论文信息
1 Domain Adaptation
We consider classification tasks where $X$ is the input space and $Y=\{0,1, \ldots, L-1\}$ is the set of $L$ possible labels. Moreover, we have two different distributions over $X \times Y$ , called the source domain $\mathcal{D}_{\mathrm{S}}$ and the target domain $\mathcal{D}_{\mathrm{T}}$ . An unsupervised domain adaptation learning algorithm is then provided with a labeled source sample $S$ drawn i.i.d. from $\mathcal{D}_{\mathrm{S}}$ , and an unlabeled target sample $T$ drawn i.i.d. from $\mathcal{D}_{\mathrm{T}}^{X}$ , where $\mathcal{D}_{\mathrm{T}}^{X}$ is the marginal distribution of $\mathcal{D}_{\mathrm{T}}$ over $X$ .
$S=\left\{\left(\mathbf{x}_{i}, y_{i}\right)\right\}_{i=1}^{n} \sim\left(\mathcal{D}_{\mathrm{S}}\right)^{n}$
$T=\left\{\mathbf{x}_{i}\right\}_{i=n+1}^{N} \sim\left(\mathcal{D}_{\mathrm{T}}^{X}\right)^{n^{\prime}}$
with $N=n+n^{\prime}$ being the total number of samples. The goal of the learning algorithm is to build a classifier $\eta: X \rightarrow Y$ with a low target risk
$R_{\mathcal{D}_{\mathrm{T}}}(\eta)=\operatorname{Pr}_{(\mathbf{x}, y) \sim \mathcal{D}_{\mathrm{T}}}(\eta(\mathbf{x}) \neq y),$
while having no information about the labels of $\mathcal{D}_{\mathrm{T}}$ .