https://www.chenk.top/en/tags/potential-functions/Recent content in Potential Functions on Chen Kai BlogHugoenWed, 04 Feb 2026 09:00:00 +0000https://www.chenk.top/en/ml-math-derivations/16-conditional-random-fields/Wed, 04 Feb 2026 09:00:00 +0000https://www.chenk.top/en/ml-math-derivations/16-conditional-random-fields/<p><figure class="article-figure"> <img src="https://blog-pic-ck.oss-cn-beijing.aliyuncs.com/posts/en/ml-math-derivations/16-Conditional-Random-Fields/illustration_1.png" alt="ML Math Derivations (16): Conditional Random Fields — Chapter overview" loading="lazy" decoding="async" class="content-image"> </figure> </p> <hr> <h2 id="what-you-will-learn" class="heading-anchor">What You Will Learn<a href="#what-you-will-learn" class="heading-link" aria-label="Permalink to this section" title="Copy link to this section">#</a> </h2><p>Named entity recognition, POS tagging, information extraction — every one of these tasks asks you to label each element of a sequence. HMMs (<a href="https://www.chenk.top/en/ml-math-derivations/15-hidden-markov-models">Part 15</a> ) attack this problem <strong>generatively</strong> by modelling the joint distribution <span class="math-inline">$P(\mathbf{X},\mathbf{Y})$</span> , but to make the joint factorise they pay a steep price: each observation is assumed independent of everything except its own hidden label. In real text, whether <em>bank</em> is a noun or a verb depends on the preceding and following words, the suffix, capitalization, and dictionary lookups — all these features together.</p>