P(stist_i)=HP(.014"i). p(sio=71.41)1=i)=.T. : The transition structure of this constrained (uncoupling) factorial Markov chain can be parameterized by L distinct KM x K(i) matrices. This is significantly simpler than the original KL L matrix as in the unconstrained case. This model is called an overlapping feature model because the independent dynam- ics of the features at different tiers cause many ways in which different feature values

doi:10.1201/9781482276237-59

Chapter

P(stist_i)=HP(.014"i). p(sio=71.41)1=i)=.T.

Chapter

ABSTRACT

The conditional PDF for the acoustic features as the output of the nonlinear mapping function can be determined directly from Eq. 10.82 to be

po[o(k)lx(k)1 =vv[o(k)— h(x(k))]. (10.83) There are many ways of choosing the static nonlinear function for h[x] as in Eq. 10.82. Let us take an illustrative example of a multi-layer perceptron (MLP) with three layers (input, hidden and output), capitalizing on the highly desirable property of the MLP as a universal nonlinear function approximator [Bishop 97]. Let wit be the MLP weights from input to hidden units and 1472i be the MLP weights from hidden to output units, where 1 is the input node index, j the hidden node index and i the output node index. Then the output signal at node i can be expressed as a (nonlinear) function of all the input nodes (making up the input vector) according to

hi(x) = > WWI • (E wfi • .0, 1 < i < /, J-1 (10.84)

where I, J and L are the numbers of nodes at the output, hidden and input layers, respectively, and s(.) is the hidden unit's nonlinear activation function, taken as the standard sigmoid function of

s(x) =(10.85) 1 + exp(—x) .