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Copy path周志华《机器学习》课后习题解答系列（二）：Ch1 - 绪论.html
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周志华《机器学习》课后习题解答系列（二）：Ch1 - 绪论.html
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<head>
<title>周志华《机器学习》课后习题解答系列（二）：Ch1 - 绪论</title>
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<body>
<h2>本章概要</h2>
<p>本章从如何挑选西瓜的经验出发，介绍了本书所涉及<strong>基本术语和概念</strong>。</p>
<blockquote>
<p>数据集、样本、特征（属性）、特征空间（属性空间、样本空间、输入空间）、特征向量、维数；</p>
<p>学习（训练）、训练数据、训练样本、假设、预测、标记、样例、标记空间（输出空间）、测试、测试样本；</p>
<p>分类、回归、聚类、簇、监督、无监督、泛化能力；</p>
<p>归纳、演绎、概念学习、假设空间、版本空间；</p>
<p>归纳偏好（偏好）、奥卡姆剃刀；</p>
</blockquote>
<p>同时简要介绍了机器学习的发展史。</p>
<blockquote>
<p>符号主义、连接主义、机器学习、数据挖掘、统计学；</p>
</blockquote>
<h2>习题解答</h2>
<h4>1.1 版本空间</h4>
<blockquote>
<p><img src="img/1.1.png" /></p>
</blockquote>
<p>当前的特征维度为3（色泽、根蒂、敲声），共3、2、2种取值，1，4的特征完全不同</p>
<p>根据版本空间的定义（版本空间指的是与训练集一致的假设空间），由表可知，1，4样例各特征取值均不同，于是得出当前的版本空间为：
<img src="img/1.1.1.png" /></p>
<hr />
<h4>1.2 折合范式提升假设空间表示能力</h4>
<blockquote>
<p><img src="img/1.2.png" /></p>
</blockquote>
<p>首先给出相关定义，合取范式：<a href="https://en.wikipedia.org/wiki/Conjunctive_normal_form">Conjunctive normal form - Wikipedia</a>，析合范式：<a href="https://en.wikipedia.org/wiki/Disjunctive_normal_form">Conjunctive normal form - Wikipedia</a>。</p>
<p>然后考虑问题。本题采用析合范式来提升假设空间，解答思路如下图：</p>
<blockquote>
<p><img src="img/1.2.1.jpg" /></p>
</blockquote>
<hr />
<h4>1.3 噪声下的归纳偏好设计</h4>
<blockquote>
<p><img src="img/1.3.png" /></p>
</blockquote>
<ul>
<li>最简单的设计就是：训练样本一致特征越多越好（一致性比例越高越好）为归纳偏好。</li>
<li>另外，考虑归纳偏好应尽量与问题相匹配，这里可使归纳偏好与噪声分布相匹配。</li>
</ul>
<hr />
<p>另外1.4与1.5题未完成。</p>
</body>
</html>
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