https://rubatotree.github.io/blog/tags/tcs/Recent content in TCS on Umbrella Coffeehttps://rubatotree.github.io/blog/images/og-default.pnghttps://rubatotree.github.io/blog/images/og-default.pngHugoen-usMon, 08 Jun 2026 00:00:00 +0800https://rubatotree.github.io/blog/posts/big-data-alg-notes-1/Mon, 08 Jun 2026 00:00:00 +0800https://rubatotree.github.io/blog/posts/big-data-alg-notes-1/<p>这是我在 2026 年春季于中科大学习<a href="https://hu-ding.github.io/index.html" target="_blank" rel="noopener noreferrer"><span style="color: #59a4ff;"><span style="text-decoration: underline">丁虎</span></span></a>老师的<a href="https://hu-ding.github.io/data%20course_2026.html" target="_blank" rel="noopener noreferrer"><span style="color: #59a4ff;"><span style="text-decoration: underline">《大数据算法》</span></span></a>课程时整理的期末考试复习笔记。非常喜欢的好课。只是可惜讲义编写得比较潦草。这里的笔记尽可能指出讲义中各种概念的几何意义与机器学习意义，并尝试找出各种定义、定理的动机。</p> <h2 id="loc-1">6 VC 维</h2> <h3 id="loc-2">VC 维及其几何概念</h3> <p>VC 维和核心集（coreset）是描述模型表达能力的数学工具。</p> <p>直观来看，VC 维描述的是一个分类器在任意的正负类指定下，能够区分（称为“打散”）的最大数据点数目。如：</p> <p></p> <ul> <li>在二维平面上，二维直线可以打散（不共线的）3 个点，但不能打散（任何分布下的）4 个点，因此二维直线的 VC 维为 3；</li> <li>X 是二维平面 <span role="math"><svg class="typst-frame" style="overflow: visible; width: 1.2372999999999998em; height: 0.683em;" viewBox="0 0 16.70355 9.2205" width="16.70355pt" height="9.2205pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:h5="http://www.w3.org/1999/xhtml"><g><g class="typst-text" transform="matrix(1 0 0 -1 0 9.2205)"><use xlink:href="#gB56EE940A3E6922E94D0196ED1F53569" x="0" y="0" fill="#000000" fill-rule="nonzero"/></g><g class="typst-text" transform="matrix(1 0 0 -1 10.570500000000001 4.320000000000001)"><use xlink:href="#g65F6F2B57D840F34A42B9F03EDDAF329" x="0" y="0" fill="#000000" fill-rule="nonzero"/></g></g><defs id="glyph"><symbol id="gB56EE940A3E6922E94D0196ED1F53569" overflow="visible"><path d="M 0 0m 8.721001 7.4655004 c 0 -0.4590001 -0.21600056 -1.3905001 -0.7425003 -1.9170003 c -0.3510003 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