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‎src/chaps/ch01_introduction.tex‎

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\end{tabular}
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\end{table}
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\textbf{2. 迁移学习 VS 终身学习：}
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\textbf{2. 迁移学习 VS 多任务学习：}
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终身学习强调连续不断地在一个概念和任务上进行学习，模型持续优化。迁移学习则侧重于模型的迁移和共同学习。
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多任务学习指多个相关的任务一起协同学习；迁移学习则强调知识由一个领域迁移到另一个领域的过程。迁移是思想，多任务是其中的一个具体形式。
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\textbf{3. 迁移学习 VS 多任务学习：}
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\textbf{3. 迁移学习 VS 终身学习：}
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多任务学习指多个相关的任务一起协同学习；迁移学习则强调知识由一个领域迁移到另一个领域的过程。迁移是思想，多任务是其中的一个具体形式。
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终身学习可以认为是序列化的多任务学习，在已经学习好若干个任务之后，面对新的任务可以继续学习而不遗忘之前学习的任务。迁移学习则侧重于模型的迁移和共同学习。
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\textbf{4. 迁移学习 VS 领域自适应：}
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\textbf{7. 迁移学习 VS 协方差漂移}
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协方差漂移也是迁移学习要研究的问题之一，它特指数据的条件概率分布发生变化。
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协方差漂移指数据的边缘概率分布发生变化。领域自适应研究问题解决的就是协方差漂移现象。
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\subsection{负迁移}
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我们都希望迁移学习能够比较顺利地进行，我们得到的结果也是满足我们要求的，皆大欢喜。然而，事情却并不总是那么顺利。这就引入了迁移学习中的一个负面现象，也就是所谓的\textbf{负迁移}。

‎src/chaps/ch04_basic.tex‎

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结合上述形式化，我们给出\textbf{领域自适应(Domain Adaptation)}这一热门研究方向的定义：
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\textbf{领域自适应(Domain Adaptation):} 给定一个有标记的源域$\mathcal{D}_s=\{\mathbf{x}_{i},y_{i}\}^n_{i=1}$和一个无标记的目标域$\mathcal{D}_t=\{\mathbf{x}_{j}\}^{n+m}_{j=n+1}$，假定它们的特征空间相同，即$\mathcal{X}_s = \mathcal{X}_t$，并且它们的类别空间也相同，即$\mathcal{Y}_s = \mathcal{Y}_t$。但是这两个域的边缘分布不同，即$P_s(\mathbf{x}_s) \ne P_t(\mathbf{x}_t)$，条件概率分布也不同，即$Q_s(y_s|\mathbf{x}_s) \ne Q_t(y_t|\mathbf{x}_t)$。迁移学习的目标就是，利用有标记的数据$\mathcal{D}_s$去学习一个分类器$f:\mathbf{x}_t \mapsto \mathbf{y}_t$来预测目标域$\mathcal{D}_t$的标签$\mathbf{y}_t \in \mathcal{Y}_t$.
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\textbf{领域自适应(Domain Adaptation):} 给定一个有标记的源域$\mathcal{D}_s=\{\mathbf{x}_{i},y_{i}\}^n_{i=1}$和一个无标记的目标域$\mathcal{D}_t=\{\mathbf{x}_{j}\}^{n+m}_{j=n+1}$，假定它们的特征空间相同，即$\mathcal{X}_s = \mathcal{X}_t$，并且它们的类别空间也相同，即$\mathcal{Y}_s = \mathcal{Y}_t$以及条件概率分布也相同，即$Q_s(y_s|\mathbf{x}_s) = Q_t(y_t|\mathbf{x}_t)$。但是这两个域的边缘分布不同，即$P_s(\mathbf{x}_s) \ne P_t(\mathbf{x}_t)$。迁移学习的目标就是，利用有标记的数据$\mathcal{D}_s$去学习一个分类器$f:\mathbf{x}_t \mapsto \mathbf{y}_t$来预测目标域$\mathcal{D}_t$的标签$\mathbf{y}_t \in \mathcal{Y}_t$.
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在实际的研究和应用中，读者可以针对自己的不同任务，结合上述表述，灵活地给出相关的形式化定义。
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\subsubsection{最大均值差异MMD}
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最大均值差异是迁移学习中使用频率最高的度量。Maximum mean discrepancy，它度量在再生希尔伯特空间中两个分布的距离，是一种核学习方法。两个随机变量的距离为
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最大均值差异是迁移学习中使用频率最高的度量。Maximum mean discrepancy，它度量在再生希尔伯特空间中两个分布的距离，是一种核学习方法。两个随机变量的MMD平方距离为
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\begin{equation}
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\label{eq-dist-mmd}
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MMD(X,Y)=\left \Vert \sum_{i=1}^{n_1}\phi(\mathbf{x}_i)- \sum_{j=1}^{n_2}\phi(\mathbf{y}_j) \right \Vert^2_\mathcal{H}
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MMD^2(X,Y)=\left \Vert \sum_{i=1}^{n_1}\phi(\mathbf{x}_i)- \sum_{j=1}^{n_2}\phi(\mathbf{y}_j) \right \Vert^2_\mathcal{H}
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\end{equation}
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其中$\phi(\cdot)$是映射，用于把原变量映射到\textit{再生核希尔伯特空间}(Reproducing Kernel Hilbert Space, RKHS)~\cite{borgwardt2006integrating}中。什么是RKHS？形式化定义太复杂，简单来说就是这个空间是对于函数的内积完备的。就是比欧几里得空间更高端的。
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其中$\phi(\cdot)$是映射，用于把原变量映射到\textit{再生核希尔伯特空间}(Reproducing Kernel Hilbert Space, RKHS)~\cite{borgwardt2006integrating}中。什么是RKHS？形式化定义太复杂，简单来说希尔伯特空间是对于函数的内积完备的，而再生核希尔伯特空间是具有再生性$\langle K(x,\cdot),K(y,\cdot)\rangle_\mathcal{H}=K(x,y)$的希尔伯特空间。就是比欧几里得空间更高端的。将平方展开后，RKHS空间中的内积就可以转换成核函数，所以最终MMD可以直接通过核函数进行计算。
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理解：就是求两堆数据在RKHS中的\textit{均值}的距离。
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\end{equation}
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其中$X,Y$是两堆数据的kernel形式。
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\subsubsection{Wasserstein Distance}
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Wasserstein Distance是一套用来衡量两个概率分部之间距离的度量方法。该距离在一个度量空间$(M,\rho)$上定义，其中$\rho(x,y)$表示集合$M$中两个实例$x$和$y$的距离函数，比如欧几里得距离。两个概率分布$\mathbb{P}$和$\mathbb{Q}$之间的$p{\text{-th}}$ Wasserstein distance可以被定义为
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\begin{equation}
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W_p(\mathbb{P}, \mathbb{Q}) = \Big(\inf_{\mu \in \Gamma(\mathbb{P}, \mathbb{Q}) } \int \rho(x,y)^p d\mu(x,y) \Big)^{1/p},
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\end{equation}
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其中$\Gamma(\mathbb{P}, \mathbb{Q})$是在集合$M\times M$内所有的以$\mathbb{P}$和$\mathbb{Q}$为边缘分布的联合分布。著名的Kantorovich-Rubinstein定理表示当$M$是可分离的时候，第一Wasserstein distance可以等价地表示成一个积分概率度量(integral probability metric)的形式
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\begin{equation}
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W_1(\mathbb{P},\mathbb{Q})= \sup_{\left \| f \right \|_L \leq 1} \mathbb{E}_{x \sim \mathbb{P}}[f(x)] - \mathbb{E}_{x \sim \mathbb{Q}}[f(x)],
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\end{equation}
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其中$\left \| f \right \|_L = \sup{|f(x) - f(y)|} / \rho(x,y)$并且$\left \| f \right \|_L \leq 1$称为$1-$利普希茨条件。
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\subsection{迁移学习的理论保证*}
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\textit{
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本部分的标题中带有*号，有一些难度，为可看可不看的内容。此部分最常见的形式是当自己提出的算法需要理论证明时，可以借鉴。}

‎src/main.toc‎

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\contentsline {subsubsection}{\numberline {4.3.5}Principal Angle}{16}{subsubsection.4.3.5}
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\contentsline {subsubsection}{\numberline {4.3.6}A-distance}{16}{subsubsection.4.3.6}
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\contentsline {subsubsection}{\numberline {4.3.7}Hilbert-Schmidt Independence Criterion}{16}{subsubsection.4.3.7}
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\contentsline {subsection}{\numberline {4.4}迁移学习的理论保证*}{16}{subsection.4.4}
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\contentsline {section}{\numberline {5}迁移学习的基本方法}{18}{section.5}
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\contentsline {subsection}{\numberline {5.1}基于样本迁移}{18}{subsection.5.1}
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\contentsline {subsection}{\numberline {5.2}基于特征迁移}{19}{subsection.5.2}
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\contentsline {subsection}{\numberline {5.3}基于模型迁移}{19}{subsection.5.3}
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\contentsline {subsection}{\numberline {5.4}基于关系迁移}{20}{subsection.5.4}
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\contentsline {section}{\numberline {6}第一类方法：数据分布自适应}{22}{section.6}
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\contentsline {subsection}{\numberline {6.1}边缘分布自适应}{22}{subsection.6.1}
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\contentsline {subsubsection}{\numberline {6.1.1}基本思路}{22}{subsubsection.6.1.1}
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\contentsline {subsubsection}{\numberline {6.1.2}核心方法}{22}{subsubsection.6.1.2}
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\contentsline {subsubsection}{\numberline {6.1.3}扩展}{24}{subsubsection.6.1.3}
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\contentsline {subsection}{\numberline {6.2}条件分布自适应}{25}{subsection.6.2}
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\contentsline {subsection}{\numberline {6.3}联合分布自适应}{26}{subsection.6.3}
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\contentsline {subsubsection}{\numberline {6.3.1}基本思路}{26}{subsubsection.6.3.1}
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\contentsline {subsubsection}{\numberline {6.3.2}核心方法}{26}{subsubsection.6.3.2}
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\contentsline {subsubsection}{\numberline {6.3.3}扩展}{28}{subsubsection.6.3.3}
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\contentsline {subsection}{\numberline {6.4}小结}{29}{subsection.6.4}
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\contentsline {section}{\numberline {7}第二类方法：特征选择}{30}{section.7}
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\contentsline {subsection}{\numberline {7.1}核心方法}{31}{subsection.7.1}
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\contentsline {subsection}{\numberline {7.2}扩展}{31}{subsection.7.2}
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\contentsline {subsection}{\numberline {7.3}小结}{31}{subsection.7.3}
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\contentsline {section}{\numberline {8}第三类方法：子空间学习}{32}{section.8}
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\contentsline {subsection}{\numberline {8.1}统计特征对齐}{32}{subsection.8.1}
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\contentsline {subsection}{\numberline {8.2}流形学习}{34}{subsection.8.2}
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\contentsline {subsection}{\numberline {8.3}扩展与小结}{36}{subsection.8.3}
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\contentsline {section}{\numberline {9}深度迁移学习}{37}{section.9}
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\contentsline {subsection}{\numberline {9.1}深度网络的可迁移性}{37}{subsection.9.1}
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\contentsline {subsection}{\numberline {9.2}最简单的深度迁移：finetune}{41}{subsection.9.2}
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\contentsline {subsection}{\numberline {9.3}深度网络自适应}{42}{subsection.9.3}
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\contentsline {subsubsection}{\numberline {9.3.1}基本思路}{42}{subsubsection.9.3.1}
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\contentsline {subsubsection}{\numberline {9.3.2}核心方法}{43}{subsubsection.9.3.2}
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\contentsline {subsubsection}{\numberline {9.3.3}小结}{48}{subsubsection.9.3.3}
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\contentsline {subsection}{\numberline {9.4}深度对抗网络迁移}{48}{subsection.9.4}
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\contentsline {subsubsection}{\numberline {9.4.1}基本思路}{48}{subsubsection.9.4.1}
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\contentsline {subsubsection}{\numberline {9.4.2}核心方法}{48}{subsubsection.9.4.2}
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\contentsline {subsubsection}{\numberline {9.4.3}小结}{51}{subsubsection.9.4.3}
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\contentsline {section}{\numberline {10}上手实践}{52}{section.10}
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\contentsline {section}{\numberline {11}迁移学习前沿}{58}{section.11}
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\contentsline {subsection}{\numberline {11.1}机器智能与人类经验结合迁移}{58}{subsection.11.1}
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\contentsline {subsection}{\numberline {11.2}传递式迁移学习}{58}{subsection.11.2}
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\contentsline {subsection}{\numberline {11.3}终身迁移学习}{59}{subsection.11.3}
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\contentsline {subsection}{\numberline {11.4}在线迁移学习}{60}{subsection.11.4}
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\contentsline {subsection}{\numberline {11.5}迁移强化学习}{61}{subsection.11.5}
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\contentsline {subsection}{\numberline {11.6}迁移学习的可解释性}{61}{subsection.11.6}
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\contentsline {section}{\numberline {12}总结语}{62}{section.12}
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\contentsline {section}{\numberline {13}附录}{63}{section.13}
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\contentsline {subsection}{\numberline {13.1}迁移学习相关的期刊和会议}{63}{subsection.13.1}
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\contentsline {subsection}{\numberline {13.2}迁移学习研究学者}{63}{subsection.13.2}
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\contentsline {subsection}{\numberline {13.3}迁移学习资源汇总}{66}{subsection.13.3}
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\contentsline {subsection}{\numberline {13.4}迁移学习常用算法及数据资源}{67}{subsection.13.4}
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\contentsline {subsubsection}{\numberline {4.3.8}Wasserstein Distance}{17}{subsubsection.4.3.8}
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\contentsline {subsection}{\numberline {4.4}迁移学习的理论保证*}{17}{subsection.4.4}
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\contentsline {section}{\numberline {5}迁移学习的基本方法}{19}{section.5}
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\contentsline {subsection}{\numberline {5.1}基于样本迁移}{19}{subsection.5.1}
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\contentsline {subsection}{\numberline {5.2}基于特征迁移}{20}{subsection.5.2}
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\contentsline {subsection}{\numberline {5.3}基于模型迁移}{20}{subsection.5.3}
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\contentsline {subsection}{\numberline {5.4}基于关系迁移}{21}{subsection.5.4}
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\contentsline {section}{\numberline {6}第一类方法：数据分布自适应}{23}{section.6}
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\contentsline {subsection}{\numberline {6.1}边缘分布自适应}{23}{subsection.6.1}
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\contentsline {subsubsection}{\numberline {6.1.1}基本思路}{23}{subsubsection.6.1.1}
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\contentsline {subsubsection}{\numberline {6.1.2}核心方法}{23}{subsubsection.6.1.2}
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\contentsline {subsubsection}{\numberline {6.1.3}扩展}{25}{subsubsection.6.1.3}
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\contentsline {subsection}{\numberline {6.2}条件分布自适应}{26}{subsection.6.2}
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\contentsline {subsection}{\numberline {6.3}联合分布自适应}{27}{subsection.6.3}
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\contentsline {subsubsection}{\numberline {6.3.1}基本思路}{27}{subsubsection.6.3.1}
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\contentsline {subsubsection}{\numberline {6.3.2}核心方法}{27}{subsubsection.6.3.2}
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\contentsline {subsubsection}{\numberline {6.3.3}扩展}{29}{subsubsection.6.3.3}
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\contentsline {subsection}{\numberline {6.4}小结}{30}{subsection.6.4}
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\contentsline {section}{\numberline {7}第二类方法：特征选择}{31}{section.7}
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\contentsline {subsection}{\numberline {7.1}核心方法}{32}{subsection.7.1}
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\contentsline {subsection}{\numberline {7.2}扩展}{32}{subsection.7.2}
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\contentsline {subsection}{\numberline {7.3}小结}{32}{subsection.7.3}
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\contentsline {section}{\numberline {8}第三类方法：子空间学习}{33}{section.8}
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\contentsline {subsection}{\numberline {8.1}统计特征对齐}{33}{subsection.8.1}
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\contentsline {subsection}{\numberline {8.2}流形学习}{35}{subsection.8.2}
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\contentsline {subsection}{\numberline {8.3}扩展与小结}{37}{subsection.8.3}
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\contentsline {section}{\numberline {9}深度迁移学习}{38}{section.9}
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\contentsline {subsection}{\numberline {9.1}深度网络的可迁移性}{38}{subsection.9.1}
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\contentsline {subsection}{\numberline {9.2}最简单的深度迁移：finetune}{42}{subsection.9.2}
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\contentsline {subsection}{\numberline {9.3}深度网络自适应}{43}{subsection.9.3}
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\contentsline {subsubsection}{\numberline {9.3.1}基本思路}{43}{subsubsection.9.3.1}
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\contentsline {subsubsection}{\numberline {9.3.2}核心方法}{44}{subsubsection.9.3.2}
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\contentsline {subsubsection}{\numberline {9.3.3}小结}{49}{subsubsection.9.3.3}
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\contentsline {subsection}{\numberline {9.4}深度对抗网络迁移}{49}{subsection.9.4}
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\contentsline {subsubsection}{\numberline {9.4.1}基本思路}{49}{subsubsection.9.4.1}
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\contentsline {subsubsection}{\numberline {9.4.2}核心方法}{49}{subsubsection.9.4.2}
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\contentsline {subsubsection}{\numberline {9.4.3}小结}{52}{subsubsection.9.4.3}
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\contentsline {section}{\numberline {10}上手实践}{53}{section.10}
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\contentsline {section}{\numberline {11}迁移学习前沿}{59}{section.11}
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\contentsline {subsection}{\numberline {11.1}机器智能与人类经验结合迁移}{59}{subsection.11.1}
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\contentsline {subsection}{\numberline {11.2}传递式迁移学习}{59}{subsection.11.2}
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\contentsline {subsection}{\numberline {11.3}终身迁移学习}{60}{subsection.11.3}
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\contentsline {subsection}{\numberline {11.4}在线迁移学习}{61}{subsection.11.4}
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\contentsline {subsection}{\numberline {11.5}迁移强化学习}{62}{subsection.11.5}
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\contentsline {subsection}{\numberline {11.6}迁移学习的可解释性}{62}{subsection.11.6}
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\contentsline {section}{\numberline {12}总结语}{63}{section.12}
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\contentsline {section}{\numberline {13}附录}{64}{section.13}
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\contentsline {subsection}{\numberline {13.1}迁移学习相关的期刊和会议}{64}{subsection.13.1}
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\contentsline {subsection}{\numberline {13.2}迁移学习研究学者}{64}{subsection.13.2}
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\contentsline {subsection}{\numberline {13.3}迁移学习资源汇总}{67}{subsection.13.3}
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\contentsline {subsection}{\numberline {13.4}迁移学习常用算法及数据资源}{68}{subsection.13.4}

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