/tags/machine-learning/ Recent content in Machine Learning on The Personal Website of Myosotics Hugo -- gohugo.io en-US Fri, 27 Oct 2023 00:00:00 +0000 /blog/2023-10-27-2023-10-21-multi-instance-learning-a-survey-1/ Fri, 27 Oct 2023 00:00:00 +0000 /blog/2023-10-27-2023-10-21-multi-instance-learning-a-survey-1/ 摘要 英文原文 In multi-instance learning, the training set comprises labeled bags that are composed of unlabeled instances, and the task is to predict the labels of unseen bags. This paper provides a survey on this topic. At first, it introduces the origin of multi-instance learning. Then, developments on the study of learnability, learningal gorithms, applications and extensions of multi-instance learning are reviewed. In particular, this paper employs a unified view to look into multi-instance learning algorithms. /blog/2023-10-27-2023-10-21-multi-instance-learning-a-survey-2/ Fri, 27 Oct 2023 00:00:00 +0000 /blog/2023-10-27-2023-10-21-multi-instance-learning-a-survey-2/ 上接：Multi-Instance Learning: A Survey Learning Algorithm supervised learning 和 multi-instance learning 的主要区别是能否(较好地)识别instances。 目前大部分现存的 multi-instance learning 算法均是从 supervised learning algorithm 改进而得到的：将 supervised learning algorithms 的 focuses 从识别 instances 转移到 识别 bags。此处主要介绍检验了五种算法。 Diverse Density Diverse Density 算法将每个 bag 当作一个包含许多特征向量(instance)的 manifold，并 且假定一个新的 positive bag 与所有 positive 的 feature-manifolds 相关，而与 negative feature-manifolds 不相关。目标是计算一个点在 feature space 中的 maximum diverse density。 给定一个数据集$D$和一组类别标签$C=\{c_1,c_2,\cdots,c_t\}$去预测，在假定 $P_r(D)$为常数和$c_k$服从均匀分布的基础上，利用 Bayes rule，标签的后验概率计算 为 \begin{equation} \begin{aligned} Obj &=Pr(C|D)]\\ &\propto \mathop{\arg \max}\limits_{1\leqslant k\leqslant t}P_r(D|c_k) \end{aligned}\tag{1} \end{equation} 公式 (1) 在目标是区分 instances 时已经足够，但是对于区分 bag 时，需要考虑 $D = \{B_1^+,\cdots,B_m^+,B^-_1,\cdots,B_n^-\}$，其中$B_i^+$和$B_j^-$分别表示 第$i$个 positive bag 和第$j$个 negative bag。在假定 bag 间是条件独立的基础上， 再次利用 Bayes rule，公式(1)进一步得到如下： \begin{equation} Obj = \mathop{\arg\max}\limits_{1\leqslant k\leqslant t} \prod_{1\leqslant i\leqslant m}Pr(c_k|B^+_i) \prod_{1\leqslant j\leqslant n} Pr(c_k|B_j^{-})\notag \end{equation}