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统计学
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<span class="md-nav__icon md-icon"></span>
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基础
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</span>
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</a>
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统计量
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</span>
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</a>
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抽样
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</span>
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</a>
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假设检验
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</span>
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</a>
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<span class="md-ellipsis">
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推断
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</span>
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|
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</a>
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</ul>
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</nav>
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<span class="md-ellipsis">
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概率论
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</span>
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<span class="md-nav__icon md-icon"></span>
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<span class="md-nav__icon md-icon"></span>
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概率论
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</label>
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<span class="md-ellipsis">
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计数
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|
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|
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|
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</span>
|
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|
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|
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|
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</a>
|
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</li>
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<li class="md-nav__item">
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<a href="../../chapter%2005%3A%20probability/02.%20probability%20concepts/" class="md-nav__link">
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<span class="md-ellipsis">
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|
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概率概念
|
||
|
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|
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|
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</span>
|
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|
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|
||
|
||
</a>
|
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</li>
|
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<li class="md-nav__item">
|
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<a href="../../chapter%2005%3A%20probability/03.%20distributions/" class="md-nav__link">
|
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|
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<span class="md-ellipsis">
|
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|
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|
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分布
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
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<li class="md-nav__item">
|
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<a href="../../chapter%2005%3A%20probability/04.%20bayesian/" class="md-nav__link">
|
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|
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<span class="md-ellipsis">
|
||
|
||
|
||
贝叶斯
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
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|
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|
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|
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|
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|
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|
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<li class="md-nav__item">
|
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<a href="../../chapter%2005%3A%20probability/05.%20information%20theory/" class="md-nav__link">
|
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|
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|
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|
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<span class="md-ellipsis">
|
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|
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|
||
信息论
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
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</li>
|
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|
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|
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|
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|
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</ul>
|
||
</nav>
|
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|
||
</li>
|
||
|
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|
||
|
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|
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|
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|
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|
||
|
||
|
||
|
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|
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|
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|
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|
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|
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<li class="md-nav__item md-nav__item--nested">
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|
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|
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|
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|
||
<span class="md-ellipsis">
|
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|
||
|
||
机器学习
|
||
|
||
|
||
|
||
</span>
|
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|
||
|
||
|
||
<span class="md-nav__icon md-icon"></span>
|
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</label>
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|
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<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_7_label" aria-expanded="false">
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<label class="md-nav__title" for="__nav_7">
|
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<span class="md-nav__icon md-icon"></span>
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|
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机器学习
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|
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|
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</label>
|
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<ul class="md-nav__list" data-md-scrollfix>
|
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<li class="md-nav__item">
|
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<a href="../../chapter%2006%3A%20machine%20learning/01.%20classical%20machine%20learning/" class="md-nav__link">
|
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|
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|
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|
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<span class="md-ellipsis">
|
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|
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|
||
经典机器学习
|
||
|
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|
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|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
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</li>
|
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<li class="md-nav__item">
|
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<a href="../../chapter%2006%3A%20machine%20learning/02.%20gradient%20machine%20learning/" class="md-nav__link">
|
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|
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|
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|
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<span class="md-ellipsis">
|
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|
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|
||
梯度机器学习
|
||
|
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|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
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</li>
|
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|
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|
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<li class="md-nav__item">
|
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<a href="../../chapter%2006%3A%20machine%20learning/03.%20deep%20learning/" class="md-nav__link">
|
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|
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|
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|
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<span class="md-ellipsis">
|
||
|
||
|
||
深度学习
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
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|
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|
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|
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|
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|
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|
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<li class="md-nav__item">
|
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<a href="../../chapter%2006%3A%20machine%20learning/04.%20reinforcement%20learning/" class="md-nav__link">
|
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|
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|
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|
||
<span class="md-ellipsis">
|
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|
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|
||
强化学习
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
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|
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|
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|
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|
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|
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|
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|
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|
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<li class="md-nav__item">
|
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<a href="../../chapter%2006%3A%20machine%20learning/05.%20distributed%20deep%20learning/" class="md-nav__link">
|
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|
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|
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|
||
<span class="md-ellipsis">
|
||
|
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|
||
分布式深度学习
|
||
|
||
|
||
|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
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</li>
|
||
|
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|
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|
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|
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</ul>
|
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</nav>
|
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|
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</li>
|
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|
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|
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|
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|
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|
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|
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|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
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|
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|
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|
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|
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|
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|
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|
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|
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<li class="md-nav__item md-nav__item--active md-nav__item--section md-nav__item--nested">
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<input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_8" checked>
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<label class="md-nav__link" for="__nav_8" id="__nav_8_label" tabindex="">
|
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|
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|
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|
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<span class="md-ellipsis">
|
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|
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|
||
计算语言学
|
||
|
||
|
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|
||
</span>
|
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|
||
|
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|
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<span class="md-nav__icon md-icon"></span>
|
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</label>
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|
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<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_8_label" aria-expanded="true">
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<label class="md-nav__title" for="__nav_8">
|
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<span class="md-nav__icon md-icon"></span>
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|
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计算语言学
|
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|
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|
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</label>
|
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<ul class="md-nav__list" data-md-scrollfix>
|
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|
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|
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<li class="md-nav__item">
|
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<a href="../01.%20linguistic%20foundations/" class="md-nav__link">
|
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|
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|
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<span class="md-ellipsis">
|
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|
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|
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语言学基础
|
||
|
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|
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|
||
</span>
|
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|
||
|
||
|
||
</a>
|
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</li>
|
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|
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|
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|
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<li class="md-nav__item md-nav__item--active">
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|
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|
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|
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|
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<span class="md-ellipsis">
|
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|
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|
||
文本处理与经典 NLP
|
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|
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|
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|
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</span>
|
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|
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|
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|
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<span class="md-nav__icon md-icon"></span>
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</label>
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<a href="./" class="md-nav__link md-nav__link--active">
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|
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|
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|
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<span class="md-ellipsis">
|
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|
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|
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文本处理与经典 NLP
|
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|
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|
||
|
||
</span>
|
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|
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|
||
|
||
</a>
|
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|
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|
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|
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<nav class="md-nav md-nav--secondary" aria-label="目录">
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<span class="md-nav__icon md-icon"></span>
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目录
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|
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<li class="md-nav__item">
|
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<a href="#colabnotebook" class="md-nav__link">
|
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<span class="md-ellipsis">
|
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|
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编程练习（使用CoLab或notebook）
|
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|
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</span>
|
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</a>
|
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|
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</li>
|
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|
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</ul>
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|
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</nav>
|
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|
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</li>
|
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|
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|
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|
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|
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<li class="md-nav__item">
|
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<a href="../03.%20embeddings%20and%20sequence%20models/" class="md-nav__link">
|
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|
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|
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|
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<span class="md-ellipsis">
|
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|
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|
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嵌入与序列模型
|
||
|
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|
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|
||
</span>
|
||
|
||
|
||
|
||
</a>
|
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</li>
|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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<li class="md-nav__item">
|
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<a href="../04.%20transformers%20and%20language%20models/" class="md-nav__link">
|
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|
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|
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|
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<span class="md-ellipsis">
|
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|
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|
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Transformer 与语言模型
|
||
|
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|
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|
||
</span>
|
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|
||
|
||
|
||
</a>
|
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</li>
|
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|
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|
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|
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<li class="md-nav__item">
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<a href="../05.%20advanced%20text%20generation/" class="md-nav__link">
|
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|
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|
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|
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<span class="md-ellipsis">
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|
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|
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高级文本生成
|
||
|
||
|
||
|
||
</span>
|
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|
||
|
||
|
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</a>
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</li>
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|
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|
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|
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</ul>
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</nav>
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</li>
|
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|
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|
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|
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|
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|
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|
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|
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|
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计算机视觉
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图像基础
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目标检测与分割
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音频与语音
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数字信号处理
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自动语音识别
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</span>
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语音合成
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</span>
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</a>
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<span class="md-ellipsis">
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说话人与音频分析
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</span>
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|
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|
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</a>
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</li>
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源分离与降噪
|
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</span>
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|
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<span class="md-ellipsis">
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多模态学习
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</span>
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<span class="md-nav__icon md-icon"></span>
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<span class="md-nav__icon md-icon"></span>
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多模态学习
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</label>
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<ul class="md-nav__list" data-md-scrollfix>
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多模态表征
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</span>
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</a>
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视觉语言模型
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</span>
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</a>
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图像与视频 Token 化
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</span>
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|
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|
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</a>
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跨模态生成
|
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</span>
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|
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|
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|
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</a>
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</li>
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<a href="../../chapter%2010%3A%20multimodal%20learning/05.%20unified%20multimodal%20architectures/" class="md-nav__link">
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<span class="md-ellipsis">
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统一多模态架构
|
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|
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|
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</span>
|
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|
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|
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|
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<li class="md-nav__item md-nav__item--nested">
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自主系统
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</span>
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<span class="md-nav__icon md-icon"></span>
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感知
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机器人学习
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</span>
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</a>
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视觉-语言-动作模型
|
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</span>
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|
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|
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|
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</a>
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自动驾驶
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</span>
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|
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|
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|
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</a>
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<a href="../../chapter%2011%3A%20autonomous%20systems/05.%20space%20and%20extreme%20robotics/" class="md-nav__link">
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<span class="md-ellipsis">
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太空与极端机器人
|
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|
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|
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|
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</span>
|
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|
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|
||
|
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图神经网络
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</span>
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<span class="md-nav__icon md-icon"></span>
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图神经网络
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几何深度学习
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</span>
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|
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ARM 与 NEON
|
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x86 与 AVX
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Triton、TPU 与 Pallas
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边缘推理
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ML 系统设计
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应用 AI
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前沿 AI
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<h1 id="nlp">文本处理与经典NLP<a class="headerlink" href="#nlp" title="Permanent link">¶</a></h1>
|
||
<p><em>文本处理将原始字符转换为模型可消费的结构化表示。本文涵盖分词（词级、子词、BPE、WordPiece）、文本规范化、编辑距离、TF-IDF、n元组语言模型、词性标注、命名实体识别和情感分析——这些经典NLP流水线至今仍是现代系统的基础。</em></p>
|
||
<ul>
|
||
<li>
|
||
<p>原始文本是混乱的。在任何NLP模型处理语言之前，文本必须经过清洗、规范化并转换为结构化表示。本文涵盖了从原始字符到模型可消费特征的完整流水线，以及深度学习兴起之前主导领域的经典NLP算法。</p>
|
||
</li>
|
||
<li>
|
||
<p><strong>文本规范化</strong>将原始文本转换为规范形式。其目标是减少不相关的变异，使"Hello"、"hello"、"HELLO"和"héllo"得到恰当的处理。</p>
|
||
</li>
|
||
<li>
|
||
<p><strong>大小写折叠</strong>将文本转换为小写。这将"The"和"the"合并为一个词元。这对大多数任务有帮助，但在某些情况下会破坏有用信息："US"（国家）vs "us"（代词），或"Apple"（公司）vs "apple"（水果）。</p>
|
||
</li>
|
||
<li>
|
||
<p><strong>Unicode规范化</strong>处理同一字符有多种编码方式的问题。字符"é"可以是单个码点（U+00E9），也可以是基础"e"加上组合变音符号（U+0065 + U+0301）。NFC规范化将它们组合成一个码点；NFD则进行分解。如果没有规范化，两个看起来相同的字符串可能无法匹配。</p>
|
||
</li>
|
||
<li>
|
||
<p><strong>编辑距离</strong>衡量两个字符串之间的差异程度。<strong>莱文斯坦距离</strong>计算将一个字符串转换为另一个所需的最少单字符插入、删除和替换次数。"kitten" → "sitting"的编辑距离为3（k→s，e→i，插入g）。</p>
|
||
</li>
|
||
<li>
|
||
<p>编辑距离使用动态规划计算（我们在算法章节中回顾）。定义 <span class="arithmatex">\(D[i][j]\)</span> 为字符串 <span class="arithmatex">\(s\)</span> 的前 <span class="arithmatex">\(i\)</span> 个字符与字符串 <span class="arithmatex">\(t\)</span> 的前 <span class="arithmatex">\(j\)</span> 个字符之间的距离：</p>
|
||
</li>
|
||
</ul>
|
||
<div class="arithmatex">\[
|
||
D[i][j] = \begin{cases} j & \text{if } i = 0 \\ i & \text{if } j = 0 \\ D[i{-}1][j{-}1] & \text{if } s[i] = t[j] \\ 1 + \min(D[i{-}1][j], \; D[i][j{-}1], \; D[i{-}1][j{-}1]) & \text{otherwise} \end{cases}
|
||
\]</div>
|
||
<ul>
|
||
<li>
|
||
<p>编辑距离支撑着拼写纠正、模糊匹配和DNA序列比对。在NLP中，它用于处理拼写错误和查找相似单词。</p>
|
||
</li>
|
||
<li>
|
||
<p><strong>分词</strong>将文本分割成模型可以处理的离散单元（词元）。这是第一个也是最重要的预处理步骤。分词策略的选择深刻影响着模型行为。</p>
|
||
</li>
|
||
<li>
|
||
<p><strong>空白分词</strong>以空格分割。简单但幼稚："New York"变成两个词元，"don't"是一个词元（或根据分割器不同，拆分为"don"和"'t"），而中文和日文等语言在词之间根本没有空格。</p>
|
||
</li>
|
||
<li>
|
||
<p><strong>基于规则的分词</strong>使用手工设计的模式（正则表达式）来处理缩写、标点符号和特殊情况。"I'm" → "I" + "'m"，"U.S.A."保持为一个词元。每种语言都需要自己的规则，这非常耗费人力。</p>
|
||
</li>
|
||
<li>
|
||
<p><strong>子词分词</strong>是现代解决方案。它不是在词边界处分割，而是从数据中学习一个高频子词单元的词汇表。这优雅地处理了未知词：如果"unhappiness"不在词汇表中，它可能被拆分为"un" + "happi" + "ness"，保留了形态结构。</p>
|
||
</li>
|
||
</ul>
|
||
<p><img alt=""unhappiness"和"transformers"的词级、字符级和子词分词对比" src="../../images/tokenisation_comparison.svg" /></p>
|
||
<ul>
|
||
<li>
|
||
<p><strong>字节对编码（BPE）</strong>从单个字符作为词汇表开始。它反复查找最频繁的相邻对并将其合并为一个新词元。经过足够次数的合并后，常见词成为单个词元，罕见词则被拆分为高频子词片段。</p>
|
||
</li>
|
||
<li>
|
||
<p>BPE算法：</p>
|
||
<ol>
|
||
<li>用训练语料中的所有单个字符初始化词汇表</li>
|
||
<li>统计每个相邻词元对的频率</li>
|
||
<li>将最频繁的对合并为一个新词元</li>
|
||
<li>重复步骤2-3，直到达到所需的合并次数（词汇表大小）</li>
|
||
</ol>
|
||
</li>
|
||
<li>
|
||
<p>例如，从"l o w"（5次）、"l o w e r"（2次）、"n e w e s t"（6次）开始：最频繁的对可能是"e s" → 合并为"es"。然后"es t" → "est"。然后"n e w" → "new"。最终的词汇表同时包含完整单词和子词片段。</p>
|
||
</li>
|
||
<li>
|
||
<p><strong>WordPiece</strong>（BERT使用）与BPE类似，但基于似然而非频率来选择合并。它合并能使训练数据的语言模型似然最大化的对。非词首的子词词元以"##"作为前缀（例如，"playing" → "play" + "##ing"）。</p>
|
||
</li>
|
||
<li>
|
||
<p><strong>Unigram</strong>（SentencePiece使用）采用相反的方法：从一个大型词汇表开始，迭代地移除那些移除后对训练数据似然损失最小的词元。最终的词汇表是最能解释语料库的子词单元集合。</p>
|
||
</li>
|
||
<li>
|
||
<p><strong>SentencePiece</strong>是一个语言无关的分词库，它将输入视为原始字节流（不在空格上进行预分词）。这使得它适用于任何语言，包括没有空格的语言。它同时实现了BPE和Unigram算法。</p>
|
||
</li>
|
||
<li>
|
||
<p>词汇表大小是一个关键超参数。典型的选择范围从30,000到100,000个词元。更大的词汇表意味着每个序列的词元更少（更高效），但需要更大的嵌入表。更小的词汇表意味着更多的子词分割和更长的序列。</p>
|
||
</li>
|
||
<li>
|
||
<p>两种技术都将词汇简化为基本形式，但方法不同。</p>
|
||
</li>
|
||
<li>
|
||
<p><strong>词干提取</strong>使用粗略规则切除后缀。波特词干提取器将"running"简化为"run"，"happiness"简化为"happi"，"studies"简化为"studi"。它速度快但不精确："university"和"universe"都被词干化为"univers"，尽管它们毫不相关。</p>
|
||
</li>
|
||
<li>
|
||
<p><strong>词形还原</strong>使用词汇表和形态学分析来找到真正的词典形式（词元）。"Running" → "run"，"better" → "good"，"mice" → "mouse"。它需要知道词性："saw"作为动词时词形还原为"see"，但作为名词时保持为"saw"。</p>
|
||
</li>
|
||
<li>
|
||
<p>现代子词分词在很大程度上已取代了神经NLP中的词干提取和词形还原，但它们在信息检索以及处理较小模型或有限数据时仍然有用。</p>
|
||
</li>
|
||
<li>
|
||
<p><strong>词性标注</strong>为每个词分配一个语法类别：名词、动词、形容词、限定词等。这是最古老的NLP任务之一，也是句法分析的基础。</p>
|
||
</li>
|
||
<li>
|
||
<p>宾州树库标签集是英语中最常用的，包含36个标签（NN表示单数名词，NNS表示复数名词，VB表示动词原形，VBD表示过去式，JJ表示形容词等）。</p>
|
||
</li>
|
||
<li>
|
||
<p>词性标注很棘手，因为许多词是有歧义的。"Book"可以是名词（"the book"）或动词（"book a flight"）。"Run"在不同词性下有数十种含义。上下文至关重要。</p>
|
||
</li>
|
||
<li>
|
||
<p>早期的标注器使用第05章中的<strong>隐马尔可夫模型（HMM）</strong>。隐藏状态是词性标签，观测值是单词。转移概率捕捉标签序列（限定词后面很可能跟名词或形容词），发射概率捕捉哪些词与哪些标签一起出现。维特比算法找出最可能的标签序列。</p>
|
||
</li>
|
||
<li>
|
||
<p>用于词性标注的HMM模型：</p>
|
||
</li>
|
||
</ul>
|
||
<div class="arithmatex">\[\\hat{t}_{1:n} = \\arg\\max_{t_{1:n}} \\prod_{i=1}^{n} P(w_i \\mid t_i) \\cdot P(t_i \\mid t_{i-1})\]</div>
|
||
<ul>
|
||
<li>
|
||
<p>现代词性标注器使用神经网络（双向LSTM或Transformer），在英语上达到超过97%的准确率，接近人类水平。</p>
|
||
</li>
|
||
<li>
|
||
<p><strong>命名实体识别（NER）</strong>识别并分类文本中的专有名词和其他特定实体：人物、组织、地点、日期、货币金额等。</p>
|
||
</li>
|
||
<li>
|
||
<p>在"Apple CEO Tim Cook announced the event in Cupertino on Monday"中，NER系统应识别出：Apple（ORG组织）、Tim Cook（PER人物）、Cupertino（LOC地点）、Monday（DATE日期）。</p>
|
||
</li>
|
||
<li>
|
||
<p>NER通常被框架化为<strong>序列标注</strong>，使用<strong>BIO标注</strong>（也称为IOB标注）。每个词元获得一个标签：</p>
|
||
<ul>
|
||
<li><strong>B-TYPE</strong>：TYPE类型实体的开始</li>
|
||
<li><strong>I-TYPE</strong>：TYPE类型实体的内部（延续）</li>
|
||
<li><strong>O</strong>：实体外部</li>
|
||
</ul>
|
||
</li>
|
||
<li>
|
||
<p>"Tim Cook visited New York"变为：Tim/B-PER Cook/I-PER visited/O New/B-LOC York/I-LOC。B标签标记新实体的起始位置，这对于两个同类型实体相邻的情况很重要。</p>
|
||
</li>
|
||
</ul>
|
||
<p><img alt="带有BIO标签颜色编码的句子：B-PER（红色）、I-PER（红色）、O（灰色）、B-LOC（蓝色）、I-LOC（蓝色）" src="../../images/bio_tagging.svg" /></p>
|
||
<ul>
|
||
<li>经典NER使用第05章中的<strong>条件随机场（CRF）</strong>，它对给定输入下整个标签序列的条件概率建模。与生成式模型（<span class="arithmatex">\(P(x, y)\)</span>）的HMM不同，CRF是判别式模型，直接建模 <span class="arithmatex">\(P(y \\mid x)\)</span>。线性链CRF定义为：</li>
|
||
</ul>
|
||
<div class="arithmatex">\[P(y_{1:n} \\mid x_{1:n}) = \\frac{1}{Z(x)} \\exp\\!\\left(\\sum_{i=1}^{n} \\left[\\sum_k \\lambda_k f_k(y_i, x, i) + \\sum_j \\mu_j g_j(y_i, y_{i-1}, x, i)\\right]\\right)\]</div>
|
||
<ul>
|
||
<li>
|
||
<p>这里 <span class="arithmatex">\(f_k\)</span> 是<strong>发射特征</strong>（给定位置 <span class="arithmatex">\(i\)</span> 的输入，标签 <span class="arithmatex">\(y_i\)</span> 的可能性），<span class="arithmatex">\(g_j\)</span> 是<strong>转移特征</strong>（给定前一个标签 <span class="arithmatex">\(y_{i-1}\)</span>，当前标签 <span class="arithmatex">\(y_i\)</span> 的可能性）。</p>
|
||
</li>
|
||
<li>
|
||
<p>配分函数 <span class="arithmatex">\(Z(x) = \\sum_{y'} \\exp(\\ldots)\)</span> 对所有可能的标签序列求和，以归一化分布。训练最大化条件对数似然，这需要使用前向算法（第05章）高效计算 <span class="arithmatex">\(Z(x)\)</span>。</p>
|
||
</li>
|
||
<li>
|
||
<p>与独立分类每个词元相比的关键优势：CRF的转移特征强制结构约束（例如，I-PER应该只跟在B-PER或I-PER之后，绝不应出现在O之后）。</p>
|
||
</li>
|
||
<li>
|
||
<p>现代NER将CRF堆叠在神经编码器之上（BiLSTM-CRF或BERT-CRF），其中神经网络产生发射分数，CRF层学习转移结构。</p>
|
||
</li>
|
||
<li>
|
||
<p><strong>句法分析</strong>将句子转换为其句法结构，可以是成分树或依存树（两者均见文件01）。</p>
|
||
</li>
|
||
<li>
|
||
<p><strong>CYK算法</strong>（Cocke-Younger-Kasami）使用动态规划结合上下文无关文法解析句子。</p>
|
||
</li>
|
||
<li>
|
||
<p>它要求文法为<strong>乔姆斯基范式</strong>（每条规则的右侧要么有两个非终结符，要么有一个终结符）。它自底向上填充一个三角表格：单元格表示句子的跨度，每个单元格存储可以生成该跨度的非终结符。</p>
|
||
</li>
|
||
<li>
|
||
<p>CYK的时间复杂度为 <span class="arithmatex">\(O(n^3 \\cdot |G|)\)</span>，其中 <span class="arithmatex">\(n\)</span> 是句子长度，<span class="arithmatex">\(|G|\)</span> 是文法规模。这是精确算法，但对于大型文法来说速度较慢。</p>
|
||
</li>
|
||
<li>
|
||
<p><strong>移进-归约解析</strong>从左到右处理句子，维护一个栈。在每一步，它要么<strong>移进</strong>（将下一个词压入栈），要么<strong>归约</strong>（从栈中弹出元素并用短语替换）。一个训练好的分类器在每一步决定操作。时间复杂度为 <span class="arithmatex">\(O(n)\)</span>，比CYK快得多。</p>
|
||
</li>
|
||
<li>
|
||
<p><strong>依存解析</strong>在实践中比成分解析更为常见。基于转换的依存解析器（如移进-归约）和基于图的解析器（对所有可能的边评分并找到最大生成树）是两种主要方法。使用BiLSTM或Transformer的神经依存解析器取得了最先进的成果。</p>
|
||
</li>
|
||
<li>
|
||
<p>在嵌入出现之前，NLP使用简单的计数方法将文档表示为向量。</p>
|
||
</li>
|
||
<li>
|
||
<p><strong>词袋模型（BoW）</strong>将文档表示为词频向量，完全忽略词序。如果词汇表有 <span class="arithmatex">\(V\)</span> 个词，每个文档就是 <span class="arithmatex">\(\\mathbb{R}^V\)</span> 空间中的一个向量（与第01章的向量空间相联系）。词 <span class="arithmatex">\(w\)</span> 对应的条目是 <span class="arithmatex">\(w\)</span> 在文档中出现的次数。</p>
|
||
</li>
|
||
</ul>
|
||
<p><img alt="词袋模型：文档转换为词频表，再转换为R^V空间中的稀疏向量，词汇表中每个词对应一个条目" src="../../images/bag_of_words.svg" /></p>
|
||
<ul>
|
||
<li>
|
||
<p>BoW简单但出奇有效，适用于文档分类和垃圾邮件过滤等任务。其主要缺点是每个词都被同等对待："the"和"revolutionary"获得相同的权重。</p>
|
||
</li>
|
||
<li>
|
||
<p><strong>TF-IDF</strong>（词频-逆文档频率）通过根据词的信息量大小来加权，解决了这个问题。在单个文档中频繁出现但在整个语料库中罕见的词，很可能对该文档很重要。</p>
|
||
</li>
|
||
</ul>
|
||
<div class="arithmatex">\[\\text{TF-IDF}(t, d) = \\text{TF}(t, d) \\times \\text{IDF}(t)\]</div>
|
||
<ul>
|
||
<li>
|
||
<p><strong>词频</strong> <span class="arithmatex">\(\\text{TF}(t, d)\)</span> 通常是词 <span class="arithmatex">\(t\)</span> 在文档 <span class="arithmatex">\(d\)</span> 中的原始计数（或其对数形式：<span class="arithmatex">\(1 + \\log(\\text{count})\)</span>）。</p>
|
||
</li>
|
||
<li>
|
||
<p><strong>逆文档频率</strong> <span class="arithmatex">\(\\text{IDF}(t) = \\log\\frac{N}{|\\{d : t \\in d\\}|}\)</span>，其中 <span class="arithmatex">\(N\)</span> 是文档总数。出现在每个文档中的词（如"the"）的IDF接近0。罕见词获得高IDF。</p>
|
||
</li>
|
||
<li>
|
||
<p>TF-IDF向量可以使用余弦相似度（来自第01章）进行比较，以衡量文档相似性。这是经典信息检索和搜索引擎的基础。</p>
|
||
</li>
|
||
<li>
|
||
<p><strong>语言模型</strong>为词序列分配概率。它回答的是：这个句子的可能性有多大？语言模型是机器翻译、语音识别、拼写纠正和文本生成的核心。</p>
|
||
</li>
|
||
<li>
|
||
<p>句子 <span class="arithmatex">\(w_1, w_2, \\ldots, w_n\)</span> 的概率，根据概率的链式法则（第05章）为：</p>
|
||
</li>
|
||
</ul>
|
||
<div class="arithmatex">\[P(w_1, w_2, \\ldots, w_n) = \\prod_{i=1}^{n} P(w_i \\mid w_1, \\ldots, w_{i-1})\]</div>
|
||
<ul>
|
||
<li>
|
||
<p>这是精确的但不实用：你需要为每个可能的历史存储概率。<strong>马尔可夫假设</strong>（第05章）将历史截断到最近 <span class="arithmatex">\(k-1\)</span> 个词，得到 <strong>n元语法模型</strong>（其中 <span class="arithmatex">\(n = k\)</span>）。</p>
|
||
</li>
|
||
<li>
|
||
<p><strong>二元模型</strong>（<span class="arithmatex">\(n = 2\)</span>）仅依赖前一个词：</p>
|
||
</li>
|
||
</ul>
|
||
<div class="arithmatex">\[P(w_i \\mid w_1, \\ldots, w_{i-1}) \\approx P(w_i \\mid w_{i-1})\]</div>
|
||
<ul>
|
||
<li><strong>三元模型</strong>（<span class="arithmatex">\(n = 3\)</span>）依赖前两个词。n元语法概率通过在语料库中计数来估计：</li>
|
||
</ul>
|
||
<div class="arithmatex">\[P(w_i \\mid w_{i-1}) = \\frac{\\text{count}(w_{i-1}, w_i)}{\\text{count}(w_{i-1})}\]</div>
|
||
<ul>
|
||
<li><strong>困惑度</strong>衡量语言模型对测试集的预测能力。它是测试集概率的倒数，按词数归一化：</li>
|
||
</ul>
|
||
<div class="arithmatex">\[\\text{PPL} = P(w_1, \\ldots, w_N)^{-1/N} = \\exp\\!\\left(-\\frac{1}{N} \\sum_{i=1}^{N} \\log P(w_i \\mid w_{<i})\\right)\]</div>
|
||
<ul>
|
||
<li>
|
||
<p>困惑度越低，说明模型对测试数据越"不惊讶"，因此性能越好。在10,000词词汇表上分配均匀概率的模型，困惑度为10,000。一个好的二元模型可能达到约200的困惑度。现代神经语言模型的困惑度低于20。</p>
|
||
</li>
|
||
<li>
|
||
<p>注意，困惑度是指数化的交叉熵（来自第05章的信息论部分）。训练期间最小化交叉熵损失直接最小化困惑度。</p>
|
||
</li>
|
||
<li>
|
||
<p><strong>平滑</strong>处理零概率问题：如果某个n元组从未在训练中出现过，模型会赋予它概率0，这会使整个句子的概率为0。<strong>拉普拉斯平滑</strong>（加1）为每个n元组添加一个小计数：</p>
|
||
</li>
|
||
</ul>
|
||
<div class="arithmatex">\[P_{\\text{Laplace}}(w_i \\mid w_{i-1}) = \\frac{\\text{count}(w_{i-1}, w_i) + 1}{\\text{count}(w_{i-1}) + V}\]</div>
|
||
<ul>
|
||
<li>
|
||
<p>对于大词汇表来说这过于激进（从已观察到的n元组中挪走了太多概率）。<strong>Kneser-Ney平滑</strong>是n元语法模型的金标准。它结合了两个思想：绝对折扣和用于回退的延续概率。</p>
|
||
</li>
|
||
<li>
|
||
<p>首先，<strong>绝对折扣</strong>从每个观察到的计数中减去一个固定折扣 <span class="arithmatex">\(d\)</span>（通常 <span class="arithmatex">\(d \\approx 0.75\)</span>），而不是添加伪计数。释放出的概率质量重新分配给未见过的n元组。插值形式为：</p>
|
||
</li>
|
||
</ul>
|
||
<div class="arithmatex">\[P_{\\text{KN}}(w_i \\mid w_{i-1}) = \\frac{\\max(\\text{count}(w_{i-1}, w_i) - d, \\; 0)}{\\text{count}(w_{i-1})} + \\lambda(w_{i-1}) \\cdot P_{\\text{cont}}(w_i)\]</div>
|
||
<ul>
|
||
<li>其中 <span class="arithmatex">\(\\lambda(w_{i-1})\)</span> 是一个归一化常数，用于分配折扣后的质量。关键的创新是<strong>延续概率</strong> <span class="arithmatex">\(P_{\\text{cont}}(w_i)\)</span>，它衡量 <span class="arithmatex">\(w_i\)</span> 出现在多少个不同的上下文中，而不是它总体上出现的频率：</li>
|
||
</ul>
|
||
<div class="arithmatex">\[P_{\\text{cont}}(w_i) = \\frac{|\\{w' : \\text{count}(w', w_i) > 0\\}|}{|\\{(w', w'') : \\text{count}(w', w'') > 0\\}|}\]</div>
|
||
<ul>
|
||
<li>
|
||
<p>分子统计在语料库中出现在 <span class="arithmatex">\(w_i\)</span> 之前的不同词的数量。像"Francisco"这样的词出现在很少的上下文中（几乎总是在"San"之后），所以即使"San Francisco"非常频繁，"Francisco"的延续概率也很低，不会在其他上下文中被错误预测。</p>
|
||
</li>
|
||
<li>
|
||
<p>相反，像"the"这样的常见词出现在许多不同词之后，获得高延续概率。这体现了这样一种直觉：对于回退估计而言，词的多功能性比其原始频率更重要。</p>
|
||
</li>
|
||
<li>
|
||
<p>n元语法模型几十年来一直是主流技术。它们速度快、可解释性强，且无需训练（只需计数）。但它们难以处理长距离依赖（"The keys that I left on the table <strong>are</strong> missing"需要知道主语"keys"是复数，而它与动词相距甚远）。神经语言模型——从RNN开始到Transformer达到顶峰——解决了这一局限性。</p>
|
||
</li>
|
||
</ul>
|
||
<h2 id="colabnotebook">编程练习（使用CoLab或notebook）<a class="headerlink" href="#colabnotebook" title="Permanent link">¶</a></h2>
|
||
<ol>
|
||
<li>
|
||
<p>使用动态规划实现莱文斯坦编辑距离。在词对上测试，并用于简单的拼写纠正。
|
||
<div class="highlight"><pre><span></span><code><a id="__codelineno-0-1" name="__codelineno-0-1" href="#__codelineno-0-1"></a><span class="kn">import</span><span class="w"> </span><span class="nn">jax.numpy</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="nn">jnp</span>
|
||
<a id="__codelineno-0-2" name="__codelineno-0-2" href="#__codelineno-0-2"></a>
|
||
<a id="__codelineno-0-3" name="__codelineno-0-3" href="#__codelineno-0-3"></a><span class="k">def</span><span class="w"> </span><span class="nf">edit_distance</span><span class="p">(</span><span class="n">s</span><span class="p">,</span> <span class="n">t</span><span class="p">):</span>
|
||
<a id="__codelineno-0-4" name="__codelineno-0-4" href="#__codelineno-0-4"></a><span class="w"> </span><span class="sd">"""Compute Levenshtein edit distance using DP."""</span>
|
||
<a id="__codelineno-0-5" name="__codelineno-0-5" href="#__codelineno-0-5"></a> <span class="n">m</span><span class="p">,</span> <span class="n">n</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">s</span><span class="p">),</span> <span class="nb">len</span><span class="p">(</span><span class="n">t</span><span class="p">)</span>
|
||
<a id="__codelineno-0-6" name="__codelineno-0-6" href="#__codelineno-0-6"></a> <span class="n">D</span> <span class="o">=</span> <span class="p">[[</span><span class="mi">0</span><span class="p">]</span> <span class="o">*</span> <span class="p">(</span><span class="n">n</span> <span class="o">+</span> <span class="mi">1</span><span class="p">)</span> <span class="k">for</span> <span class="n">_</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">m</span> <span class="o">+</span> <span class="mi">1</span><span class="p">)]</span>
|
||
<a id="__codelineno-0-7" name="__codelineno-0-7" href="#__codelineno-0-7"></a>
|
||
<a id="__codelineno-0-8" name="__codelineno-0-8" href="#__codelineno-0-8"></a> <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">m</span> <span class="o">+</span> <span class="mi">1</span><span class="p">):</span>
|
||
<a id="__codelineno-0-9" name="__codelineno-0-9" href="#__codelineno-0-9"></a> <span class="n">D</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="mi">0</span><span class="p">]</span> <span class="o">=</span> <span class="n">i</span>
|
||
<a id="__codelineno-0-10" name="__codelineno-0-10" href="#__codelineno-0-10"></a> <span class="k">for</span> <span class="n">j</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">n</span> <span class="o">+</span> <span class="mi">1</span><span class="p">):</span>
|
||
<a id="__codelineno-0-11" name="__codelineno-0-11" href="#__codelineno-0-11"></a> <span class="n">D</span><span class="p">[</span><span class="mi">0</span><span class="p">][</span><span class="n">j</span><span class="p">]</span> <span class="o">=</span> <span class="n">j</span>
|
||
<a id="__codelineno-0-12" name="__codelineno-0-12" href="#__codelineno-0-12"></a>
|
||
<a id="__codelineno-0-13" name="__codelineno-0-13" href="#__codelineno-0-13"></a> <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">m</span> <span class="o">+</span> <span class="mi">1</span><span class="p">):</span>
|
||
<a id="__codelineno-0-14" name="__codelineno-0-14" href="#__codelineno-0-14"></a> <span class="k">for</span> <span class="n">j</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">n</span> <span class="o">+</span> <span class="mi">1</span><span class="p">):</span>
|
||
<a id="__codelineno-0-15" name="__codelineno-0-15" href="#__codelineno-0-15"></a> <span class="k">if</span> <span class="n">s</span><span class="p">[</span><span class="n">i</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span> <span class="o">==</span> <span class="n">t</span><span class="p">[</span><span class="n">j</span><span class="o">-</span><span class="mi">1</span><span class="p">]:</span>
|
||
<a id="__codelineno-0-16" name="__codelineno-0-16" href="#__codelineno-0-16"></a> <span class="n">D</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">j</span><span class="p">]</span> <span class="o">=</span> <span class="n">D</span><span class="p">[</span><span class="n">i</span><span class="o">-</span><span class="mi">1</span><span class="p">][</span><span class="n">j</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span>
|
||
<a id="__codelineno-0-17" name="__codelineno-0-17" href="#__codelineno-0-17"></a> <span class="k">else</span><span class="p">:</span>
|
||
<a id="__codelineno-0-18" name="__codelineno-0-18" href="#__codelineno-0-18"></a> <span class="n">D</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">j</span><span class="p">]</span> <span class="o">=</span> <span class="mi">1</span> <span class="o">+</span> <span class="nb">min</span><span class="p">(</span><span class="n">D</span><span class="p">[</span><span class="n">i</span><span class="o">-</span><span class="mi">1</span><span class="p">][</span><span class="n">j</span><span class="p">],</span> <span class="n">D</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">j</span><span class="o">-</span><span class="mi">1</span><span class="p">],</span> <span class="n">D</span><span class="p">[</span><span class="n">i</span><span class="o">-</span><span class="mi">1</span><span class="p">][</span><span class="n">j</span><span class="o">-</span><span class="mi">1</span><span class="p">])</span>
|
||
<a id="__codelineno-0-19" name="__codelineno-0-19" href="#__codelineno-0-19"></a>
|
||
<a id="__codelineno-0-20" name="__codelineno-0-20" href="#__codelineno-0-20"></a> <span class="k">return</span> <span class="n">D</span><span class="p">[</span><span class="n">m</span><span class="p">][</span><span class="n">n</span><span class="p">]</span>
|
||
<a id="__codelineno-0-21" name="__codelineno-0-21" href="#__codelineno-0-21"></a>
|
||
<a id="__codelineno-0-22" name="__codelineno-0-22" href="#__codelineno-0-22"></a><span class="c1"># Test</span>
|
||
<a id="__codelineno-0-23" name="__codelineno-0-23" href="#__codelineno-0-23"></a><span class="n">pairs</span> <span class="o">=</span> <span class="p">[(</span><span class="s2">"kitten"</span><span class="p">,</span> <span class="s2">"sitting"</span><span class="p">),</span> <span class="p">(</span><span class="s2">"sunday"</span><span class="p">,</span> <span class="s2">"saturday"</span><span class="p">),</span> <span class="p">(</span><span class="s2">"hello"</span><span class="p">,</span> <span class="s2">"hallo"</span><span class="p">)]</span>
|
||
<a id="__codelineno-0-24" name="__codelineno-0-24" href="#__codelineno-0-24"></a><span class="k">for</span> <span class="n">s</span><span class="p">,</span> <span class="n">t</span> <span class="ow">in</span> <span class="n">pairs</span><span class="p">:</span>
|
||
<a id="__codelineno-0-25" name="__codelineno-0-25" href="#__codelineno-0-25"></a> <span class="nb">print</span><span class="p">(</span><span class="sa">f</span><span class="s2">"d('</span><span class="si">{</span><span class="n">s</span><span class="si">}</span><span class="s2">', '</span><span class="si">{</span><span class="n">t</span><span class="si">}</span><span class="s2">') = </span><span class="si">{</span><span class="n">edit_distance</span><span class="p">(</span><span class="n">s</span><span class="p">,</span><span class="w"> </span><span class="n">t</span><span class="p">)</span><span class="si">}</span><span class="s2">"</span><span class="p">)</span>
|
||
<a id="__codelineno-0-26" name="__codelineno-0-26" href="#__codelineno-0-26"></a>
|
||
<a id="__codelineno-0-27" name="__codelineno-0-27" href="#__codelineno-0-27"></a><span class="c1"># Simple spelling correction</span>
|
||
<a id="__codelineno-0-28" name="__codelineno-0-28" href="#__codelineno-0-28"></a><span class="n">dictionary</span> <span class="o">=</span> <span class="p">[</span><span class="s2">"the"</span><span class="p">,</span> <span class="s2">"their"</span><span class="p">,</span> <span class="s2">"there"</span><span class="p">,</span> <span class="s2">"then"</span><span class="p">,</span> <span class="s2">"than"</span><span class="p">,</span> <span class="s2">"this"</span><span class="p">,</span> <span class="s2">"that"</span><span class="p">,</span> <span class="s2">"these"</span><span class="p">,</span> <span class="s2">"those"</span><span class="p">]</span>
|
||
<a id="__codelineno-0-29" name="__codelineno-0-29" href="#__codelineno-0-29"></a><span class="n">misspelled</span> <span class="o">=</span> <span class="s2">"thier"</span>
|
||
<a id="__codelineno-0-30" name="__codelineno-0-30" href="#__codelineno-0-30"></a><span class="n">corrections</span> <span class="o">=</span> <span class="nb">sorted</span><span class="p">(</span><span class="n">dictionary</span><span class="p">,</span> <span class="n">key</span><span class="o">=</span><span class="k">lambda</span> <span class="n">w</span><span class="p">:</span> <span class="n">edit_distance</span><span class="p">(</span><span class="n">misspelled</span><span class="p">,</span> <span class="n">w</span><span class="p">))</span>
|
||
<a id="__codelineno-0-31" name="__codelineno-0-31" href="#__codelineno-0-31"></a><span class="nb">print</span><span class="p">(</span><span class="sa">f</span><span class="s2">"</span><span class="se">\n</span><span class="s2">Closest to '</span><span class="si">{</span><span class="n">misspelled</span><span class="si">}</span><span class="s2">': </span><span class="si">{</span><span class="n">corrections</span><span class="p">[:</span><span class="mi">3</span><span class="p">]</span><span class="si">}</span><span class="s2">"</span><span class="p">)</span>
|
||
</code></pre></div></p>
|
||
</li>
|
||
<li>
|
||
<p>从头实现BPE分词。从字符级词元开始，迭代地合并最频繁的对。
|
||
<div class="highlight"><pre><span></span><code><a id="__codelineno-1-1" name="__codelineno-1-1" href="#__codelineno-1-1"></a><span class="kn">from</span><span class="w"> </span><span class="nn">collections</span><span class="w"> </span><span class="kn">import</span> <span class="n">Counter</span>
|
||
<a id="__codelineno-1-2" name="__codelineno-1-2" href="#__codelineno-1-2"></a>
|
||
<a id="__codelineno-1-3" name="__codelineno-1-3" href="#__codelineno-1-3"></a><span class="k">def</span><span class="w"> </span><span class="nf">get_pairs</span><span class="p">(</span><span class="n">corpus</span><span class="p">):</span>
|
||
<a id="__codelineno-1-4" name="__codelineno-1-4" href="#__codelineno-1-4"></a><span class="w"> </span><span class="sd">"""Count adjacent token pairs across all words."""</span>
|
||
<a id="__codelineno-1-5" name="__codelineno-1-5" href="#__codelineno-1-5"></a> <span class="n">pairs</span> <span class="o">=</span> <span class="n">Counter</span><span class="p">()</span>
|
||
<a id="__codelineno-1-6" name="__codelineno-1-6" href="#__codelineno-1-6"></a> <span class="k">for</span> <span class="n">word</span><span class="p">,</span> <span class="n">freq</span> <span class="ow">in</span> <span class="n">corpus</span><span class="o">.</span><span class="n">items</span><span class="p">():</span>
|
||
<a id="__codelineno-1-7" name="__codelineno-1-7" href="#__codelineno-1-7"></a> <span class="n">symbols</span> <span class="o">=</span> <span class="n">word</span><span class="o">.</span><span class="n">split</span><span class="p">()</span>
|
||
<a id="__codelineno-1-8" name="__codelineno-1-8" href="#__codelineno-1-8"></a> <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">symbols</span><span class="p">)</span> <span class="o">-</span> <span class="mi">1</span><span class="p">):</span>
|
||
<a id="__codelineno-1-9" name="__codelineno-1-9" href="#__codelineno-1-9"></a> <span class="n">pairs</span><span class="p">[(</span><span class="n">symbols</span><span class="p">[</span><span class="n">i</span><span class="p">],</span> <span class="n">symbols</span><span class="p">[</span><span class="n">i</span><span class="o">+</span><span class="mi">1</span><span class="p">])]</span> <span class="o">+=</span> <span class="n">freq</span>
|
||
<a id="__codelineno-1-10" name="__codelineno-1-10" href="#__codelineno-1-10"></a> <span class="k">return</span> <span class="n">pairs</span>
|
||
<a id="__codelineno-1-11" name="__codelineno-1-11" href="#__codelineno-1-11"></a>
|
||
<a id="__codelineno-1-12" name="__codelineno-1-12" href="#__codelineno-1-12"></a><span class="k">def</span><span class="w"> </span><span class="nf">merge_pair</span><span class="p">(</span><span class="n">pair</span><span class="p">,</span> <span class="n">corpus</span><span class="p">):</span>
|
||
<a id="__codelineno-1-13" name="__codelineno-1-13" href="#__codelineno-1-13"></a><span class="w"> </span><span class="sd">"""Merge all occurrences of a pair in the corpus."""</span>
|
||
<a id="__codelineno-1-14" name="__codelineno-1-14" href="#__codelineno-1-14"></a> <span class="n">new_corpus</span> <span class="o">=</span> <span class="p">{}</span>
|
||
<a id="__codelineno-1-15" name="__codelineno-1-15" href="#__codelineno-1-15"></a> <span class="n">bigram</span> <span class="o">=</span> <span class="s1">' '</span><span class="o">.</span><span class="n">join</span><span class="p">(</span><span class="n">pair</span><span class="p">)</span>
|
||
<a id="__codelineno-1-16" name="__codelineno-1-16" href="#__codelineno-1-16"></a> <span class="n">replacement</span> <span class="o">=</span> <span class="s1">''</span><span class="o">.</span><span class="n">join</span><span class="p">(</span><span class="n">pair</span><span class="p">)</span>
|
||
<a id="__codelineno-1-17" name="__codelineno-1-17" href="#__codelineno-1-17"></a> <span class="k">for</span> <span class="n">word</span><span class="p">,</span> <span class="n">freq</span> <span class="ow">in</span> <span class="n">corpus</span><span class="o">.</span><span class="n">items</span><span class="p">():</span>
|
||
<a id="__codelineno-1-18" name="__codelineno-1-18" href="#__codelineno-1-18"></a> <span class="n">new_word</span> <span class="o">=</span> <span class="n">word</span><span class="o">.</span><span class="n">replace</span><span class="p">(</span><span class="n">bigram</span><span class="p">,</span> <span class="n">replacement</span><span class="p">)</span>
|
||
<a id="__codelineno-1-19" name="__codelineno-1-19" href="#__codelineno-1-19"></a> <span class="n">new_corpus</span><span class="p">[</span><span class="n">new_word</span><span class="p">]</span> <span class="o">=</span> <span class="n">freq</span>
|
||
<a id="__codelineno-1-20" name="__codelineno-1-20" href="#__codelineno-1-20"></a> <span class="k">return</span> <span class="n">new_corpus</span>
|
||
<a id="__codelineno-1-21" name="__codelineno-1-21" href="#__codelineno-1-21"></a>
|
||
<a id="__codelineno-1-22" name="__codelineno-1-22" href="#__codelineno-1-22"></a><span class="c1"># Training corpus with word frequencies</span>
|
||
<a id="__codelineno-1-23" name="__codelineno-1-23" href="#__codelineno-1-23"></a><span class="n">text</span> <span class="o">=</span> <span class="s2">"low low low low low lower lower newest newest newest newest newest newest"</span>
|
||
<a id="__codelineno-1-24" name="__codelineno-1-24" href="#__codelineno-1-24"></a><span class="n">word_freqs</span> <span class="o">=</span> <span class="n">Counter</span><span class="p">(</span><span class="n">text</span><span class="o">.</span><span class="n">split</span><span class="p">())</span>
|
||
<a id="__codelineno-1-25" name="__codelineno-1-25" href="#__codelineno-1-25"></a><span class="c1"># Initialise: split each word into characters with end-of-word marker</span>
|
||
<a id="__codelineno-1-26" name="__codelineno-1-26" href="#__codelineno-1-26"></a><span class="n">corpus</span> <span class="o">=</span> <span class="p">{</span><span class="s1">' '</span><span class="o">.</span><span class="n">join</span><span class="p">(</span><span class="n">word</span><span class="p">)</span> <span class="o">+</span> <span class="s1">' _'</span><span class="p">:</span> <span class="n">freq</span> <span class="k">for</span> <span class="n">word</span><span class="p">,</span> <span class="n">freq</span> <span class="ow">in</span> <span class="n">word_freqs</span><span class="o">.</span><span class="n">items</span><span class="p">()}</span>
|
||
<a id="__codelineno-1-27" name="__codelineno-1-27" href="#__codelineno-1-27"></a>
|
||
<a id="__codelineno-1-28" name="__codelineno-1-28" href="#__codelineno-1-28"></a><span class="nb">print</span><span class="p">(</span><span class="s2">"Initial corpus:"</span><span class="p">)</span>
|
||
<a id="__codelineno-1-29" name="__codelineno-1-29" href="#__codelineno-1-29"></a><span class="k">for</span> <span class="n">word</span><span class="p">,</span> <span class="n">freq</span> <span class="ow">in</span> <span class="n">corpus</span><span class="o">.</span><span class="n">items</span><span class="p">():</span>
|
||
<a id="__codelineno-1-30" name="__codelineno-1-30" href="#__codelineno-1-30"></a> <span class="nb">print</span><span class="p">(</span><span class="sa">f</span><span class="s2">" </span><span class="si">{</span><span class="n">word</span><span class="si">}</span><span class="s2">: </span><span class="si">{</span><span class="n">freq</span><span class="si">}</span><span class="s2">"</span><span class="p">)</span>
|
||
<a id="__codelineno-1-31" name="__codelineno-1-31" href="#__codelineno-1-31"></a>
|
||
<a id="__codelineno-1-32" name="__codelineno-1-32" href="#__codelineno-1-32"></a><span class="c1"># Run BPE for 10 merges</span>
|
||
<a id="__codelineno-1-33" name="__codelineno-1-33" href="#__codelineno-1-33"></a><span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">10</span><span class="p">):</span>
|
||
<a id="__codelineno-1-34" name="__codelineno-1-34" href="#__codelineno-1-34"></a> <span class="n">pairs</span> <span class="o">=</span> <span class="n">get_pairs</span><span class="p">(</span><span class="n">corpus</span><span class="p">)</span>
|
||
<a id="__codelineno-1-35" name="__codelineno-1-35" href="#__codelineno-1-35"></a> <span class="k">if</span> <span class="ow">not</span> <span class="n">pairs</span><span class="p">:</span>
|
||
<a id="__codelineno-1-36" name="__codelineno-1-36" href="#__codelineno-1-36"></a> <span class="k">break</span>
|
||
<a id="__codelineno-1-37" name="__codelineno-1-37" href="#__codelineno-1-37"></a> <span class="n">best_pair</span> <span class="o">=</span> <span class="nb">max</span><span class="p">(</span><span class="n">pairs</span><span class="p">,</span> <span class="n">key</span><span class="o">=</span><span class="n">pairs</span><span class="o">.</span><span class="n">get</span><span class="p">)</span>
|
||
<a id="__codelineno-1-38" name="__codelineno-1-38" href="#__codelineno-1-38"></a> <span class="n">corpus</span> <span class="o">=</span> <span class="n">merge_pair</span><span class="p">(</span><span class="n">best_pair</span><span class="p">,</span> <span class="n">corpus</span><span class="p">)</span>
|
||
<a id="__codelineno-1-39" name="__codelineno-1-39" href="#__codelineno-1-39"></a> <span class="nb">print</span><span class="p">(</span><span class="sa">f</span><span class="s2">"</span><span class="se">\n</span><span class="s2">Merge </span><span class="si">{</span><span class="n">i</span><span class="o">+</span><span class="mi">1</span><span class="si">}</span><span class="s2">: </span><span class="si">{</span><span class="n">best_pair</span><span class="si">}</span><span class="s2"> (freq=</span><span class="si">{</span><span class="n">pairs</span><span class="p">[</span><span class="n">best_pair</span><span class="p">]</span><span class="si">}</span><span class="s2">)"</span><span class="p">)</span>
|
||
<a id="__codelineno-1-40" name="__codelineno-1-40" href="#__codelineno-1-40"></a> <span class="k">for</span> <span class="n">word</span><span class="p">,</span> <span class="n">freq</span> <span class="ow">in</span> <span class="n">corpus</span><span class="o">.</span><span class="n">items</span><span class="p">():</span>
|
||
<a id="__codelineno-1-41" name="__codelineno-1-41" href="#__codelineno-1-41"></a> <span class="nb">print</span><span class="p">(</span><span class="sa">f</span><span class="s2">" </span><span class="si">{</span><span class="n">word</span><span class="si">}</span><span class="s2">: </span><span class="si">{</span><span class="n">freq</span><span class="si">}</span><span class="s2">"</span><span class="p">)</span>
|
||
</code></pre></div></p>
|
||
</li>
|
||
<li>
|
||
<p>构建一个二元语言模型，并计算测试句子的困惑度。尝试拉普拉斯平滑。
|
||
<div class="highlight"><pre><span></span><code><a id="__codelineno-2-1" name="__codelineno-2-1" href="#__codelineno-2-1"></a><span class="kn">from</span><span class="w"> </span><span class="nn">collections</span><span class="w"> </span><span class="kn">import</span> <span class="n">Counter</span><span class="p">,</span> <span class="n">defaultdict</span>
|
||
<a id="__codelineno-2-2" name="__codelineno-2-2" href="#__codelineno-2-2"></a><span class="kn">import</span><span class="w"> </span><span class="nn">math</span>
|
||
<a id="__codelineno-2-3" name="__codelineno-2-3" href="#__codelineno-2-3"></a>
|
||
<a id="__codelineno-2-4" name="__codelineno-2-4" href="#__codelineno-2-4"></a><span class="c1"># Training corpus</span>
|
||
<a id="__codelineno-2-5" name="__codelineno-2-5" href="#__codelineno-2-5"></a><span class="n">train</span> <span class="o">=</span> <span class="s2">"""the cat sat on the mat . the dog chased the cat .</span>
|
||
<a id="__codelineno-2-6" name="__codelineno-2-6" href="#__codelineno-2-6"></a><span class="s2">the cat ran from the dog . a dog sat on a mat ."""</span><span class="o">.</span><span class="n">split</span><span class="p">()</span>
|
||
<a id="__codelineno-2-7" name="__codelineno-2-7" href="#__codelineno-2-7"></a>
|
||
<a id="__codelineno-2-8" name="__codelineno-2-8" href="#__codelineno-2-8"></a><span class="c1"># Count bigrams and unigrams</span>
|
||
<a id="__codelineno-2-9" name="__codelineno-2-9" href="#__codelineno-2-9"></a><span class="n">bigrams</span> <span class="o">=</span> <span class="n">Counter</span><span class="p">(</span><span class="nb">zip</span><span class="p">(</span><span class="n">train</span><span class="p">[:</span><span class="o">-</span><span class="mi">1</span><span class="p">],</span> <span class="n">train</span><span class="p">[</span><span class="mi">1</span><span class="p">:]))</span>
|
||
<a id="__codelineno-2-10" name="__codelineno-2-10" href="#__codelineno-2-10"></a><span class="n">unigrams</span> <span class="o">=</span> <span class="n">Counter</span><span class="p">(</span><span class="n">train</span><span class="p">)</span>
|
||
<a id="__codelineno-2-11" name="__codelineno-2-11" href="#__codelineno-2-11"></a><span class="n">vocab_size</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="nb">set</span><span class="p">(</span><span class="n">train</span><span class="p">))</span>
|
||
<a id="__codelineno-2-12" name="__codelineno-2-12" href="#__codelineno-2-12"></a>
|
||
<a id="__codelineno-2-13" name="__codelineno-2-13" href="#__codelineno-2-13"></a><span class="k">def</span><span class="w"> </span><span class="nf">bigram_prob</span><span class="p">(</span><span class="n">w2</span><span class="p">,</span> <span class="n">w1</span><span class="p">,</span> <span class="n">alpha</span><span class="o">=</span><span class="mi">0</span><span class="p">):</span>
|
||
<a id="__codelineno-2-14" name="__codelineno-2-14" href="#__codelineno-2-14"></a><span class="w"> </span><span class="sd">"""P(w2 | w1) with optional Laplace smoothing."""</span>
|
||
<a id="__codelineno-2-15" name="__codelineno-2-15" href="#__codelineno-2-15"></a> <span class="k">return</span> <span class="p">(</span><span class="n">bigrams</span><span class="p">[(</span><span class="n">w1</span><span class="p">,</span> <span class="n">w2</span><span class="p">)]</span> <span class="o">+</span> <span class="n">alpha</span><span class="p">)</span> <span class="o">/</span> <span class="p">(</span><span class="n">unigrams</span><span class="p">[</span><span class="n">w1</span><span class="p">]</span> <span class="o">+</span> <span class="n">alpha</span> <span class="o">*</span> <span class="n">vocab_size</span><span class="p">)</span>
|
||
<a id="__codelineno-2-16" name="__codelineno-2-16" href="#__codelineno-2-16"></a>
|
||
<a id="__codelineno-2-17" name="__codelineno-2-17" href="#__codelineno-2-17"></a><span class="c1"># Compute perplexity</span>
|
||
<a id="__codelineno-2-18" name="__codelineno-2-18" href="#__codelineno-2-18"></a><span class="n">test</span> <span class="o">=</span> <span class="s2">"the cat sat on a mat ."</span><span class="o">.</span><span class="n">split</span><span class="p">()</span>
|
||
<a id="__codelineno-2-19" name="__codelineno-2-19" href="#__codelineno-2-19"></a>
|
||
<a id="__codelineno-2-20" name="__codelineno-2-20" href="#__codelineno-2-20"></a><span class="k">for</span> <span class="n">alpha</span> <span class="ow">in</span> <span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mf">0.1</span><span class="p">]:</span>
|
||
<a id="__codelineno-2-21" name="__codelineno-2-21" href="#__codelineno-2-21"></a> <span class="n">log_prob</span> <span class="o">=</span> <span class="mi">0</span>
|
||
<a id="__codelineno-2-22" name="__codelineno-2-22" href="#__codelineno-2-22"></a> <span class="k">for</span> <span class="n">w1</span><span class="p">,</span> <span class="n">w2</span> <span class="ow">in</span> <span class="nb">zip</span><span class="p">(</span><span class="n">test</span><span class="p">[:</span><span class="o">-</span><span class="mi">1</span><span class="p">],</span> <span class="n">test</span><span class="p">[</span><span class="mi">1</span><span class="p">:]):</span>
|
||
<a id="__codelineno-2-23" name="__codelineno-2-23" href="#__codelineno-2-23"></a> <span class="n">p</span> <span class="o">=</span> <span class="n">bigram_prob</span><span class="p">(</span><span class="n">w2</span><span class="p">,</span> <span class="n">w1</span><span class="p">,</span> <span class="n">alpha</span><span class="o">=</span><span class="n">alpha</span><span class="p">)</span>
|
||
<a id="__codelineno-2-24" name="__codelineno-2-24" href="#__codelineno-2-24"></a> <span class="k">if</span> <span class="n">p</span> <span class="o">></span> <span class="mi">0</span><span class="p">:</span>
|
||
<a id="__codelineno-2-25" name="__codelineno-2-25" href="#__codelineno-2-25"></a> <span class="n">log_prob</span> <span class="o">+=</span> <span class="n">math</span><span class="o">.</span><span class="n">log</span><span class="p">(</span><span class="n">p</span><span class="p">)</span>
|
||
<a id="__codelineno-2-26" name="__codelineno-2-26" href="#__codelineno-2-26"></a> <span class="k">else</span><span class="p">:</span>
|
||
<a id="__codelineno-2-27" name="__codelineno-2-27" href="#__codelineno-2-27"></a> <span class="n">log_prob</span> <span class="o">+=</span> <span class="nb">float</span><span class="p">(</span><span class="s1">'-inf'</span><span class="p">)</span>
|
||
<a id="__codelineno-2-28" name="__codelineno-2-28" href="#__codelineno-2-28"></a>
|
||
<a id="__codelineno-2-29" name="__codelineno-2-29" href="#__codelineno-2-29"></a> <span class="n">ppl</span> <span class="o">=</span> <span class="n">math</span><span class="o">.</span><span class="n">exp</span><span class="p">(</span><span class="o">-</span><span class="n">log_prob</span> <span class="o">/</span> <span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">test</span><span class="p">)</span> <span class="o">-</span> <span class="mi">1</span><span class="p">))</span> <span class="k">if</span> <span class="n">log_prob</span> <span class="o">></span> <span class="nb">float</span><span class="p">(</span><span class="s1">'-inf'</span><span class="p">)</span> <span class="k">else</span> <span class="nb">float</span><span class="p">(</span><span class="s1">'inf'</span><span class="p">)</span>
|
||
<a id="__codelineno-2-30" name="__codelineno-2-30" href="#__codelineno-2-30"></a> <span class="nb">print</span><span class="p">(</span><span class="sa">f</span><span class="s2">"Smoothing α=</span><span class="si">{</span><span class="n">alpha</span><span class="si">}</span><span class="s2">: perplexity = </span><span class="si">{</span><span class="n">ppl</span><span class="si">:</span><span class="s2">.2f</span><span class="si">}</span><span class="s2">"</span><span class="p">)</span>
|
||
</code></pre></div></p>
|
||
</li>
|
||
<li>
|
||
<p>从头实现TF-IDF，并使用余弦相似度找到与查询最相似的文档。
|
||
<div class="highlight"><pre><span></span><code><a id="__codelineno-3-1" name="__codelineno-3-1" href="#__codelineno-3-1"></a><span class="kn">import</span><span class="w"> </span><span class="nn">jax.numpy</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="nn">jnp</span>
|
||
<a id="__codelineno-3-2" name="__codelineno-3-2" href="#__codelineno-3-2"></a><span class="kn">import</span><span class="w"> </span><span class="nn">math</span>
|
||
<a id="__codelineno-3-3" name="__codelineno-3-3" href="#__codelineno-3-3"></a><span class="kn">from</span><span class="w"> </span><span class="nn">collections</span><span class="w"> </span><span class="kn">import</span> <span class="n">Counter</span>
|
||
<a id="__codelineno-3-4" name="__codelineno-3-4" href="#__codelineno-3-4"></a>
|
||
<a id="__codelineno-3-5" name="__codelineno-3-5" href="#__codelineno-3-5"></a><span class="n">documents</span> <span class="o">=</span> <span class="p">[</span>
|
||
<a id="__codelineno-3-6" name="__codelineno-3-6" href="#__codelineno-3-6"></a> <span class="s2">"the cat sat on the mat"</span><span class="p">,</span>
|
||
<a id="__codelineno-3-7" name="__codelineno-3-7" href="#__codelineno-3-7"></a> <span class="s2">"the dog chased the cat around the park"</span><span class="p">,</span>
|
||
<a id="__codelineno-3-8" name="__codelineno-3-8" href="#__codelineno-3-8"></a> <span class="s2">"a mat was placed on the floor by the door"</span><span class="p">,</span>
|
||
<a id="__codelineno-3-9" name="__codelineno-3-9" href="#__codelineno-3-9"></a> <span class="s2">"the quick brown fox jumped over the lazy dog"</span><span class="p">,</span>
|
||
<a id="__codelineno-3-10" name="__codelineno-3-10" href="#__codelineno-3-10"></a><span class="p">]</span>
|
||
<a id="__codelineno-3-11" name="__codelineno-3-11" href="#__codelineno-3-11"></a>
|
||
<a id="__codelineno-3-12" name="__codelineno-3-12" href="#__codelineno-3-12"></a><span class="c1"># Build vocabulary</span>
|
||
<a id="__codelineno-3-13" name="__codelineno-3-13" href="#__codelineno-3-13"></a><span class="n">vocab</span> <span class="o">=</span> <span class="nb">sorted</span><span class="p">(</span><span class="nb">set</span><span class="p">(</span><span class="n">word</span> <span class="k">for</span> <span class="n">doc</span> <span class="ow">in</span> <span class="n">documents</span> <span class="k">for</span> <span class="n">word</span> <span class="ow">in</span> <span class="n">doc</span><span class="o">.</span><span class="n">split</span><span class="p">()))</span>
|
||
<a id="__codelineno-3-14" name="__codelineno-3-14" href="#__codelineno-3-14"></a><span class="n">word_to_idx</span> <span class="o">=</span> <span class="p">{</span><span class="n">w</span><span class="p">:</span> <span class="n">i</span> <span class="k">for</span> <span class="n">i</span><span class="p">,</span> <span class="n">w</span> <span class="ow">in</span> <span class="nb">enumerate</span><span class="p">(</span><span class="n">vocab</span><span class="p">)}</span>
|
||
<a id="__codelineno-3-15" name="__codelineno-3-15" href="#__codelineno-3-15"></a><span class="n">V</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">vocab</span><span class="p">)</span>
|
||
<a id="__codelineno-3-16" name="__codelineno-3-16" href="#__codelineno-3-16"></a><span class="n">N</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">documents</span><span class="p">)</span>
|
||
<a id="__codelineno-3-17" name="__codelineno-3-17" href="#__codelineno-3-17"></a>
|
||
<a id="__codelineno-3-18" name="__codelineno-3-18" href="#__codelineno-3-18"></a><span class="c1"># Compute TF-IDF matrix</span>
|
||
<a id="__codelineno-3-19" name="__codelineno-3-19" href="#__codelineno-3-19"></a><span class="n">doc_freq</span> <span class="o">=</span> <span class="n">Counter</span><span class="p">()</span>
|
||
<a id="__codelineno-3-20" name="__codelineno-3-20" href="#__codelineno-3-20"></a><span class="k">for</span> <span class="n">doc</span> <span class="ow">in</span> <span class="n">documents</span><span class="p">:</span>
|
||
<a id="__codelineno-3-21" name="__codelineno-3-21" href="#__codelineno-3-21"></a> <span class="k">for</span> <span class="n">word</span> <span class="ow">in</span> <span class="nb">set</span><span class="p">(</span><span class="n">doc</span><span class="o">.</span><span class="n">split</span><span class="p">()):</span>
|
||
<a id="__codelineno-3-22" name="__codelineno-3-22" href="#__codelineno-3-22"></a> <span class="n">doc_freq</span><span class="p">[</span><span class="n">word</span><span class="p">]</span> <span class="o">+=</span> <span class="mi">1</span>
|
||
<a id="__codelineno-3-23" name="__codelineno-3-23" href="#__codelineno-3-23"></a>
|
||
<a id="__codelineno-3-24" name="__codelineno-3-24" href="#__codelineno-3-24"></a><span class="n">tfidf_matrix</span> <span class="o">=</span> <span class="n">jnp</span><span class="o">.</span><span class="n">zeros</span><span class="p">((</span><span class="n">N</span><span class="p">,</span> <span class="n">V</span><span class="p">))</span>
|
||
<a id="__codelineno-3-25" name="__codelineno-3-25" href="#__codelineno-3-25"></a><span class="k">for</span> <span class="n">i</span><span class="p">,</span> <span class="n">doc</span> <span class="ow">in</span> <span class="nb">enumerate</span><span class="p">(</span><span class="n">documents</span><span class="p">):</span>
|
||
<a id="__codelineno-3-26" name="__codelineno-3-26" href="#__codelineno-3-26"></a> <span class="n">word_counts</span> <span class="o">=</span> <span class="n">Counter</span><span class="p">(</span><span class="n">doc</span><span class="o">.</span><span class="n">split</span><span class="p">())</span>
|
||
<a id="__codelineno-3-27" name="__codelineno-3-27" href="#__codelineno-3-27"></a> <span class="k">for</span> <span class="n">word</span><span class="p">,</span> <span class="n">count</span> <span class="ow">in</span> <span class="n">word_counts</span><span class="o">.</span><span class="n">items</span><span class="p">():</span>
|
||
<a id="__codelineno-3-28" name="__codelineno-3-28" href="#__codelineno-3-28"></a> <span class="n">tf</span> <span class="o">=</span> <span class="mi">1</span> <span class="o">+</span> <span class="n">math</span><span class="o">.</span><span class="n">log</span><span class="p">(</span><span class="n">count</span><span class="p">)</span>
|
||
<a id="__codelineno-3-29" name="__codelineno-3-29" href="#__codelineno-3-29"></a> <span class="n">idf</span> <span class="o">=</span> <span class="n">math</span><span class="o">.</span><span class="n">log</span><span class="p">(</span><span class="n">N</span> <span class="o">/</span> <span class="n">doc_freq</span><span class="p">[</span><span class="n">word</span><span class="p">])</span>
|
||
<a id="__codelineno-3-30" name="__codelineno-3-30" href="#__codelineno-3-30"></a> <span class="n">j</span> <span class="o">=</span> <span class="n">word_to_idx</span><span class="p">[</span><span class="n">word</span><span class="p">]</span>
|
||
<a id="__codelineno-3-31" name="__codelineno-3-31" href="#__codelineno-3-31"></a> <span class="n">tfidf_matrix</span> <span class="o">=</span> <span class="n">tfidf_matrix</span><span class="o">.</span><span class="n">at</span><span class="p">[</span><span class="n">i</span><span class="p">,</span> <span class="n">j</span><span class="p">]</span><span class="o">.</span><span class="n">set</span><span class="p">(</span><span class="n">tf</span> <span class="o">*</span> <span class="n">idf</span><span class="p">)</span>
|
||
<a id="__codelineno-3-32" name="__codelineno-3-32" href="#__codelineno-3-32"></a>
|
||
<a id="__codelineno-3-33" name="__codelineno-3-33" href="#__codelineno-3-33"></a><span class="c1"># Query</span>
|
||
<a id="__codelineno-3-34" name="__codelineno-3-34" href="#__codelineno-3-34"></a><span class="n">query</span> <span class="o">=</span> <span class="s2">"cat on the mat"</span>
|
||
<a id="__codelineno-3-35" name="__codelineno-3-35" href="#__codelineno-3-35"></a><span class="n">query_vec</span> <span class="o">=</span> <span class="n">jnp</span><span class="o">.</span><span class="n">zeros</span><span class="p">(</span><span class="n">V</span><span class="p">)</span>
|
||
<a id="__codelineno-3-36" name="__codelineno-3-36" href="#__codelineno-3-36"></a><span class="n">query_counts</span> <span class="o">=</span> <span class="n">Counter</span><span class="p">(</span><span class="n">query</span><span class="o">.</span><span class="n">split</span><span class="p">())</span>
|
||
<a id="__codelineno-3-37" name="__codelineno-3-37" href="#__codelineno-3-37"></a><span class="k">for</span> <span class="n">word</span><span class="p">,</span> <span class="n">count</span> <span class="ow">in</span> <span class="n">query_counts</span><span class="o">.</span><span class="n">items</span><span class="p">():</span>
|
||
<a id="__codelineno-3-38" name="__codelineno-3-38" href="#__codelineno-3-38"></a> <span class="k">if</span> <span class="n">word</span> <span class="ow">in</span> <span class="n">word_to_idx</span><span class="p">:</span>
|
||
<a id="__codelineno-3-39" name="__codelineno-3-39" href="#__codelineno-3-39"></a> <span class="n">tf</span> <span class="o">=</span> <span class="mi">1</span> <span class="o">+</span> <span class="n">math</span><span class="o">.</span><span class="n">log</span><span class="p">(</span><span class="n">count</span><span class="p">)</span>
|
||
<a id="__codelineno-3-40" name="__codelineno-3-40" href="#__codelineno-3-40"></a> <span class="n">idf</span> <span class="o">=</span> <span class="n">math</span><span class="o">.</span><span class="n">log</span><span class="p">(</span><span class="n">N</span> <span class="o">/</span> <span class="n">doc_freq</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="n">word</span><span class="p">,</span> <span class="mi">1</span><span class="p">))</span>
|
||
<a id="__codelineno-3-41" name="__codelineno-3-41" href="#__codelineno-3-41"></a> <span class="n">query_vec</span> <span class="o">=</span> <span class="n">query_vec</span><span class="o">.</span><span class="n">at</span><span class="p">[</span><span class="n">word_to_idx</span><span class="p">[</span><span class="n">word</span><span class="p">]]</span><span class="o">.</span><span class="n">set</span><span class="p">(</span><span class="n">tf</span> <span class="o">*</span> <span class="n">idf</span><span class="p">)</span>
|
||
<a id="__codelineno-3-42" name="__codelineno-3-42" href="#__codelineno-3-42"></a>
|
||
<a id="__codelineno-3-43" name="__codelineno-3-43" href="#__codelineno-3-43"></a><span class="c1"># Cosine similarity (from chapter 01)</span>
|
||
<a id="__codelineno-3-44" name="__codelineno-3-44" href="#__codelineno-3-44"></a><span class="k">def</span><span class="w"> </span><span class="nf">cosine_sim</span><span class="p">(</span><span class="n">a</span><span class="p">,</span> <span class="n">b</span><span class="p">):</span>
|
||
<a id="__codelineno-3-45" name="__codelineno-3-45" href="#__codelineno-3-45"></a> <span class="k">return</span> <span class="n">jnp</span><span class="o">.</span><span class="n">dot</span><span class="p">(</span><span class="n">a</span><span class="p">,</span> <span class="n">b</span><span class="p">)</span> <span class="o">/</span> <span class="p">(</span><span class="n">jnp</span><span class="o">.</span><span class="n">linalg</span><span class="o">.</span><span class="n">norm</span><span class="p">(</span><span class="n">a</span><span class="p">)</span> <span class="o">*</span> <span class="n">jnp</span><span class="o">.</span><span class="n">linalg</span><span class="o">.</span><span class="n">norm</span><span class="p">(</span><span class="n">b</span><span class="p">)</span> <span class="o">+</span> <span class="mf">1e-8</span><span class="p">)</span>
|
||
<a id="__codelineno-3-46" name="__codelineno-3-46" href="#__codelineno-3-46"></a>
|
||
<a id="__codelineno-3-47" name="__codelineno-3-47" href="#__codelineno-3-47"></a><span class="nb">print</span><span class="p">(</span><span class="sa">f</span><span class="s2">"Query: '</span><span class="si">{</span><span class="n">query</span><span class="si">}</span><span class="s2">'</span><span class="se">\n</span><span class="s2">"</span><span class="p">)</span>
|
||
<a id="__codelineno-3-48" name="__codelineno-3-48" href="#__codelineno-3-48"></a><span class="k">for</span> <span class="n">i</span><span class="p">,</span> <span class="n">doc</span> <span class="ow">in</span> <span class="nb">enumerate</span><span class="p">(</span><span class="n">documents</span><span class="p">):</span>
|
||
<a id="__codelineno-3-49" name="__codelineno-3-49" href="#__codelineno-3-49"></a> <span class="n">sim</span> <span class="o">=</span> <span class="n">cosine_sim</span><span class="p">(</span><span class="n">query_vec</span><span class="p">,</span> <span class="n">tfidf_matrix</span><span class="p">[</span><span class="n">i</span><span class="p">])</span>
|
||
<a id="__codelineno-3-50" name="__codelineno-3-50" href="#__codelineno-3-50"></a> <span class="nb">print</span><span class="p">(</span><span class="sa">f</span><span class="s2">" Doc </span><span class="si">{</span><span class="n">i</span><span class="si">}</span><span class="s2"> (sim=</span><span class="si">{</span><span class="n">sim</span><span class="si">:</span><span class="s2">.3f</span><span class="si">}</span><span class="s2">): '</span><span class="si">{</span><span class="n">doc</span><span class="si">}</span><span class="s2">'"</span><span class="p">)</span>
|
||
</code></pre></div></p>
|
||
</li>
|
||
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|
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