then the 'posterior' (i.e., conditional) probability of a
class given X = x is the usual Bayes estimate

With this in hand we can define the mapping T as the conditional
expectation

In terms of our model assumptions T can be expressed as

      There appears to be no reason for statistical dependence
between X and Y which are paired only because they are aligned to the
same index I=i; they are related instead by having related (similar)
probability distributions conditioned on I=i.  This suggests the
assumption of conditional independence.  Were this not the case, we
would have to estimate the conditional cross covariance matrices
Sigma sub i (2,1) as well as the means and covariances.  Assuming
conditional independence given I=i yields and Sigma sub i (2,1) and
hence the simpler mapping

      This map has a simple interpretation, to wit, it predicts a Y -
value as a convex linear combination of the Y - centroids nu sub i.
The coefficients in this linea...