HTK 3.5手册：构建HMM语音处理工具的基础

语音识别

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《HTK Book 3.5》是一本详细指南，专为利用Hidden Markov Models (HMMs)进行语音处理，尤其是语音识别任务而设计。作者包括Steve Young、Gunnar Evermann等多位知名专家，版权由微软公司和剑桥大学工程系共同持有。本书自1995年首次出版以来，随着HTK（Hidden Markov Toolkit）版本的更新，不断修订以适应新的技术和需求。第一部分是教程概述，主要讲解了HMM的基础原理。HMMs是一种统计建模工具，用于分析随时间变化的序列数据，它们特别适用于时序信号，如语音信号。书中首先介绍了HMM的一般原则，包括状态转移概率、观测概率以及如何通过这些概率来理解和预测序列的行为。孤立词识别（ISLR）作为基础应用，展示了如何使用HMM识别单个词汇。输出概率的指定是关键环节，它定义了模型如何根据观测到的数据决定状态转移。Baum-Welch算法在此处扮演重要角色，用于在训练阶段根据已知的输入和期望输出重新估计模型参数，从而优化模型性能。后续章节探讨了HMM在连续语音识别中的应用，涉及帧级的特征提取、语言模型集成以及解码算法的选择，如Viterbi算法，它提供了最可能的路径估计，以找到给定观测序列的最佳状态序列。此外，书中还涵盖了如何通过 Speaker Adaptation 技术，让模型适应不同说话人的声音特性，提高识别的鲁棒性。第二部分则全面介绍了HTK工具集，包括其架构、核心组件（如声学模型、语言模型和解码器）、命令行接口以及与实际语音识别系统集成的方法。这部分内容对于开发者来说非常实用，涵盖了从模型训练到实时识别的整个工作流程。《HTK Book 3.5》为语音识别领域的研究人员和工程师提供了一套完整的工具和理论框架，涵盖了从基础概念到高级技术的深入讲解，对于理解和实现基于HMM的语音识别系统具有重要的参考价值。

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1.3 Output Probability Speciﬁcation 6

1.3 Output Probability Speciﬁcation

Before the problem of parameter estimation can be discussed in more detail, the form of the output

distributions {b

)} needs to be made explicit. HTK is designed primarily for modelling con-

tinuous parameters using continuous density multivariate output distributions. It can also handle

observation sequences consisting of discrete symbols in which case, the output distributions are

discrete probabilities. For simplicity, however, the presentation in this chapter will assume that

continuous density distributions are being used. The minor diﬀerences that the use of discrete

probabilities entail are noted in chapter 7 and discussed in more detail in chapter 11.

In common with most other continuous density HMM systems, HTK represents output distri-

butions by Gaussian Mixture Densities. In HTK, however, a further generalisation is made. HTK

allows each observation vector at time t to be split into a number of S independent data streams

. The formula for computing b

) is then

) =

s=1

m=1

jsm

N(o

; µ

jsm

, Σ

jsm

)

(1.8)

where M

is the number of mixture components in stream s, c

jsm

is the weight of the m’th compo-

nent and N(·; µ, Σ) is a multivariate Gaussian with mean vector µ and covariance matrix Σ, that

N(o; µ, Σ) =

(2π)

|Σ|

−

(o−µ)

−1

(o−µ)

(1.9)

where n is the dimensionality of o.

The exponent γ

is a stream weight

. It can be used to give a particular stream more emphasis,

however, it can only be set manually. No current HTK training tools can estimate values for it.

Multiple data streams are used to enable separate modelling of multiple information sources. In

HTK, the processing of streams is completely general. However, the speech input modules assume

that the source data is split into at most 4 streams. Chapter 5 discusses this in more detail but for

now it is suﬃcient to remark that the default streams are the basic parameter vector, ﬁrst (delta)

and second (acceleration) diﬀerence coeﬃcients and log energy.

1.4 Baum-Welch Re-Estimation

To determine the parameters of a HMM it is ﬁrst necessary to make a rough guess at what they

might be. Once this is done, more accurate (in the maximum likelihood sense) parameters can be

found by applying the so-called Baum-Welch re-estimation formulae.

...

Single

Gaussians

M-component

Gaussian

mixture

Fig. 1.5 Representing a Mixture

Chapter 8 gives the formulae used in HTK in full detail. Here the basis of the formulae will

be presented in a very informal way. Firstly, it should be noted that the inclusion of multiple

data streams does not alter matters signiﬁcantly since each stream is considered to be statistically

often referred to as a codebook exponent.

1.4 Baum-Welch Re-Estimation 7

independent. Furthermore, mixture components can be considered to be a special form of sub-state

in which the transition probabilities are the mixture weights (see Fig. 1.5).

Thus, the essential problem is to estimate the means and variances of a HMM in which each

state output distribution is a single component Gaussian, that is

) =

(2π)

|Σ

−

−µ

)

−1

−µ

)

(1.10)

If there was just one state j in the HMM, this parameter estimation would be easy. The maximum

likelihood estimates of µ

and Σ

would be just the simple averages, that is

t=1

(1.11)

and

t=1

− µ

)(o

− µ

)

(1.12)

In practice, of course, there are multiple states and there is no direct assignment of observation

vectors to individual states because the underlying state sequence is unknown. Note, however, that

if some approximate assignment of vectors to states could be made then equations 1.11 and 1.12

could be used to give the required initial values for the parameters. Indeed, this is exactly what

is done in the HTK tool called HInit. HInit ﬁrst divides the training observation vectors equally

amongst the model states and then uses equations 1.11 and 1.12 to give initial values for the mean

and variance of each state. It then ﬁnds the maximum likelihood state sequence using the Viterbi

algorithm described below, reassigns the observation vectors to states and then uses equations 1.11

and 1.12 again to get better initial values. This process is repeated until the estimates do not

change.

Since the full likelihood of each observation sequence is based on the summation of all possi-

ble state sequences, each observation vector o

contributes to the computation of the maximum

likelihood parameter values for each state j. In other words, instead of assigning each observation

vector to a speciﬁc state as in the above approximation, each observation is assigned to every state

in proportion to the probability of the model being in that state when the vector was observed.

Thus, if L

(t) denotes the probability of being in state j at time t then the equations 1.11 and 1.12

given above become the following weighted averages

t=1

(t)o

t=1

(t)

(1.13)

and

t=1

(t)(o

− µ

)(o

− µ

)

t=1

(t)

(1.14)

where the summations in the denominators are included to give the required normalisation.

Equations 1.13 and 1.14 are the Baum-Welch re-estimation formulae for the means and covari-

ances of a HMM. A similar but slightly more complex formula can be derived for the transition

probabilities (see chapter 8).

Of course, to apply equations 1.13 and 1.14, the probability of state occupation L

(t) must

be calculated. This is done eﬃciently using the so-called Forward-Backward algorithm. Let the

forward probability

(t) for some model M with N states be deﬁned as

(t) = P (o

, . . . , o

, x(t) = j|M). (1.15)

That is, α

(t) is the joint probability of observing the ﬁrst t speech vectors and being in state j at

time t. This forward probability can be eﬃciently calculated by the following recursion

(t) =

N−1

i=2

(t − 1)a

). (1.16)

Since the output distributions are densities, these are not really probabilities but it is a convenient ﬁction.

1.4 Baum-Welch Re-Estimation 8

This recursion depends on the fact that the probability of being in state j at time t and seeing

observation o

can be deduced by summing the forward probabilities for all possible predecessor

states i weighted by the transition probability a

. The slightly odd limits are caused by the fact

that states 1 and N are non-emitting

. The initial conditions for the above recursion are

(1) = 1 (1.17)

(1) = a

) (1.18)

for 1 < j < N and the ﬁnal condition is given by

(T ) =

N−1

i=2

(T )a

. (1.19)

Notice here that from the deﬁnition of α

(t),

P (O|M) = α

(T ). (1.20)

Hence, the calculation of the forward probability also yields the total likelihood P (O|M).

The backward probability β

(t) is deﬁned as

(t) = P (o

t+1

, . . . , o

|x(t) = j, M ). (1.21)

As in the forward case, this backward probability can be computed eﬃciently using the following

recursion

(t) =

N−1

j=2

t+1

)β

(t + 1) (1.22)

with initial condition given by

(T ) = a

(1.23)

for 1 < i < N and ﬁnal condition given by

(1) =

N−1

j=2

)β

(1). (1.24)

Notice that in the deﬁnitions above, the forward probability is a joint probability whereas the

backward probability is a conditional probability. This somewhat asymmetric deﬁnition is deliberate

since it allows the probability of state occupation to be determined by taking the product of the

two probabilities. From the deﬁnitions,

(t)β

(t) = P (O, x(t) = j|M). (1.25)

Hence,

(t) = P (x(t) = j|O, M) (1.26)

P (O, x(t) = j|M)

P (O|M)

(t)β

(t)

where P = P (O|M).

All of the information needed to perform HMM parameter re-estimation using the Baum-Welch

algorithm is now in place. The steps in this algorithm may be summarised as follows

1. For every parameter vector/matrix requiring re-estimation, allocate storage for the numerator

and denominator summations of the form illustrated by equations 1.13 and 1.14. These storage

locations are referred to as accumulators

To understand equations involving a non-emitting state at time t, the time should be thought of as being t − δt

if it is an entry state, and t + δt if it is an exit state. This becomes important when HMMs are connected together

in sequence so that transitions across non-emitting states take place between frames.

Note that normally the summations in the denominators of the re-estimation formulae are identical across the

parameter sets of a given state and therefore only a single common storage location for the denominators is required

and it need only be calculated once. However, HTK supports a generalised parameter tying mechanism which can

result in the denominator summations being diﬀerent. Hence, in HTK the denominator summations are always

stored and calculated individually for each distinct parameter vector or matrix.

1.5 Recognition and Viterbi Decoding 9

2. Calculate the forward and backward probabilities for all states j and times t.

3. For each state j and time t, use the probability L

(t) and the current observation vector o

to update the accumulators for that state.

4. Use the ﬁnal accumulator values to calculate new parameter values.

5. If the value of P = P (O|M) for this iteration is not higher than the value at the previous

iteration then stop, otherwise repeat the above steps using the new re-estimated parameter

values.

All of the above assumes that the parameters for a HMM are re-estimated from a single ob-

servation sequence, that is a single example of the spoken word. In practice, many examples are

needed to get good parameter estimates. However, the use of multiple observation sequences adds

no additional complexity to the algorithm. Steps 2 and 3 above are simply repeated for each distinct

training sequence.

One ﬁnal point that should be mentioned is that the computation of the forward and backward

probabilities involves taking the product of a large number of probabilities. In practice, this means

that the actual numbers involved become very small. Hence, to avoid numerical problems, the

forward-backward computation is computed in HTK using log arithmetic.

The HTK program which implements the above algorithm is called HRest. In combination

with the tool HInit for estimating initial values mentioned earlier, HRest allows isolated word

HMMs to be constructed from a set of training examples using Baum-Welch re-estimation.

1.5 Recognition and Viterbi Decoding

The previous section has described the basic ideas underlying HMM parameter re-estimation using

the Baum-Welch algorithm. In passing, it was noted that the eﬃcient recursive algorithm for

computing the forward probability also yielded as a by-product the total likelihood P (O|M). Thus,

this algorithm could also be used to ﬁnd the model which yields the maximum value of P (O|M

and hence, it could be used for recognition.

In practice, however, it is preferable to base recognition on the maximum likelihood state se-

quence since this generalises easily to the continuous speech case whereas the use of the total

probability does not. This likelihood is computed using essentially the same algorithm as the for-

ward probability calculation except that the summation is replaced by a maximum operation. For

a given model M, let φ

(t) represent the maximum likelihood of observing speech vectors o

and being in state j at time t. This partial likelihood can be computed eﬃciently using the

following recursion (cf. equation 1.16)

(t) = max

{φ

(t − 1)a

). (1.27)

where

(1) = 1 (1.28)

(1) = a

) (1.29)

for 1 < j < N. The maximum likelihood

P (O|M ) is then given by

(T ) = max

{φ

(T )a

} (1.30)

As for the re-estimation case, the direct computation of likelihoods leads to underﬂow, hence,

log likelihoods are used instead. The recursion of equation 1.27 then becomes

(t) = max

{ψ

(t − 1) + log(a

)} + log(b

)). (1.31)

This recursion forms the basis of the so-called Viterbi algorithm. As shown in Fig. 1.6, this algorithm

can be visualised as ﬁnding the best path through a matrix where the vertical dimension represents

the states of the HMM and the horizontal dimension represents the frames of speech (i.e. time).

Each large dot in the picture represents the log probability of observing that frame at that time and

each arc between dots corresponds to a log transition probability. The log probability of any path

1.6 Continuous Speech Recognition 10

is computed simply by summing the log transition probabilities and the log output probabilities

along that path. The paths are grown from left-to-right column-by-column. At time t, each partial

path ψ

(t − 1) is known for all states i, hence equation 1.31 can be used to compute ψ

(t) thereby

extending the partial paths by one time frame.

State

Speech

Frame

(Time)

1 2 3 4 5 6

( )

Fig. 1.6 The Viterbi Algorithm for Isolated Word

Recognition

This concept of a path is extremely important and it is generalised below to deal with the

continuous speech case.

This completes the discussion of isolated word recognition using HMMs. There is no HTK tool

which implements the above Viterbi algorithm directly. Instead, a tool called HVite is provided

which along with its supporting libraries, HNet and HRec, is designed to handle continuous

speech. Since this recogniser is syntax directed, it can also perform isolated word recognition as a

special case. This is discussed in more detail below.

1.6 Continuous Speech Recognition

Returning now to the conceptual model of speech production and recognition exempliﬁed by Fig. 1.1,

it should be clear that the extension to continuous speech simply involves connecting HMMs together

in sequence. Each model in the sequence corresponds directly to the assumed underlying symbol.

These could be either whole words for so-called connected speech recognition or sub-words such as

phonemes for continuous speech recognition. The reason for including the non-emitting entry and

exit states should now be evident, these states provide the glue needed to join models together.

There are, however, some practical diﬃculties to overcome. The training data for continuous

speech must consist of continuous utterances and, in general, the boundaries dividing the segments

of speech corresponding to each underlying sub-word model in the sequence will not be known. In

practice, it is usually feasible to mark the boundaries of a small amount of data by hand. All of

the segments corresponding to a given model can then be extracted and the isolated word style

of training described above can be used. However, the amount of data obtainable in this way is

usually very limited and the resultant models will be poor estimates. Furthermore, even if there

was a large amount of data, the boundaries imposed by hand-marking may not be optimal as far

as the HMMs are concerned. Hence, in HTK the use of HInit and HRest for initialising sub-word

models is regarded as a bootstrap operation

. The main training phase involves the use of a tool

called HERest which does embedded training.

Embedded training uses the same Baum-Welch procedure as for the isolated case but rather

than training each model individually all models are trained in parallel. It works in the following

steps:

They can even be avoided altogether by using a ﬂat start as described in section 8.3.

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