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<div id="pf1" class="pf w0 h0" data-page-no="1"><div class="pc pc1 w0 h0"><img class="bi x0 y0 w1 h1" alt="" src="https://static.pudn.com/prod/directory_preview_static/62722075c0b40515e3da688c/bg1.jpg"><div class="c x0 y1 w2 h2"><div class="t m0 x1 h3 y2 ff1 fs0 fc0 sc0 ls0 ws0">　　隐马尔科夫模型（<span class="ff2"></span>）依然是读者访问“我爱自然语言处理”的一个热门相关关键词，我曾在</div><div class="t m0 x1 h3 y3 ff1 fs0 fc0 sc0 ls0 ws0">《<span class="ff2 fc1"><span class="_ _0"> </span><span class="ff1">学习最佳范例与崔晓源的博客</span></span>》中介绍过国外的一个不错的<span class="_ _0"> </span><span class="ff2 fc1"><span class="_ _0"> </span><span class="ff1">学习教程</span></span>，并且国内崔晓</div><div class="t m0 x1 h3 y4 ff1 fs0 fc0 sc0 ls0 ws0">源师兄有一个相应的<span class="fc1">翻译版本</span>，不过这个版本比较简化和粗略，有些地方只是概况性的翻译了一下，</div><div class="t m0 x1 h3 y5 ff1 fs0 fc0 sc0 ls0 ws0">省去了一些内容，所以从今天开始计划在<span class="_ _0"> </span><span class="ff2"><span class="_ _0"> </span></span>上系统的重新翻译这个学习教程，希望对大家有点</div><div class="t m0 x1 h3 y6 ff1 fs0 fc0 sc0 ls0 ws0">用。</div><div class="t m0 x1 h3 y7 ff1 fs0 fc0 sc0 ls0 ws0">一、<span class="sc1">介绍（</span><span class="ff3">Introduction</span><span class="sc1">）</span></div><div class="t m0 x1 h3 y8 ff1 fs0 fc0 sc0 ls0 ws0">　　我们通常都习惯寻找一个事物在一段时间里的变化模式（规律）。这些模式发生在很多领域，</div><div class="t m0 x1 h3 y9 ff1 fs0 fc0 sc0 ls0 ws0">比如计算机中的指令序列，句子中的词语顺序和口语单词中的音素序列等等，事实上任何领域中的</div><div class="t m0 x1 h3 ya ff1 fs0 fc0 sc0 ls0 ws0">一系列事件都有可能产生有用的模式。</div><div class="t m0 x1 h3 yb ff1 fs0 fc0 sc0 ls0 ws0">　　考虑一个简单的例子，有人试图通过一片海藻推断天气——民间传说告诉我们‘湿透的’海藻意味</div><div class="t m0 x1 h3 yc ff1 fs0 fc0 sc0 ls0 ws0">着潮湿阴雨，而‘干燥的’海藻则意味着阳光灿烂。如果它处于一个中间状态（‘有湿气’），我们就无</div><div class="t m0 x1 h3 yd ff1 fs0 fc0 sc0 ls0 ws0">法确定天气如何。然而，天气的状态并没有受限于海藻的状态，所以我们可以在观察的基础上预测</div><div class="t m0 x1 h3 ye ff1 fs0 fc0 sc0 ls0 ws0">天气是雨天或晴天的可能性。另一个有用的线索是前一天的天气状态（或者，至少是它的可能状</div><div class="t m0 x1 h3 yf ff1 fs0 fc0 sc0 ls0 ws0">态）——通过综合昨天的天气及相应观察到的海藻状态，我们有可能更好的预测今天的天气。</div><div class="t m0 x1 h3 y10 ff1 fs0 fc0 sc0 ls0 ws0">　　这是本教程中我们将考虑的一个典型的系统类型。</div><div class="t m0 x1 h3 y11 ff1 fs0 fc0 sc0 ls0 ws0">　　首先，我们将介绍产生概率模式的系统，如晴天及雨天间的天气波动。</div><div class="t m0 x1 h3 y12 ff1 fs0 fc0 sc0 ls0 ws0">　　然后，我们将会看到这样一个系统，我们希望预测的状态并不是观察到的——其底层系统是隐</div><div class="t m0 x1 h3 y13 ff1 fs0 fc0 sc0 ls0 ws0">藏的。在上面的例子中，观察到的序列将是海藻而隐藏的系统将是实际的天气。</div><div class="t m0 x1 h4 y14 ff1 fs0 fc0 sc0 ls0 ws0">　　最后，我们会利用已经建立的模型解决一些实际的问<span class="ff4">题</span>。对于上<span class="ff4">述</span>例子，我们<span class="ff4">想知道：</span></div><div class="t m0 x1 h4 y15 ff1 fs0 fc0 sc0 ls0 ws0">　　<span class="ff2"><span class="ff4">给出</span></span>一个<span class="ff4">星期每</span>天的海藻观察状态，<span class="ff4">之</span>后的天气将会是<span class="ff4">什么<span class="ff2"></span></span></div><div class="t m0 x1 h4 y16 ff1 fs0 fc0 sc0 ls0 ws0">　　<span class="ff2"><span class="ff4">给</span></span>定一个海藻的观察状态序列，预测一下<span class="ff4">此</span>时是<span class="ff4">冬季还</span>是<span class="ff4">夏季？直</span>观地，如果一段时间内海</div><div class="t m0 x1 h4 y17 ff1 fs0 fc0 sc0 ls0 ws0">藻都是干燥的，<span class="ff4">那么</span>这段时间很可能是<span class="ff4">夏季</span>，<span class="ff4">反之</span>，如果一段时间内海藻都是潮湿的，<span class="ff4">那么</span>这段时</div><div class="t m0 x1 h4 y18 ff1 fs0 fc0 sc0 ls0 ws0">间可能是<span class="ff4">冬季</span>。</div><div class="t m0 x1 h4 y19 ff4 fs0 fc0 sc1 ls0 ws0">二<span class="ff1">、生</span>成<span class="ff1">模式（<span class="ff3 sc0">Generating Patterns</span>）</span></div><div class="t m0 x1 h3 y1a ff2 fs0 fc0 sc0 ls0 ws0"><span class="ff1">、确定性模式（</span><span class="ff1">）</span></div><div class="t m0 x1 h4 y1b ff1 fs0 fc0 sc0 ls0 ws0">　　考虑一<span class="ff4">套交</span>通<span class="ff4">信号灯</span>，<span class="ff4">灯</span>的<span class="ff4">颜色</span>变化序列依<span class="ff4">次</span>是<span class="ff4">红色<span class="ff2"></span>红色<span class="ff2"></span>黄色<span class="ff2"></span>绿色<span class="ff2"></span>黄色<span class="ff2"></span>红色</span>。这个序列可</div><div class="t m0 x1 h4 y1c ff1 fs0 fc0 sc0 ls0 ws0">以<span class="ff4">作为</span>一个状态机<span class="ff4">器</span>，<span class="ff4">交</span>通<span class="ff4">信号灯</span>的不<span class="ff4">同</span>状态都<span class="ff4">紧跟</span>着上一个状态。</div><div class="t m0 x1 h3 y1d ff1 fs0 fc0 sc0 ls0 ws0">　　　　</div><div class="t m0 x1 h4 y1e ff1 fs0 fc0 sc0 ls0 ws0">　　<span class="ff4">注</span>意<span class="ff4">每</span>一个状态都是<span class="ff4">唯</span>一的依<span class="ff4">赖</span>于前一个状态，所以，如果<span class="ff4">交</span>通<span class="ff4">灯为绿色</span>，<span class="ff4">那么</span>下一个<span class="ff4">颜色</span>状</div><div class="t m0 x1 h4 y1f ff1 fs0 fc0 sc0 ls0 ws0">态将始<span class="ff4">终</span>是<span class="ff4">黄色</span>——<span class="ff4">也</span>就是说，<span class="ff4">该</span>系统是确定性的。确定性系统相对比较容<span class="ff4">易</span>理解和<span class="ff4">分析</span>，<span class="ff4">因为</span>状</div><div class="t m0 x1 h4 y20 ff1 fs0 fc0 sc0 ls0 ws0">态间的<span class="ff4">转移</span>是<span class="ff4">完全</span>已<span class="ff4">知</span>的。</div><div class="t m0 x1 h4 y21 ff2 fs0 fc0 sc0 ls0 ws0"><span class="ff1">、<span class="ff4">非</span>确定性模式（</span><span class="ff1">）</span></div><div class="t m0 x1 h4 y22 ff1 fs0 fc0 sc0 ls0 ws0">　　<span class="ff4">为</span>了<span class="ff4">使</span>天气<span class="ff4">那</span>个例子更<span class="ff4">符</span>合实际，<span class="ff4">加入第三</span>个状态——多<span class="ff4">云</span>。与<span class="ff4">交</span>通<span class="ff4">信号灯</span>例子不<span class="ff4">同</span>，我们并</div><div class="t m0 x1 h4 y23 ff1 fs0 fc0 sc0 ls0 ws0">不<span class="ff4">期</span>望这<span class="ff4">三</span>个天气状态<span class="ff4">之</span>间的变化是确定性的，<span class="ff4">但</span>是我们依然希望对这个系统建模以<span class="ff4">便</span>生<span class="ff4">成</span>一个天</div><div class="t m0 x1 h3 y24 ff1 fs0 fc0 sc0 ls0 ws0">气变化模式（规律）。</div><div class="t m0 x1 h4 y25 ff1 fs0 fc0 sc0 ls0 ws0">　　一<span class="ff4">种做</span>法是<span class="ff4">假设</span>模型的<span class="ff4">当</span>前状态<span class="ff4">仅仅</span>依<span class="ff4">赖</span>于前面的<span class="ff4">几</span>个状态，这<span class="ff4">被称为</span>马尔科夫<span class="ff4">假设</span>，它<span class="ff4">极</span>大</div><div class="t m0 x1 h4 y26 ff1 fs0 fc0 sc0 ls0 ws0">地简化了问<span class="ff4">题</span>。<span class="ff4">显</span>然，这可能是一<span class="ff4">种</span>粗<span class="ff4">糙</span>的<span class="ff4">假设</span>，并且<span class="ff4">因此</span>可能将一些<span class="ff4">非</span>常重<span class="ff4">要</span>的<span class="ff4">信息丢失</span>。</div><div class="t m0 x1 h4 y27 ff1 fs0 fc0 sc0 ls0 ws0">　　<span class="ff4">当</span>考虑天气问<span class="ff4">题</span>时，马尔科夫<span class="ff4">假设假</span>定今天的天气只能通过过去<span class="ff4">几</span>天已<span class="ff4">知</span>的天气<span class="ff4">情</span>况<span class="ff4">进行</span>预测</div><div class="t m0 x1 h4 y28 ff1 fs0 fc0 sc0 ls0 ws0">——而对于其<span class="ff4">他因</span>素，<span class="ff4">譬</span>如<span class="ff4">风力</span>、气<span class="ff4">压</span>等则没有考虑。在这个例子以及其<span class="ff4">他</span>相<span class="ff4">似</span>的例子中，这样的</div></div><a class="l" rel='nofollow' onclick='return false;'><div class="d m1"></div></a><a class="l" rel='nofollow' onclick='return false;'><div class="d m1"></div></a><a class="l" rel='nofollow' onclick='return false;'><div class="d m1"></div></a></div><div class="pi" data-data='{"ctm":[1.611850,0.000000,0.000000,1.611850,0.000000,0.000000]}'></div></div>
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<div id="pf2" class="pf w0 h0" data-page-no="2"><div class="pc pc2 w0 h0"><img class="bi x0 y0 w1 h1" alt="" src="https://static.pudn.com/prod/directory_preview_static/62722075c0b40515e3da688c/bg2.jpg"><div class="c x0 y1 w2 h2"><div class="t m0 x1 h4 y2 ff4 fs0 fc0 sc0 ls0 ws0">假设显<span class="ff1">然是不</span>现<span class="ff1">实的。然而，</span>由<span class="ff1">于这样经过简化的系统可以用</span>来分析<span class="ff1">，我们常常</span>接<span class="ff1">受这样的</span>知识假</div><div class="t m0 x1 h4 y3 ff4 fs0 fc0 sc0 ls0 ws0">设<span class="ff1">，</span>虽<span class="ff1">然它产生的</span>某<span class="ff1">些</span>信息<span class="ff1">不</span>完全准<span class="ff1">确。</span></div><div class="t m0 x1 h3 y29 ff1 fs0 fc0 sc0 ls0 ws0">　　　　　　　　　　<span class="_ _1"> </span>　<span class="_ _1"> </span>　</div><div class="t m0 x1 h4 y6 ff1 fs0 fc0 sc0 ls0 ws0">　　一个马尔科夫过程是状态间的<span class="ff4">转移仅</span>依<span class="ff4">赖</span>于前<span class="_ _0"> </span><span class="ff2"><span class="_ _0"> </span></span>个状态的过程。这个过程<span class="ff4">被称之为<span class="_ _0"> </span><span class="ff2"><span class="_ _2"> </span></span>阶</span>马尔科</div><div class="t m0 x1 h4 y7 ff1 fs0 fc0 sc0 ls0 ws0">夫模型，其中<span class="_ _2"> </span><span class="ff2"><span class="_ _0"> </span></span>是<span class="ff4">影响</span>下一个状态<span class="ff4">选择</span>的（前）<span class="ff2"><span class="_ _0"> </span></span>个状态。最简单的马尔科夫过程是一<span class="ff4">阶</span>模型，它</div><div class="t m0 x1 h4 y8 ff1 fs0 fc0 sc0 ls0 ws0">的状态<span class="ff4">选择仅</span>与前一个状态有关。这里<span class="ff4">要注</span>意它与确定性系统并不相<span class="ff4">同</span>，<span class="ff4">因为</span>下一个状态的<span class="ff4">选择由</span></div><div class="t m0 x1 h3 y9 ff1 fs0 fc0 sc0 ls0 ws0">相应的概率决定，并不是确定性的。</div><div class="t m0 x1 h4 ya ff1 fs0 fc0 sc0 ls0 ws0">　　下图是天气例子中状态间所有可能的一<span class="ff4">阶</span>状态<span class="ff4">转移情</span>况<span class="ff4">：</span></div><div class="t m0 x1 h3 y2a ff1 fs0 fc0 sc0 ls0 ws0">　　　　</div><div class="t m0 x1 h4 y2b ff1 fs0 fc0 sc0 ls0 ws0">　　对于有<span class="_ _2"> </span><span class="ff2"><span class="_ _0"> </span></span>个状态的一<span class="ff4">阶</span>马尔科夫模型，<span class="ff4">共</span>有<span class="_ _3"> </span>个状态<span class="ff4">转移</span>，<span class="ff4">因为</span>任何一个状态都有可能是所</div><div class="t m0 x1 h4 y14 ff1 fs0 fc0 sc0 ls0 ws0">有状态的下一个<span class="ff4">转移</span>状态。<span class="ff4">每</span>一个状态<span class="ff4">转移</span>都有一个概率<span class="ff4">值</span>，<span class="ff4">称为</span>状态<span class="ff4">转移</span>概率——这是从一个状</div><div class="t m0 x1 h4 y2c ff1 fs0 fc0 sc0 ls0 ws0">态<span class="ff4">转移</span>到另一个状态的概率。所有的<span class="_ _3"> </span>个概率可以用一个状态<span class="ff4">转移矩阵表示</span>。<span class="ff4">注</span>意这些概率并不</div><div class="t m0 x1 h4 y17 ff4 fs0 fc0 sc0 ls0 ws0">随<span class="ff1">时间变化而不</span>同<span class="ff1">——这是一个</span>非<span class="ff1">常重</span>要<span class="ff1">（</span>但<span class="ff1">常常不</span>符<span class="ff1">合实际）的</span>假设<span class="ff1">。</span></div><div class="t m0 x1 h4 y18 ff1 fs0 fc0 sc0 ls0 ws0">　　下面的状态<span class="ff4">转移矩阵显示</span>的是天气例子中可能的状态<span class="ff4">转移</span>概率<span class="ff4">：</span></div><div class="t m0 x1 h3 y2d ff1 fs0 fc0 sc0 ls0 ws0">　　　　</div><div class="t m0 x1 h4 y2e ff1 fs0 fc0 sc0 ls0 ws0">　　<span class="ff2"><span class="ff4">也</span></span>就是说，如果昨天是晴天，<span class="ff4">那么</span>今天是晴天的概率<span class="ff4">为<span class="_ _0"> </span><span class="ff2"></span></span>，是多<span class="ff4">云</span>的概率<span class="ff4">为<span class="_ _2"> </span><span class="ff2"></span></span>。<span class="ff4">注</span>意，</div><div class="t m0 x1 h4 y2f ff4 fs0 fc0 sc0 ls0 ws0">每<span class="ff1">一</span>行<span class="ff1">的概率</span>之<span class="ff1">和</span>为<span class="_ _2"> </span><span class="ff2"><span class="ff1">。</span></span></div><div class="t m0 x1 h4 y1e ff1 fs0 fc0 sc0 ls0 ws0">　　<span class="ff4">要初</span>始化这样一个系统，我们<span class="ff4">需要</span>确定<span class="ff4">起</span>始<span class="ff4">日</span>天气的（或可能的）<span class="ff4">情</span>况，定<span class="ff4">义</span>其<span class="ff4">为</span>一个<span class="ff4">初</span>始概</div><div class="t m0 x1 h4 y30 ff1 fs0 fc0 sc0 ls0 ws0">率<span class="ff4">向量</span>，<span class="ff4">称为<span class="_ _4"> </span>向量</span>。</div><div class="t m0 x1 h3 y31 ff1 fs0 fc0 sc0 ls0 ws0">　　　　　　　　　　</div><div class="t m0 x1 h4 y24 ff1 fs0 fc0 sc0 ls0 ws0">　　<span class="ff2"><span class="ff4">也</span></span>就是说，<span class="ff4">第</span>一天<span class="ff4">为</span>晴天的概率<span class="ff4">为<span class="_ _0"> </span><span class="ff2"></span></span>。</div><div class="t m0 x1 h4 y25 ff1 fs0 fc0 sc0 ls0 ws0">　　<span class="ff4">现</span>在我们定<span class="ff4">义</span>一个一<span class="ff4">阶</span>马尔科夫过程如下<span class="ff4">：</span></div><div class="t m0 x1 h4 y26 ff1 fs0 fc0 sc0 ls0 ws0">　　　<span class="sc1">状态</span><span class="ff4">：三</span>个状态——晴天，多<span class="ff4">云</span>，雨天。</div><div class="t m0 x1 h4 y32 ff1 fs0 fc0 sc0 ls0 ws0">　　　<span class="_ _4"> </span><span class="ff4 sc1">向量<span class="sc0">：</span></span>定<span class="ff4">义</span>系统<span class="ff4">初</span>始化时<span class="ff4">每</span>一个状态的概率。</div></div></div><div class="pi" data-data='{"ctm":[1.611850,0.000000,0.000000,1.611850,0.000000,0.000000]}'></div></div>
<div id="pf3" class="pf w0 h0" data-page-no="3"><div class="pc pc3 w0 h0"><img class="bi x0 y0 w1 h1" alt="" src="https://static.pudn.com/prod/directory_preview_static/62722075c0b40515e3da688c/bg3.jpg"><div class="c x0 y1 w2 h2"><div class="t m0 x1 h4 y2 ff1 fs0 fc0 sc0 ls0 ws0">　　　<span class="sc1">状态<span class="ff4">转移矩阵<span class="sc0">：给</span></span></span>定前一天天气<span class="ff4">情</span>况下的<span class="ff4">当</span>前天气概率。</div><div class="t m0 x1 h4 y3 ff1 fs0 fc0 sc0 ls0 ws0">　　任何一个可以用这<span class="ff4">种</span>方式<span class="ff4">描述</span>的系统都是一个马尔科夫过程。</div><div class="t m0 x1 h4 y4 ff2 fs0 fc0 sc0 ls0 ws0"><span class="ff1">、<span class="ff4">总结</span></span></div><div class="t m0 x1 h4 y5 ff1 fs0 fc0 sc0 ls0 ws0">　　我们<span class="ff4">尝</span>试<span class="ff4">识别</span>时间变化中的模式，并且<span class="ff4">为</span>了<span class="ff4">达</span>到这个<span class="ff4">目</span>我们试图对这个过程建模以<span class="ff4">便</span>产生这样</div><div class="t m0 x1 h4 y6 ff1 fs0 fc0 sc0 ls0 ws0">的模式。我们<span class="ff4">使</span>用了<span class="ff4">离散</span>时间点、<span class="ff4">离散</span>状态以及<span class="ff4">做</span>了马尔科夫<span class="ff4">假设</span>。在<span class="ff4">采</span>用了这些<span class="ff4">假设之</span>后，系统</div><div class="t m0 x1 h4 y33 ff1 fs0 fc0 sc0 ls0 ws0">产生了这个<span class="ff4">被描述为</span>马尔科夫过程的模式，它<span class="ff4">包含</span>了一个<span class="_ _4"> </span><span class="ff4">向量</span>（<span class="ff4">初</span>始概率）和一个状态<span class="ff4">转移矩阵</span>。</div><div class="t m0 x1 h4 y8 ff1 fs0 fc0 sc0 ls0 ws0">关于<span class="ff4">假设</span>，重<span class="ff4">要</span>的一点是状态<span class="ff4">转移矩阵</span>并不<span class="ff4">随</span>时间的<span class="ff4">改</span>变而<span class="ff4">改</span>变——这个<span class="ff4">矩阵</span>在<span class="ff4">整</span>个系统的生<span class="ff4">命周</span></div><div class="t m0 x1 h4 y9 ff4 fs0 fc0 sc0 ls0 ws0">期<span class="ff1">中是</span>固<span class="ff1">定不变的。</span></div><div class="t m0 x1 h4 ya ff4 fs0 fc0 sc1 ls0 ws0">三<span class="ff1">、隐藏模式（<span class="ff3 sc0">Hidden Patterns</span>）</span></div><div class="t m0 x1 h4 yb ff2 fs0 fc0 sc0 ls0 ws0"><span class="ff1">、马尔科夫过程的<span class="ff4">局</span>限性</span></div><div class="t m0 x1 h4 yc ff1 fs0 fc0 sc0 ls0 ws0">　　在<span class="ff4">某</span>些<span class="ff4">情</span>况下，我们希望找到的模式用马尔科夫过程<span class="ff4">描述还显得</span>不<span class="ff4">充分</span>。<span class="ff4">回顾</span>一下天气<span class="ff4">那</span>个例</div><div class="t m0 x1 h4 yd ff1 fs0 fc0 sc0 ls0 ws0">子，一个隐<span class="ff4">士也许</span>不能<span class="ff4">够直接获取</span>到天气的观察<span class="ff4">情</span>况，<span class="ff4">但</span>是<span class="ff4">他</span>有一些<span class="ff4">水</span>藻。民间传说告诉我们<span class="ff4">水</span>藻</div><div class="t m0 x1 h4 ye ff1 fs0 fc0 sc0 ls0 ws0">的状态与天气状态有一定的概率关系——天气和<span class="ff4">水</span>藻的状态是<span class="ff4">紧密</span>相关的。在这个例子中我们有<span class="ff4">两</span></div><div class="t m0 x1 h4 yf ff4 fs0 fc0 sc0 ls0 ws0">组<span class="ff1">状态，观察的状态（</span>水<span class="ff1">藻的状态）和隐藏的状态（天气的状态）。我们希望</span>为<span class="ff1">隐</span>士设<span class="ff1">计一</span>种<span class="ff1">算法，</span></div><div class="t m0 x1 h4 y10 ff1 fs0 fc0 sc0 ls0 ws0">在不能<span class="ff4">够直接</span>观察天气的<span class="ff4">情</span>况下，通过<span class="ff4">水</span>藻和马尔科夫<span class="ff4">假设来</span>预测天气。</div><div class="t m0 x1 h4 y11 ff1 fs0 fc0 sc0 ls0 ws0">　　一个更实际的问<span class="ff4">题</span>是语音<span class="ff4">识别</span>，我们<span class="ff4">听</span>到的<span class="ff4">声</span>音是<span class="ff4">来</span>自于<span class="ff4">声带</span>、<span class="ff4">喉咙</span>大<span class="ff4">小</span>、<span class="ff4">舌头位置</span>以及其<span class="ff4">他</span></div><div class="t m0 x1 h4 y12 ff1 fs0 fc0 sc0 ls0 ws0">一些<span class="ff4">东西</span>的<span class="ff4">组</span>合<span class="ff4">结</span>果。所有这些<span class="ff4">因</span>素相<span class="ff4">互作</span>用产生一个单词的<span class="ff4">声</span>音，一<span class="ff4">套</span>语音<span class="ff4">识别</span>系统<span class="ff4">检</span>测的<span class="ff4">声</span>音</div><div class="t m0 x1 h4 y13 ff1 fs0 fc0 sc0 ls0 ws0">就是<span class="ff4">来</span>自于个人发音时<span class="ff4">身体</span>内<span class="ff4">部</span>物理变化所<span class="ff4">引起</span>的不断<span class="ff4">改</span>变的<span class="ff4">声</span>音。</div><div class="t m0 x1 h4 y14 ff1 fs0 fc0 sc0 ls0 ws0">　　一些语音<span class="ff4">识别装置工作</span>的<span class="ff4">原</span>理是<span class="fc2">将内<span class="ff4">部</span>的语音产<span class="ff4">出</span>看<span class="ff4">作</span>是隐藏的状态</span>，而<span class="fc2">将<span class="ff4">声</span>音<span class="ff4">结</span>果<span class="ff4">作为</span>一系</span></div><div class="t m0 x1 h4 y15 ff1 fs0 fc2 sc0 ls0 ws0">列观察的状态<span class="fc0">，这些<span class="ff4">由</span>语音过程生<span class="ff4">成</span>并且最好的<span class="ff4">近似</span>了实际（隐藏）的状态。在这<span class="ff4">两</span>个例子中，<span class="ff4">需</span></span></div><div class="t m0 x1 h4 y16 ff4 fs0 fc0 sc0 ls0 ws0">要<span class="ff1">着重指</span>出<span class="ff1">的是，隐藏状态的</span>数目<span class="ff1">与观察状态的</span>数目<span class="ff1">可以是不</span>同<span class="ff1">的。一个</span>包含三<span class="ff1">个状态的天气系统</span></div><div class="t m0 x1 h4 y17 ff1 fs0 fc0 sc0 ls0 ws0">（晴天、多<span class="ff4">云</span>、雨天）中，可以观察到<span class="_ _2"> </span><span class="ff2"><span class="_ _0"> </span></span>个等<span class="ff4">级</span>的海藻湿<span class="ff4">润情</span>况（干、<span class="ff4">稍</span>干、潮湿、湿<span class="ff4">润</span>）<span class="ff4">；纯粹</span></div><div class="t m0 x1 h4 y18 ff1 fs0 fc0 sc0 ls0 ws0">的语音可以<span class="ff4">由<span class="_ _2"> </span><span class="ff2"><span class="_ _0"> </span></span></span>个音素<span class="ff4">描述</span>，而<span class="ff4">身体</span>的发音系统会产生<span class="ff4">出</span>不<span class="ff4">同数目</span>的<span class="ff4">声</span>音，或者比<span class="_ _0"> </span><span class="ff2"><span class="_ _2"> </span></span>多，或者比</div><div class="t m0 x1 h3 y19 ff2 fs0 fc0 sc0 ls0 ws0"><span class="_ _2"> </span><span class="ff1">少。</span></div><div class="t m0 x1 h4 y1a ff1 fs0 fc0 sc0 ls0 ws0">　　在这<span class="ff4">种情</span>况下，观察到的状态序列与隐藏过程有一定的概率关系。我们<span class="ff4">使</span>用隐马尔科夫模型对</div><div class="t m0 x1 h4 y1b ff1 fs0 fc0 sc0 ls0 ws0">这样的过程建模，这个模型<span class="ff4">包含</span>了一个<span class="fc2">底层隐藏的<span class="ff4">随</span>时间<span class="ff4">改</span>变的马尔科夫过程</span>，以及一个<span class="fc2">与隐藏状</span></div><div class="t m0 x1 h4 y1c ff1 fs0 fc2 sc0 ls0 ws0">态<span class="ff4">某种</span>程<span class="ff4">度</span>相关的可观察到的状态<span class="ff4">集</span>合<span class="fc0">。</span></div><div class="t m0 x1 h3 y34 ff2 fs0 fc0 sc0 ls0 ws0"><span class="ff1">、隐马尔科夫模型（</span> !<span class="ff1">）</span></div><div class="t m0 x1 h4 y35 ff1 fs0 fc0 sc0 ls0 ws0">　　下图<span class="ff4">显示</span>的是天气例子中的隐藏状态和观察状态。<span class="ff4">假设</span>隐藏状态（实际的天气）<span class="ff4">由</span>一个简单的</div><div class="t m0 x1 h4 y36 ff1 fs0 fc0 sc0 ls0 ws0">一<span class="ff4">阶</span>马尔科夫过程<span class="ff4">描述</span>，<span class="ff4">那么</span>它们<span class="ff4">之</span>间都相<span class="ff4">互连接</span>。</div><div class="t m0 x1 h3 y37 ff1 fs0 fc0 sc0 ls0 ws0">　　</div><div class="t m0 x1 h4 y28 ff1 fs0 fc0 sc0 ls0 ws0">　　<span class="fc2">隐藏状态和观察状态<span class="ff4">之</span>间的<span class="ff4">连接<span class="fc0">表示：</span></span></span>在<span class="ff4">给</span>定的马尔科夫过程中，一个<span class="ff4">特</span>定的<span class="fc2">隐藏状态生<span class="ff4">成特</span></span></div></div></div><div class="pi" data-data='{"ctm":[1.611850,0.000000,0.000000,1.611850,0.000000,0.000000]}'></div></div>
<div id="pf4" class="pf w0 h0" data-page-no="4"><div class="pc pc4 w0 h0"><img class="bi x0 y0 w1 h1" alt="" src="https://static.pudn.com/prod/directory_preview_static/62722075c0b40515e3da688c/bg4.jpg"><div class="c x0 y1 w2 h2"><div class="t m0 x1 h4 y2 ff1 fs0 fc2 sc0 ls0 ws0">定的观察状态的概率<span class="fc0">。这很<span class="ff4">清晰</span>的<span class="ff4">表示</span>了‘<span class="ff4">进入</span>’一个观察状态的所有概率<span class="ff4">之</span>和<span class="ff4">为<span class="_ _2"> </span><span class="ff2"></span></span>，在上面这个例子</span></div><div class="t m0 x1 h4 y3 ff1 fs0 fc0 sc0 ls0 ws0">中就是<span class="_ _2"> </span><span class="ff2">"#$%&'()<span class="_ _5"></span>"#$%*'(</span>及<span class="ff4"> <span class="ff2">"#$%+(</span>之</span>和。（对这句<span class="ff4">话</span>我有点<span class="ff4">疑惑？</span>）</div><div class="t m0 x1 h4 y4 ff1 fs0 fc0 sc0 ls0 ws0">　　<span class="ff4">除</span>了定<span class="ff4">义</span>了马尔科夫过程的概率关系，我们<span class="ff4">还</span>有另一个<span class="ff4">矩阵</span>，定<span class="ff4">义为<span class="fc2">混淆矩阵</span></span>（<span class="ff2">,'</span></div><div class="t m0 x1 h4 y5 ff2 fs0 fc0 sc0 ls0 ws0">-<span class="ff1">），它<span class="ff4">包含</span>了<span class="ff4">给</span>定一个<span class="fc2">隐藏状态后<span class="ff4">得</span>到的观察状态的概率</span>。对于天气例子，<span class="ff4">混淆矩阵</span>是<span class="ff4">：</span></span></div><div class="t m0 x1 h3 y38 ff1 fs0 fc0 sc0 ls0 ws0">　　</div><div class="t m0 x1 h4 yd ff1 fs0 fc0 sc0 ls0 ws0">　　<span class="ff4">注</span>意<span class="ff4">矩阵</span>的<span class="ff4">每</span>一<span class="ff4">行之</span>和是<span class="_ _2"> </span><span class="ff2"></span>。</div><div class="t m0 x1 h4 ye ff2 fs0 fc0 sc0 ls0 ws0"><span class="ff1">、<span class="ff4">总结</span>（</span>&'.<span class="ff1">）</span></div><div class="t m0 x1 h3 yf ff1 fs0 fc0 sc0 ls0 ws0">　　我们已经看到在一些过程中一个观察序列与一个底层马尔科夫过程是概率相关的。在这些例子</div><div class="t m0 x1 h4 y10 ff1 fs0 fc0 sc0 ls0 ws0">中，观察状态的<span class="ff4">数目</span>可以和隐藏状态的<span class="ff4">数码</span>不<span class="ff4">同</span>。</div><div class="t m0 x1 h4 y11 ff1 fs0 fc0 sc0 ls0 ws0">　　我们<span class="ff4">使</span>用一个隐马尔科夫模型（<span class="ff2"></span>）对这些例子建模。这个模型<span class="ff4">包含两组</span>状态<span class="ff4">集</span>合和<span class="ff4">三组</span>概</div><div class="t m0 x1 h4 y12 ff1 fs0 fc0 sc0 ls0 ws0">率<span class="ff4">集</span>合<span class="ff4">：</span></div><div class="t m0 x1 h4 y13 ff1 fs0 fc0 sc0 ls0 ws0">　　<span class="ff2">/</span>隐藏状态<span class="ff4">：</span>一个系统的<span class="fc2">（<span class="ff4">真</span>实）状态，可以<span class="ff4">由</span>一个马尔科夫过程<span class="ff4">进行描述</span></span>（例如，天气）。</div><div class="t m0 x1 h4 y14 ff1 fs0 fc0 sc0 ls0 ws0">　　<span class="ff2">/</span>观察状态<span class="ff4">：</span>在这个过程中<span class="fc2">‘可<span class="ff4">视</span>’的状态</span>（例如，海藻的湿<span class="ff4">度</span>）。</div><div class="t m0 x1 h4 y39 ff1 fs0 fc0 sc0 ls0 ws0">　　<span class="ff2">/<span class="_ _4"> </span><span class="ff4">向量：包含</span></span>了（隐）模型在时间<span class="_ _2"> </span><span class="ff2">0<span class="_ _0"> </span></span>时一个<span class="ff4">特殊</span>的隐藏状态的概率（<span class="ff4 fc2">初<span class="ff1">始概率</span></span>）。</div><div class="t m0 x1 h4 y16 ff1 fs0 fc0 sc0 ls0 ws0">　　<span class="ff2">/</span>状态<span class="ff4">转移矩阵：<span class="fc2">包含<span class="ff1">了一个隐藏状态到另一个隐藏状态的概率</span></span></span></div><div class="t m0 x1 h4 y17 ff1 fs0 fc0 sc0 ls0 ws0">　　<span class="ff2">/<span class="ff4">混淆矩阵：包含</span></span>了<span class="ff4">给</span>定隐马尔科夫模型的<span class="ff4">某</span>一个<span class="ff4">特殊</span>的<span class="fc2">隐藏状态</span>，<span class="fc2">观察到的<span class="ff4">某</span>个观察状态的</span></div><div class="t m0 x1 h3 y18 ff1 fs0 fc2 sc0 ls0 ws0">概率。</div><div class="t m0 x1 h4 y19 ff1 fs0 fc0 sc0 ls0 ws0">　　<span class="ff4">因此</span>一个<span class="fc2">隐马尔科夫模型</span>是在一个<span class="ff4 fc2">标准<span class="ff1">的马尔科夫过程</span></span>中<span class="ff4">引入</span>一<span class="ff4">组</span><span class="fc2">观察状态</span>，以及<span class="fc2">其与隐藏状</span></div><div class="t m0 x1 h3 y1a ff1 fs0 fc2 sc0 ls0 ws0">态间的一些概率关系。</div><div class="t m0 x1 h4 y1b ff4 fs0 fc0 sc1 ls0 ws0">四<span class="ff1">、隐马尔科夫模型（<span class="ff3 sc0">Hidden Markov Models</span>）</span></div><div class="t m0 x1 h4 y1c ff2 fs0 fc0 sc0 ls0 ws0"><span class="ff1">、定<span class="ff4">义</span>（</span>1,2 !<span class="_ _5"></span><span class="ff1">）</span></div><div class="t m0 x1 h4 y3a ff1 fs0 fc0 sc0 ls0 ws0">　　一个隐马尔科夫模型是一个<span class="ff4">三元组</span>（<span class="_ _4"> </span><span class="ff2">)3)4</span>）。</div><div class="t m0 x1 h4 y3b ff1 fs0 fc0 sc0 ls0 ws0">　　<span class="_ _6"> </span><span class="ff4">：初</span>始化概率<span class="ff4">向量；</span></div><div class="t m0 x1 h4 y3c ff1 fs0 fc0 sc0 ls0 ws0">　　<span class="_ _7"> </span><span class="ff4">：</span>状态<span class="ff4">转移矩阵；</span></div><div class="t m0 x1 h4 y3d ff1 fs0 fc0 sc0 ls0 ws0">　　<span class="_ _8"> </span><span class="ff4">：混淆矩阵；</span></div><div class="t m0 x1 h4 y1f ff1 fs0 fc0 sc0 ls0 ws0">　　在状态<span class="ff4">转移矩阵</span>及<span class="ff4">混淆矩阵</span>中的<span class="ff4">每</span>一个概率都是<span class="fc2">时间无关</span>的——<span class="ff4">也</span>就是说，<span class="ff4">当</span>系统<span class="ff4">演</span>化时这些</div><div class="t m0 x1 h4 y20 ff4 fs0 fc0 sc0 ls0 ws0">矩阵<span class="ff1">并不</span>随<span class="ff1">时间</span>改<span class="ff1">变。实际上，这是马尔科夫模型关于</span>真<span class="ff1">实</span>世界<span class="ff1 fc2">最不<span class="ff4">现</span>实的一个<span class="ff4">假设</span><span class="fc0">。</span></span></div><div class="t m0 x1 h3 y21 ff2 fs0 fc0 sc0 ls0 ws0"><span class="ff1">、应用（</span>562<span class="ff1">）</span></div><div class="t m0 x1 h4 y22 ff1 fs0 fc0 sc0 ls0 ws0">　　一<span class="ff4">旦</span>一个系统可以<span class="ff4">作为<span class="_ _2"> </span><span class="ff2"><span class="_ _0"> </span></span>被描述</span>，就可以用<span class="ff4">来</span>解决<span class="ff4">三</span>个基本问<span class="ff4">题</span>。其中前<span class="ff4">两</span>个是模式<span class="ff4">识别</span></div><div class="t m0 x1 h4 y23 ff1 fs0 fc0 sc0 ls0 ws0">的问<span class="ff4">题：给</span>定<span class="_ _2"> </span><span class="ff2"><span class="_ _0"> </span><span class="ff4">求</span></span>一个观察序列的概率（<span class="ff4 fc2">评估</span>）<span class="ff4">；搜</span>索最有可能生<span class="ff4">成</span>一个观察序列的隐藏状态</div><div class="t m0 x1 h4 y24 ff4 fs0 fc0 sc0 ls0 ws0">训练<span class="ff1">（<span class="fc2">解<span class="ff4">码</span></span>）。</span>第三<span class="ff1">个问</span>题<span class="ff1">是</span>给<span class="ff1">定观察序列生</span>成<span class="ff1">一个<span class="_ _2"> </span><span class="ff2"><span class="_ _5"></span></span>（<span class="fc2">学习</span>）。</span></div><div class="t m0 x1 h4 y25 ff1 fs0 fc0 sc0 ls0 ws0">　<span class="ff2">(<span class="ff4">评估</span></span>（<span class="ff2">7!'</span>）</div><div class="t m0 x1 h4 y3e ff1 fs0 fc0 sc0 ls0 ws0">　　考虑这样的问<span class="ff4">题</span>，我们有一些<span class="ff4">描述</span>不<span class="ff4">同</span>系统的隐马尔科夫模型（<span class="ff4">也</span>就是一些<span class="ff2">"<span class="_ _4"> </span>)3)4(<span class="ff4">三元组</span></span>的</div><div class="t m0 x1 h4 y27 ff4 fs0 fc0 sc0 ls0 ws0">集<span class="ff1">合）及一个观察序列。我们</span>想知道哪<span class="ff1">一个<span class="_ _2"> </span><span class="ff2"><span class="_ _0"> </span></span>最有可能产生了这个</span>给<span class="ff1">定的观察序列。例如，对</span></div><div class="t m0 x1 h4 y28 ff1 fs0 fc0 sc0 ls0 ws0">于海藻<span class="ff4">来</span>说，我们<span class="ff4">也许</span>会有一个“<span class="ff4">夏季</span>”模型和一个“<span class="ff4">冬季</span>”模型，<span class="ff4">因为</span>不<span class="ff4">同季节之</span>间的<span class="ff4">情</span>况是不<span class="ff4">同</span>的—</div></div></div><div class="pi" data-data='{"ctm":[1.611850,0.000000,0.000000,1.611850,0.000000,0.000000]}'></div></div>
<div id="pf5" class="pf w0 h0" data-page-no="5"><div class="pc pc5 w0 h0"><img class="bi x0 y0 w1 h1" alt="" src="https://static.pudn.com/prod/directory_preview_static/62722075c0b40515e3da688c/bg5.jpg"><div class="c x0 y1 w2 h2"><div class="t m0 x1 h4 y2 ff1 fs0 fc0 sc0 ls0 ws0">—我们<span class="ff4">也许想根据</span>海藻湿<span class="ff4">度</span>的观察序列<span class="ff4">来</span>确定<span class="ff4">当</span>前的<span class="ff4">季节</span>。</div><div class="t m0 x1 h4 y3 ff1 fs0 fc0 sc0 ls0 ws0">　　我们<span class="ff4">使</span>用前<span class="ff4">向</span>算法（<span class="ff2">,682</span>）<span class="ff4">来</span>计算<span class="ff4">给</span>定隐马尔科夫模型（<span class="ff2"></span>）后的一个观察</div><div class="t m0 x1 h4 y4 ff1 fs0 fc0 sc0 ls0 ws0">序列的概率，并<span class="ff4">因此选择</span>最合<span class="ff4">适</span>的隐马尔科夫模型<span class="ff2">"(</span>。</div><div class="t m0 x1 h4 y5 ff1 fs0 fc0 sc0 ls0 ws0">　　在语音<span class="ff4">识别</span>中这<span class="ff4">种</span>类型的问<span class="ff4">题</span>发生在<span class="ff4">当</span>一大<span class="ff4">堆数目</span>的马尔科夫模型<span class="ff4">被使</span>用，并且<span class="ff4">每</span>一个模型都</div><div class="t m0 x1 h4 y6 ff1 fs0 fc0 sc0 ls0 ws0">对一个<span class="ff4">特殊</span>的单词<span class="ff4">进行</span>建模时。一个观察序列从一个发音单词中<span class="ff4">形成</span>，并且通过寻找对于<span class="ff4">此</span>观察序</div><div class="t m0 x1 h4 y7 ff1 fs0 fc0 sc0 ls0 ws0">列最有可能的隐马尔科夫模型（<span class="ff2"></span>）<span class="ff4">识别</span>这个单词。</div><div class="t m0 x1 h4 y8 ff1 fs0 fc0 sc0 ls0 ws0">　<span class="ff2">$(</span>解<span class="ff4">码</span>（<span class="ff4"> <span class="ff2">8</span></span>）</div><div class="t m0 x1 h4 y9 ff1 fs0 fc0 sc0 ls0 ws0">　　<span class="ff4 sc1">给<span class="ff1">定观察序列</span>搜<span class="ff1">索最可能的隐藏状态序列。</span></span></div><div class="t m0 x1 h4 ya ff1 fs0 fc0 sc0 ls0 ws0">　　另一个相关问<span class="ff4">题</span>，<span class="ff4">也</span>是最<span class="ff4">感兴趣</span>的一个，就是<span class="ff4">搜</span>索生<span class="ff4">成输出</span>序列的隐藏状态序列。在<span class="ff4">许</span>多<span class="ff4">情</span>况</div><div class="t m0 x1 h4 yb ff1 fs0 fc0 sc0 ls0 ws0">下我们对于模型中的隐藏状态更<span class="ff4">感兴趣</span>，<span class="ff4">因为</span>它们<span class="ff4">代表</span>了一些更有<span class="ff4">价值</span>的<span class="ff4">东西</span>，而这些<span class="ff4">东西</span>通常不</div><div class="t m0 x1 h4 yc ff1 fs0 fc0 sc0 ls0 ws0">能<span class="ff4">直接</span>观察到。</div><div class="t m0 x1 h4 yd ff1 fs0 fc0 sc0 ls0 ws0">　　考虑海藻和天气这个例子，一个<span class="ff4">盲</span>人隐<span class="ff4">士</span>只能<span class="ff4">感觉</span>到海藻的状态，<span class="ff4">但</span>是<span class="ff4">他</span>更<span class="ff4">想知道</span>天气的<span class="ff4">情</span>况，</div><div class="t m0 x1 h3 ye ff1 fs0 fc0 sc0 ls0 ws0">天气状态在这里就是隐藏状态。</div><div class="t m0 x1 h4 yf ff1 fs0 fc0 sc0 ls0 ws0">　　我们<span class="ff4">使</span>用<span class="_ _2"> </span><span class="ff2">9$</span>算法（<span class="ff2">9$<span class="_ _5"></span>82</span>）确定（<span class="ff4">搜</span>索）已<span class="ff4">知</span>观察序列及<span class="_ _0"> </span><span class="ff2"><span class="_ _2"> </span></span>下最可能的</div><div class="t m0 x1 h3 y10 ff1 fs0 fc0 sc0 ls0 ws0">隐藏状态序列。</div><div class="t m0 x1 h4 y11 ff1 fs0 fc0 sc0 ls0 ws0">　　<span class="ff2">9$<span class="_ _2"> </span></span>算法（<span class="ff2">9$<span class="_ _5"></span>82</span>）的另一<span class="ff4">广泛</span>应用是自然语言处理中的词性<span class="ff4">标注</span>。在词性<span class="ff4">标</span></div><div class="t m0 x1 h4 y12 ff4 fs0 fc0 sc0 ls0 ws0">注<span class="ff1">中，句子中的单词是观察状态，词性（语法类</span>别<span class="ff1">）是隐藏状态（</span>注<span class="ff1">意对于</span>许<span class="ff1">多单词，如</span></div><div class="t m0 x1 h4 y13 ff2 fs0 fc0 sc0 ls0 ws0">6<span class="ff1">，</span>12<span class="_ _2"> </span><span class="ff4">拥<span class="ff1">有不</span>止<span class="ff1">一个词性）。对于</span>每<span class="ff1">句</span>话<span class="ff1">中的单词，通过</span>搜<span class="ff1">索其最可能的隐藏状态，我们就可</span></span></div><div class="t m0 x1 h4 y14 ff1 fs0 fc0 sc0 ls0 ws0">以在<span class="ff4">给</span>定的上下<span class="ff4">文</span>中找到<span class="ff4">每</span>个单词最可能的词性<span class="ff4">标注</span>。</div><div class="t m0 x1 h3 y15 ff1 fs0 fc0 sc0 ls0 ws0">　<span class="ff2">*</span>）学习（<span class="ff2">:8</span>）</div><div class="t m0 x1 h4 y16 ff1 fs0 fc0 sc0 ls0 ws0">　　<span class="ff4 sc1">根据<span class="ff1">观察序列生</span>成<span class="ff1">隐马尔科夫模型。</span></span></div><div class="t m0 x1 h4 y17 ff1 fs0 fc0 sc0 ls0 ws0">　　<span class="ff4">第三</span>个问<span class="ff4">题</span>，<span class="ff4">也</span>是与<span class="_ _2"> </span><span class="ff2"><span class="_ _0"> </span></span>相关的问<span class="ff4">题</span>中最<span class="ff4">难</span>的，<span class="ff4">根据</span>一个观察序列（<span class="ff4">来</span>自于已<span class="ff4">知</span>的<span class="ff4">集</span>合），</div><div class="t m0 x1 h4 y18 ff1 fs0 fc0 sc0 ls0 ws0">以及与其有关的一个隐藏状态<span class="ff4">集</span>，<span class="ff4">估</span>计一个最合<span class="ff4">适</span>的隐马尔科夫模型（<span class="ff2"></span>），<span class="ff4">也</span>就是确定对已<span class="ff4">知</span></div><div class="t m0 x1 h4 y3f ff1 fs0 fc0 sc0 ls0 ws0">序列<span class="ff4">描述</span>的最合<span class="ff4">适</span>的（<span class="_ _4"> </span><span class="ff2">)3)4</span>）<span class="ff4">三元组</span>。</div><div class="t m0 x1 h4 y1a ff1 fs0 fc0 sc0 ls0 ws0">　　<span class="ff4">当矩阵<span class="_ _2"> </span><span class="ff2">3<span class="_ _0"> </span></span></span>和<span class="_ _0"> </span><span class="ff2">4<span class="_ _2"> </span></span>不能<span class="ff4">够直接被</span>（<span class="ff4">估</span>计）测<span class="ff4">量</span>时，前<span class="ff4">向<span class="ff2"><span class="_ _5"></span></span></span>后<span class="ff4">向</span>算法（<span class="ff2">,6$ 6</span></div><div class="t m0 x1 h4 y1b ff2 fs0 fc0 sc0 ls0 ws0">82<span class="ff1">）<span class="ff4">被</span>用<span class="ff4">来进行</span>学习（<span class="ff4">参数估</span>计），这<span class="ff4">也</span>是实际应用中常<span class="ff4">见</span>的<span class="ff4">情</span>况。<span class="ff4"> </span></span></div><div class="t m0 x1 h4 y1c ff2 fs0 fc0 sc0 ls0 ws0"><span class="ff1">、<span class="ff4">总结</span>（</span>&'.<span class="ff1">）</span></div><div class="t m0 x1 h4 y3a ff1 fs0 fc0 sc0 ls0 ws0">　　<span class="ff4">由</span>一个<span class="ff4">向量</span>和<span class="ff4">两</span>个<span class="ff4">矩阵<span class="ff2">"<span class="_ _4"> </span>)3)4(</span>描述</span>的隐马尔科夫模型对于实际系统有着<span class="ff4">巨</span>大的<span class="ff4">价值</span>，<span class="ff4">虽</span>然经常</div><div class="t m0 x1 h4 y35 ff1 fs0 fc0 sc0 ls0 ws0">只是一<span class="ff4">种近似</span>，<span class="ff4">但</span>它们<span class="ff4">却</span>是经<span class="ff4">得起分析</span>的。隐马尔科夫模型通常解决的问<span class="ff4">题包括：</span></div><div class="t m0 x1 h4 y36 ff1 fs0 fc0 sc0 ls0 ws0">　　<span class="ff2"></span>对于一个观察序列<span class="ff4">匹配</span>最可能的系统——<span class="ff4">评估</span>，<span class="ff4">使</span>用前<span class="ff4">向</span>算法（<span class="ff2">,682</span>）解决<span class="ff4">；</span></div><div class="t m0 x1 h4 y40 ff1 fs0 fc0 sc0 ls0 ws0">　　<span class="ff2"></span>对于已生<span class="ff4">成</span>的一个观察序列，确定最可能的隐藏状态序列——解<span class="ff4">码</span>，<span class="ff4">使</span>用<span class="_ _2"> </span><span class="ff2">9$<span class="_ _5"></span></span>算法</div><div class="t m0 x1 h4 y2e ff1 fs0 fc0 sc0 ls0 ws0">（<span class="ff2">9$82</span>）解决<span class="ff4">；</span></div><div class="t m0 x1 h4 y2f ff1 fs0 fc0 sc0 ls0 ws0">　　<span class="ff2"></span>对于已生<span class="ff4">成</span>的观察序列，决定最可能的模型<span class="ff4">参数</span>——学习，<span class="ff4">使</span>用前<span class="ff4">向<span class="ff2"></span></span>后<span class="ff4">向</span>算法（<span class="ff2">,6</span></div><div class="t m0 x1 h3 y1e ff2 fs0 fc0 sc0 ls0 ws0">$ 682<span class="ff1">）解决。</span></div><div class="t m0 x1 h5 y41 ff5 fs1 fc0 sc0 ls0 ws0">HMM<span class="_ _9"> </span><span class="ff1">学习最佳范例<span class="ff4">五：</span>前<span class="ff4">向</span>算法<span class="_ _9"> </span></span>1</div><div class="t m0 x1 h4 y21 ff4 fs0 fc0 sc1 ls0 ws0">五<span class="ff1">、前</span>向<span class="ff1">算法（<span class="ff3 sc0">Forward Algorithm</span>）</span></div><div class="t m0 x1 h3 y22 ff1 fs0 fc0 sc0 ls0 ws0">计算观察序列的概率（<span class="ff2">;82$$.,$!<'<span class="_ _5"></span></span>）</div><div class="t m0 x1 h4 y23 ff2 fs0 fc0 sc0 ls0 ws0"><span class="ff4">穷举搜<span class="ff1">索（</span> </span>7-2'!2,'<span class="ff1">）</span></div><div class="t m0 x1 h4 y42 ff1 fs0 fc0 sc0 ls0 ws0">　　<span class="ff4">给</span>定隐马尔科夫模型，<span class="ff4">也</span>就是在模型<span class="ff4">参数</span>（<span class="_ _4"> </span><span class="ff2">)3)4(</span>已<span class="ff4">知</span>的<span class="ff4">情</span>况下，我们<span class="ff4">想</span>找到观察序列的概</div><div class="t m0 x1 h4 y25 ff1 fs0 fc0 sc0 ls0 ws0">率。<span class="ff4">还</span>是考虑天气这个例子，我们有一个用<span class="ff4">来描述</span>天气及与它<span class="ff4">密切</span>相关的海藻湿<span class="ff4">度</span>状态的隐马尔科</div><div class="t m0 x1 h4 y26 ff1 fs0 fc0 sc0 ls0 ws0">夫模型<span class="ff2">"(</span>，另外我们<span class="ff4">还</span>有一个海藻的湿<span class="ff4">度</span>状态观察序列。<span class="ff4">假设连续<span class="_ _0"> </span><span class="ff2"><span class="_ _2"> </span></span></span>天海藻湿<span class="ff4">度</span>的观察<span class="ff4">结</span>果是</div><div class="t m0 x1 h4 y27 ff1 fs0 fc0 sc0 ls0 ws0">（干燥、湿<span class="ff4">润</span>、湿透）——而这<span class="ff4">三</span>天<span class="ff4">每</span>一天都可能是晴天、多<span class="ff4">云</span>或下雨，对于观察序列以及隐藏的</div><div class="t m0 x1 h4 y28 ff1 fs0 fc0 sc0 ls0 ws0">状态，可以将其<span class="ff4">视为网格：</span></div></div><a class="l" rel='nofollow' onclick='return false;'><div class="d m1"></div></a></div><div class="pi" data-data='{"ctm":[1.611850,0.000000,0.000000,1.611850,0.000000,0.000000]}'></div></div>
