文章目录一、论文信息二、论文内容总结1. 写作目的2. 论文结构与内容Ⅰ–Ⅱ. 引入从离散马尔可夫链到 HMMⅢ. HMM 的三个基本问题全文核心Ⅳ. 连续观测密度的 HMMⅤ. 自回归 HMMⅥ. 空转移与状态捆绑tied parametersⅦ. 实际问题实现要点极具工程价值Ⅷ–Ⅸ. 在语音识别中的应用与展望3. 历史地位与影响摘要I. 引言一、论文信息项目内容论文标题英文A Tutorial on Hidden Markov Models and Selected Applications in Speech Recognition论文标题中文隐马尔可夫模型及其在语音识别中若干应用的教程作者Lawrence R. Rabiner劳伦斯·拉宾纳机构ATT Bell LaboratoriesATT 贝尔实验室美国新泽西州默里山发表期刊Proceedings of the IEEEIEEE 会报发表时间1989 年 2 月第 77 卷第 2 期第 257–286 页DOI10.1109/5.18626论文地址https://www.cs.ubc.ca/~murphyk/Bayes/rabiner.pdf说明这是期刊论文Proceedings of the IEEE 是期刊而非会议它是 HMM 领域被引用最多的综述之一引用量数万次也是几乎所有 HMM 课程和教材的标准入门读物。二、论文内容总结1. 写作目的HMM 的数学理论早在 1960 年代末由 Baum 等人建立但散落在数学期刊中工程界难以理解和应用。本文的目标是面向工程师而非数学家用直观、实用、可实现的视角系统讲解 HMM 理论并展示它如何成功应用于语音识别。2. 论文结构与内容Ⅰ–Ⅱ. 引入从离散马尔可夫链到 HMM先用离散马尔可夫过程状态可见做铺垫引出经典例子——缸与球模型urn and ball观测序列只告诉你球的颜色但球是从哪个缸取的状态是隐藏的这就是隐的含义。给出 HMM 的完整形式化定义一个模型由五要素刻画状态数N NN、观测符号数M MM、状态转移矩阵A AA、观测概率分布B BB、初始状态分布π \piπ简记为λ ( A , B , π ) \lambda (A, B, \pi)λ(A,B,π)。给出生成观测序列的过程并区分了各态历经模型ergodic状态任意互通和左右模型left-right状态只能向前推进——语音识别中常用。Ⅲ. HMM 的三个基本问题全文核心问题一评估Evaluation——给定模型λ \lambdaλ和观测序列O OO计算P ( O ∣ λ ) P(O \mid \lambda)P(O∣λ)。直接枚举所有状态序列是指数级复杂度不可行。解法**前向算法forward procedure**与后向算法利用动态规划将复杂度从O ( N T ⋅ T ) O(N^T \cdot T)O(NT⋅T)降到O ( N 2 T ) O(N^2T)O(N2T)。问题二解码Decoding——给定观测序列找出最可能的隐藏状态序列。讨论最优性准则单状态最优 vs. 整条路径最优采用后者。解法Viterbi 算法本质是动态规划找最优路径。问题三训练Learning/Training——给定观测序列如何调整模型参数λ \lambdaλ使P ( O ∣ λ ) P(O \mid \lambda)P(O∣λ)最大化。这是最困难的问题没有闭式解。解法Baum-Welch 算法即 EM 算法在 HMM 上的特例通过前向-后向概率迭代重估参数A AA、B BB、π \piπ保证收敛到局部最优。Ⅳ. 连续观测密度的 HMM前述模型观测是离散符号需向量量化会损失信息。本节扩展到连续观测给出多种概率密度形式高斯密度、高斯混合密度GMM、以及带状态持续时间建模的半马尔可夫变体并给出相应的参数重估公式。这就是后来统治语音识别二十年的GMM-HMM框架。Ⅴ. 自回归 HMM针对高度相关的观测信号如语音的线性预测系数讨论观测由自回归过程生成的 HMM 变体。Ⅵ. 空转移与状态捆绑tied parameters讨论允许不发射观测的空转移null transition和按转移对观测符号分组Bakis 模型等技术用于压缩参数、灵活建模。Ⅶ. 实际问题实现要点极具工程价值缩放scaling前向/后向概率随序列长度指数衰减会下溢必须每步归一化。多观测序列的训练孤立词识别中每个词多条样本。初始参数估计好的初始化影响收敛效果无严格方法但有经验做法。对数域计算、删除插值deleted interpolation等技巧。Ⅷ–Ⅸ. 在语音识别中的应用与展望孤立词识别每个词训练一个 HMM识别时对每个模型算P ( O ∣ λ w ) P(O \mid \lambda_w)P(O∣λw​)取最大介绍了分词、码本训练VQ等完整流程。大词汇量连续语音识别以音素/子词为单元建模词由子词模型拼接以 IBM Tangora 等系统为例说明可行性。总结 HMM 在语音领域成功的根本原因数学理论扎实、算法可有效实现、能直接从数据中学习。3. 历史地位与影响把 HMM 从数学家的论文变成工程师的工具直接推动了 1980–2000 年代语音识别以及后来的词性标注、生物信息学等的 HMM/GMM-HMM 时代。文中总结的三个基本问题 三个算法前向、Viterbi、Baum-Welch至今仍是所有 HMM 教材的标准框架。摘要Although initially introduced and studied in the late 1960s and early 1970s, statistical methods of Markov source or hidden Markov modeling have become increasingly popular in the last several years. There are two strong reasons why this has occurred. First the models are very rich in mathematical structure and hence can form the theoretical basis for use in a wide range of applications. Second the models, when applied properly, work very well in practice for several important applications. In this paper we attempt to carefully and methodically review the theoretical aspects of this type of statistical modeling and show how they have been applied to selected problems in machine recognition of speech.尽管马尔可夫信源或隐马尔可夫模型在20世纪60年代末和70年代初已被引入和研究但在过去的几年里这些统计方法变得越来越受欢迎。这主要有两个强有力的原因。首先这些模型在数学结构上非常丰富因此可以作为理论基础应用于更广泛的领域。其次这些模型在应用得当的情况下在几个重要的实际应用中表现优异。本文旨在仔细而系统地回顾这类统计模型的理论方面并展示它们如何应用于语音机器识别中的选定问题。I. 引言Real-world processes generally produce observable outputs which can be characterized as signals. The signals can be discrete in nature (e.g., characters from a finite alphabet, quantized vectors from a codebook, etc.), or continuous in nature (e.g., speech samples, temperature measurements, music, etc.). The signal source can be stationary (i.e., its statistical properties do not vary with time), or nonstationary (i.e., the signal properties vary over time). The signals can be pure (i.e., coming strictly from a single source), or can be corrupted from other signal sources (e.g., noise) or bytransmission distortions,reverberation, etc.现实世界的过程通常会产生可观测的输出这些输出可以被描述为信号。信号可以是离散的例如来自有限字母表的字符、来自码本的量化向量等也可以是连续的例如语音样本、温度测量、音乐等。信号源可以是平稳的即其统计特性不随时间变化或非平稳的即信号特性随时间变化。信号可以是纯净的即严格来自单一源也可以受到其他信号源例如噪声或传输失真、混响等的干扰。A problem of fundamental interest is characterizing such real-world signals in terms of signal models. There are several reasons why one is interested in applying signal models. First of all, a signal model can provide the basis for a theoretical description of a signal processing system which can be used to process the signal so as to provide a desired output. For example if we are interested in enhancing a speech signal corrupted by noise and transmission distortion, we can use the signal model to design a system which will optimally remove the noise and undo the transmission distortion. A second reason why signal models are important is that they are potentially capable of letting us learn a great deal about the signal source (i.e., the real-world process which produced the signal) without having to have the source available. This property is especially important when the cost of getting signals from the actual source is high.一个根本性的问题是根据信号模型来表征这些真实世界信号。人们对应用信号模型感兴趣有几个原因。首先信号模型可以为信号处理系统的理论描述提供基础该系统可用于处理信号以提供期望的输出。例如如果我们希望增强被噪声和传输失真破坏的语音信号我们可以使用信号模型来设计一个系统该系统可以最优地去除噪声并消除传输失真。信号模型之所以重要的第二个原因是它们有潜力让我们在无需信号源可用的情况下就能深入了解信号源即产生信号的真实世界过程。当从实际源获取信号的成本很高时此属性尤其重要。In this case, with a good signal model, we cansimulate the sourceand learn as much as possible via simulations. Finally, the most important reason why signal models are important is that they often work extremely well in practice, and enable us to realize important practical systems—e.g., prediction systems, recognition systems,identification systems, etc., in a very efficient manner.在此情况下通过一个良好的信号模型我们可以通过仿真来模拟信源并尽可能多地学习。最后信号模型之所以重要的最根本原因在于它们在实践中往往表现优异并能使我们以非常高效的方式实现重要的实际系统例如预测系统、识别系统、辨识系统等。These are several possible choices for what type of signal model is used for characterizing the properties of a given signal.Broadly onecandichotomizethe types of signal models into the class of deterministic models, and the class of statistical models. Deterministic models generally exploit some known specific properties of the signal, e.g., that the signal is asine wave, or a sum of exponentials, etc. In these cases,specification of the signal model is generally straightforward; all that is required is to determine (estimate) values of the parameters of the signal model (e.g.,amplitude, frequency, phase of a sine wave,amplitudes and rates of exponentials, etc.). The second broad class of signal models is the set of statistical models in which one tries to characterize only the statistical properties of the signal. Examples of such statistical models include Gaussian processes, Poisson processes, Markov processes, and hidden Markov processes, among others. The underlying assumption of the statistical model is that the signal can be well characterized as a parametric random process, and that the parameters of the stochastic process can be determined (estimated) in a precise, well-defined manner.在表征给定信号的特性时信号模型有几种可能的选择。广义上可以将信号模型的类型二分为 确定性模型类和统计模型类。确定性模型通常利用信号的某些已知特定属性例如信号是正弦波或是指数函数之和等。在这些情况下信号模型的设定通常很直接所需做的只是确定估计信号模型参数的值例如正弦波的幅度、频率、相位指数函数的幅度和衰减速率等。信号模型的第二大类是统计模型在这类模型中人们试图仅表征信号的统计特性。这类统计模型的例子包括高斯过程、泊松过程、马尔可夫过程以及隐马尔可夫过程等。统计模型的基本假设是信号可以被很好地表征为参数化随机过程且该随机过程的参数能够以精确、定义明确的方式确定估计。注dichotomize /daɪˈkɒtəmaɪz/ 含义将某事物一分为二、二分、分成两类通常指两个相互排斥或对立的类别。For the applications of interest,namelyspeech processing, both deterministic and stochastic signal models have had good success. In this paperwe will concern ourselves strictly with one type of stochastic signal model, namely the hidden Markov model (HMM). (These modelsare referred to as Markov sourcesor probabilistic functions of Markov chains in thecommunications literature.) We will first review the theory of Markov chains and then extend the ideas to the class of hidden Markov models using several simple examples. We will then focus our attention on the three fundamental problems1for HMM design, namely: the evaluation of the probability (or likelihood) of a sequence of observations given a specific HMM; the determination of a best sequence of model states; and the adjustment of model parameters so as to bestaccount forthe observed signal. We will show that once these three fundamental problems are solved, we can apply HMMs to selected problems in speech recognition.对于我们感兴趣的应用领域即语音处理确定性信号模型和随机信号模型都取得了很好的效果。在本文中我们将严格关注一种随机信号模型即隐马尔可夫模型HMM。在通信文献中这些模型被称为马尔可夫信源或马尔可夫链的概率函数。我们将首先回顾马尔可夫链理论然后通过几个简单的例子将这些思想扩展到隐马尔可夫模型这一类。随后我们将把注意力集中在 HMM 设计中的三个基本问题上即评估问题给定一个特定的 HMM计算某个观测序列的概率或似然解码问题确定最优的模型状态序列学习问题调整模型参数以便最好地解释观测到的信号。我们将说明一旦这三个基本问题得到解决就可以将 HMM 应用于语音识别中的特定问题。1The idea ofcharacterizingthetheoretical aspectsof hidden Markov modelingin terms ofsolving three fundamental problems is due to Jack Ferguson of IDA (Institute for Defense Analysis) who introduced it in lectures and writing.将隐马尔可夫建模的理论内涵归结为求解三个基本问题**这一思想源自国防分析研究所IDA的杰克·弗格森Jack Ferguson他在讲座和著述中首次提出了这一框架。注 The idea of characterizing … in terms of …characterizing 刻画、描述、概括in terms of 用……的方式、从……角度所以这部分意思是用某种方式来概括/描述 HMM 理论的这个思路具体是什么方式呢就是 solving three fundamental problems求解三个基本问题。也就是说主语整体是把隐马尔可夫模型HMM的理论概括为’三个基本问题’来研究的这个思路/框架is due to 归功于、源自、是由……提出的所以意思是这个思路是由 Jack Ferguson 提出的Neither the theory of hidden Markov models nor its applications to speech recognition is new. The basic theory was published in a series of classic papers by Baum and his colleagues [1]–[5] in the late 1960s and early 1970s and was implemented for speech processing applications by Baker [6] at CMU, and by Jelinek and his colleagues at IBM [7]–[13] in the 1970s. However, widespread understanding and application of the theory of HMMs to speech processing has occurred only within the past several years.隐马尔可夫模型的理论及其在语音识别中的应用都算不上新鲜事物。其基础理论由 Baum 及其同事在 1960 年代末至 1970 年代初发表的一系列经典论文中提出 [1]–[5]而在 1970 年代Baker 在卡内基梅隆大学CMU[6]以及 Jelinek 及其同事在 IBM [7]–[13] 已将其实现并应用于语音处理。然而HMM 理论在语音处理领域的广泛理解与普及应用却仅仅是过去几年间才发生的事。There are several reasons why this has been the case. First, the basic theory of hidden Markov models was published in mathematical journals which were not generally read by engineers working on problems in speech processing. The second reason was that the original applications of the theory to speech processing did not provide sufficient tutorial material for most readers to understand the theory and to be able to apply it to their own research. As a result, several tutorial papers were written which provided a sufficient level of detail for a number of research labs to begin work using HMMs in individual speech processing applications [14]–[19].之所以如此有以下几个原因。首先隐马尔可夫模型的基础理论发表于数学期刊而从事语音处理工程问题研究的学者通常不会阅读这类刊物。第二个原因是该理论最初在语音处理中的应用并未提供足够的教程性材料使得大多数读者既难以理解其理论也无法将其应用到自己的研究中。因此后来出现了若干篇教程性论文为众多研究实验室提供了足够详细的入门指导使其得以开始在各自的语音处理应用中使用 HMM [14]–[19]。This tutorial is intended to provide an overview of the basic theory of HMMs (as originated by Baum and his colleagues), provide practical details on methods of implementation of the theory, and describe a couple ofselected applicationsof the theory todistinctproblems in speech recognition. The paper combines results from a number of original sources and hopefully provides a single source for acquiring the backgroundrequiredtopursue furtherthis fascinating area of research.本教程旨在概述 HMM 的基础理论源于 Baum 及其同事的开创性工作提供理论实现方法上的实践细节并介绍该理论在语音识别中几个不同具体问题上的精选应用。本文综合了若干原始文献的研究成果希望能为读者提供一个单一的资料来源使其获取进入这一引人入胜的研究领域所需的背景知识。注and hopefully provides… 意思是本文希望/旨在提供…… 提供什么single source 单一的来源、一站式资料 这个来源用来干嘛acquiring 获取、获得 the background 背景知识指入门所需的基础知识什么样的背景知识 required 所需的修饰 backgroundpursue further 进一步深入研究注意这里语序是 “pursue further this area”正常语序是 “pursuethis area further”this fascinating area of research 这个引人入胜的/令人着迷的研究领域The organization of this paper is as follows.本文的组织结构如下。In Section II we review the theory of discrete Markov chains and show how the concept of hidden states, where the observation is a probabilistic function of the state, can be used effectively. We illustrate the theory with two simple examples, namelycoin-tossing, and the classicballs-in-urnssystem.在第二节中我们回顾离散马尔可夫链理论并阐述隐藏状态的概念其中观测是状态的概率函数如何被有效利用。我们通过两个简单的例子来阐释该理论即抛硬币和经典的瓮中取球系统。In Section III we discuss the three fundamental problems of HMMs, and give several practical techniques for solving these problems.在第三节中我们讨论 HMM 的三个基本问题并给出求解这些问题的几种实用技术。In Section IV we discuss the various types of HMMs that have been studied includingergodicas well asleft-right models. In this section we also discuss the various model features including the form of theobservation density function,the state duration density, and theoptimization criterionfor choosing optimal HMM parameter values.在第四节中我们讨论已研究过的各种类型的 HMM包括遍历模型ergodic以及从左到右模型left-right。在本节中我们还讨论各种模型特征包括观测密度函数的形式、状态持续时间密度以及选择最优 HMM 参数值的优化准则。In Section V we discuss the issues that arise in implementing HMMs including the topics of scaling, initial parameter estimates, model size, model form, missing data, and multiple observation sequences.在第五节中我们讨论实现 HMM 时出现的一些问题包括缩放scaling、初始参数估计、模型规模、模型形式、缺失数据以及多观测序列等主题。In Section VI we describe anisolated word speech recognizer, implemented with HMM ideas, and show how it performs as compared to alternative implementations.在第六节中我们描述一个基于 HMM 思想实现的孤立词语音识别器并展示其与其他实现方案相比的性能表现。In Section VII we extend the ideas presented in Section VI to the problem ofrecognizing a string of spoken wordsbased onconcatenatingindividual HMMs of each word in the vocabulary.在第七节中我们将第六节提出的思想扩展到识别连续语音词串的问题即通过拼接词汇表中每个词的独立 HMM 来实现。In Section VIII we briefly outline how the ideas of HMM have been applied to a large vocabulary speech recognizer, and in Section IX we summarize the ideas discussedthroughoutthe paper.在第八节中我们简要概述 HMM 的思想如何应用于大词汇量语音识别器在第九节中我们总结全文讨论的思想。注throughout 在这里的意思是 “遍及、贯穿整个”。 throughout the paper 通篇、整篇论文、从头到尾