摘要: 给定a,b,扩展欧几里得算法求得最大公约数的同时,还会给出ax+by=gcd(a,b)的整数解x,y 假设 $$ d_{i-2}=d_{i-1} c_i+d_i \ d_{i-1}=d_ic_{i+1}+d_{i+1} $$ 假设a,b的最大公约数为$g$,当某一步的$d_{i-1}=0$时,$1d 阅读全文
posted @ 2022-08-26 15:24 19376273 阅读(3) 评论(0) 推荐(0) 编辑
摘要: Independent Components Analysis Ambiguity ICA is ambiguous to scaling and permutation. but usually it doesn't matter. As long as the data is not Gauss 阅读全文
posted @ 2022-08-25 22:43 19376273 阅读(5) 评论(0) 推荐(0) 编辑
摘要: Principal Components Analysis Intuition PCA tries to identify the subspace in which the data approximately lies. Intuitively, we choose a direction fo 阅读全文
posted @ 2022-08-25 19:49 19376273 阅读(1) 评论(0) 推荐(0) 编辑
摘要: Decision Tree Greedy, Top-down, Recurrent Classification Tree misclassification loss is not suitable for decision tree loss, because $$ L(R_p) - (\lam 阅读全文
posted @ 2022-08-24 22:18 19376273 阅读(2) 评论(0) 推荐(0) 编辑
摘要: Factor Analysis Background when m (number of samples) < n (dimension of samples), the covariance matrix might be singular. So it is necessary to find 阅读全文
posted @ 2022-08-23 18:13 19376273 阅读(6) 评论(0) 推荐(0) 编辑
摘要: EM Algorithm Jensen's inequality convex function: $f''(x) \ge 0$ or $H \ge 0$ (Hessian matrix when x is a vector) $$ E[f(x)] \ge f(EX) $$ EM Algorithm 阅读全文
posted @ 2022-08-22 19:23 19376273 阅读(2) 评论(0) 推荐(0) 编辑
摘要: Reinforcement Learning Background Credit Assignment Problem: Explore how actions in an action sequence contribute to the outcome finally. MDP(Markov D 阅读全文
posted @ 2022-08-17 21:08 19376273 阅读(7) 评论(0) 推荐(0) 编辑
摘要: Learning Mathematical Theorem Feature Selection If we have n features, the VC dimension if hypothesis class would be O(n), if n>>m, over-fitting would 阅读全文
posted @ 2022-08-15 16:16 19376273 阅读(6) 评论(0) 推荐(0) 编辑
摘要: Support Vector Machine Two Margins Functional Margin $\gamma$ and Geometrical Margin $\hat{\gamma}$ $$ \hat{\gamma^{(i)}}=\frac{\gamma^{(i)}}{||w||} $ 阅读全文
posted @ 2022-08-13 10:56 19376273 阅读(2) 评论(0) 推荐(0) 编辑
摘要: Error Theorem in ML Basic Concepts $$ \varepsilon(h) = \text{Generalization Error} = E_{(x,y)\sim D}[1(h(x) \neq y)] $$ $$ \hat{\varepsilon}(h)=\text{ 阅读全文
posted @ 2022-08-12 15:30 19376273 阅读(6) 评论(0) 推荐(0) 编辑