From c28d377483b0ac898a415c699a31fada16be191d Mon Sep 17 00:00:00 2001 From: BlitherBoom812 Date: Mon, 20 May 2024 17:14:50 +0800 Subject: [PATCH] 20240520 --- source/_posts/AI.md | 84 +++++++++++++++++++++++++++++ source/_posts/Antenna.md | 1 + source/images/AI/1716191759894.png | Bin 0 -> 555073 bytes source/images/AI/1716192135361.png | Bin 0 -> 669590 bytes source/images/AI/1716192175996.png | Bin 0 -> 512097 bytes source/images/AI/1716192519850.png | Bin 0 -> 512868 bytes source/images/AI/1716192534058.png | Bin 0 -> 519364 bytes source/images/AI/1716193180893.png | Bin 0 -> 634989 bytes source/images/AI/1716193473766.png | Bin 0 -> 60564 bytes source/images/AI/1716194228666.png | Bin 0 -> 580189 bytes source/images/AI/1716194320872.png | Bin 0 -> 511187 bytes source/images/AI/1716194583833.png | Bin 0 -> 433771 bytes source/images/AI/1716194633162.png | Bin 0 -> 607961 bytes source/images/AI/1716194757145.png | Bin 0 -> 506048 bytes source/images/AI/1716195002371.png | Bin 0 -> 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a/source/_posts/AI.md b/source/_posts/AI.md index fc35cb4f..14eeac8d 100644 --- a/source/_posts/AI.md +++ b/source/_posts/AI.md @@ -417,3 +417,87 @@ $$ p(x_1,...,x_K)=p(x_K|x_1,...,x_{K-1})\cdots p(x_2|x_1)p(x_1) $$ +#### Variable Elimination + +用于计算概率的边缘分布 + +![1716191759894](../images/AI/1716191759894.png) + +一般而言是 NP-hard 问题。 + +对于 Markov chain,复杂度为 $O(nk^2)$;对于一般的图,$O(k^{n-1})$;如果确定每个节点的父节点数不超过 m,则复杂度为 $O(nk^{m-1})$ + +#### Message Passing + +Reuse the computation from $P(Y|E=e)$ when calcuating another probability $P(Y_1|E_1=e_1)$ + +![1716192135361](../images/AI/1716192135361.png) + +![1716192175996](../images/AI/1716192175996.png) + +“$\propto$” 意味着只需要知道概率的相对值就够了,因为可以通过归一化算出最终的概率值。 + +MAP 需要求概率分布的最大值。 + +sum 与 max 同为聚合操作,因此同样满足分配律,只需要对应替换就可以得到第二种 Message Passing: + +![1716192534058](../images/AI/1716192534058.png) + + +![1716192519850](../images/AI/1716192519850.png) + +![1716193180893](../images/AI/1716193180893.png) + +### Bayes Approach + +![1716193473766](../images/AI/1716193473766.png) + +### MLE method + +如果概率模型的参数知道,称为概率;不知道,称为统计推断。 + +估计高斯分布的参数: + +方差是有偏估计,所以一般× $1/(n-1)$。 + +![1716194228666](../images/AI/1716194228666.png) + +### Bayes Decision Rule + +![1716194320872](../images/AI/1716194320872.png) + +对于回归问题,可以采用高斯噪声假设: + +![1716194583833](../images/AI/1716194583833.png) + +这样就得到了最小二乘估计。 + +MLE 是先验概率相等的 MAP。 + +放在机器学习中,MAP 可以定义为:模型 = 数据 + 先验。 + +![1716194633162](../images/AI/1716194633162.png) + +先验信息在机器学习中体现为正则化: + +2 范数正则化就是在认为模型参数服从高斯分布的先验假设情况下,利用 MAP 准则来估计参数。 + +这也就是为什么正则化倾向于避免过拟合:高斯分布先验希望模型参数足够简单。 + +![1716194757145](../images/AI/1716194757145.png) + +### Bayesian Model Averaging + +![1716195002371](../images/AI/1716195002371.png) + +意义:模型集成。 + +### Discriminative Models + +上面的理论足够解释判别式模型的原理了。 + +### Generative Models + +![1716195398036](../images/AI/1716195398036.png) + +![1716195442145](../images/AI/1716195442145.png) \ No newline at end of file diff --git a/source/_posts/Antenna.md 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