/categories/article/ Recent content in Article on The Personal Website of Myosotics Hugo -- gohugo.io en-US Thu, 14 Dec 2023 00:00:00 +0000 /blog/2023-12-14-a-variational-approach-to-sparsity-optimization-based-on-lagrange-multiplier-theorey/ Thu, 14 Dec 2023 00:00:00 +0000 /blog/2023-12-14-a-variational-approach-to-sparsity-optimization-based-on-lagrange-multiplier-theorey/ 论文索引：Kong, X., Wang, X., & Zheng, W. (2023). Asymptotic distributions of a new type of design-based incomplete U-statistics. Stat, 12(1), e543.https://doi.org/10.1002/sta4.54 Orthogonal Array 定义：正交阵列 (Orthogonal Array) 是一类组合设计，设$A$是$L$元集$X$上的$m\times d$矩阵，若对任意$t(2≤t≤k)$列所构成的子矩阵，$X$上的每一个$t$元排列作为子矩阵的行各出现$λ$次，则称$A$为大小$m$，约束数$d$，水平数$L$，强度$t$和指数$λ$的正交阵列，在试验设计中称正交表，记为$OA(m,d,L,t)$，由定义有$m=λL^t$。 /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} /blog/2023-10-10-a-review-of/ Tue, 10 Oct 2023 00:00:00 +0000 /blog/2023-10-10-a-review-of/ 摘要 英文原文 Computer applications have considerably shifted from single data processing to machine learning in recent years due to the accessibility and availability of massive volumes of data obtained through the internet and various sources. Machine learning is automating human assistance by training an algorithm on relevant data. Supervised, Unsupervised, and Reinforcement Learning are the three fundamental categories of machine learning techniques. In this paper, we have discussed the different learning styles used in the field of Computer vision, Deep Learning, Neural networks, and machine learning.