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   <h2 class="chapterHead"><span class="titlemark">Chapter&#x00A0;4</span><br /><a 
  name="x21-290004"></a>Simple Sample Complexity bounds</h2>
<!--l. 868--><p class="noindent">The observations presented in this chapter are mostly &#x201C;common knowledge&#x201D; in the
learning theory community. The goal of this chapter is to introduce basic common
learning theory which the remainder of the thesis will depend upon.
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   <div class="sectionTOCS"><span class="sectionToc">&#x00A0;4.1.&#x00A0;&#x00A0;<a 
href="thesisse15.xml#x22-300004.1" name="QQ2-22-31">Simple Holdout</a></span><br /><span class="subsectionToc">&#x00A0;&#x00A0;&#x00A0;4.1.1.&#x00A0;&#x00A0;<a 
href="thesisse15.xml#x22-310004.1.1" name="QQ2-22-33">Cross Validation</a></span><br /><span class="sectionToc">&#x00A0;4.2.&#x00A0;&#x00A0;<a 
href="thesisse16.xml#x23-320004.2" name="QQ2-23-34">The basic training set bound</a></span><br /><span class="sectionToc">&#x00A0;4.3.&#x00A0;&#x00A0;<a 
href="thesisse17.xml#x24-330004.3" name="QQ2-24-35">Lower
Bounds</a></span><br /><span class="sectionToc">&#x00A0;4.4.&#x00A0;&#x00A0;<a 
href="thesisse18.xml#x25-340004.4" name="QQ2-25-36">Lower Upper Bounds</a></span><br /><span class="sectionToc">&#x00A0;4.5.&#x00A0;&#x00A0;<a 
href="thesisse19.xml#x26-350004.5" name="QQ2-26-37">Structural Risk Minimization</a></span><br /><span class="sectionToc">&#x00A0;4.6.&#x00A0;&#x00A0;<a 
href="thesisse20.xml#x27-360004.6" name="QQ2-27-38">Incorporating a &#x201C;Prior&#x201D;</a></span><br />
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