论文标题
通过线性转换的域换档适应
Domain-shift adaptation via linear transformations
论文作者
论文摘要
一个预测变量，$ f_a：x \ to y $，从源域（a）中学习的数据（当它们的分布不同时）可能不准确。域的适应性旨在减少该分布不匹配的负面影响。在这里，我们分析了$ p_a（y \ | \ x）\ neq p_b（y \ | \ x）$，$ p_a（x）\ neq p_b（x）$但是$ p_a（y）= p_b（y）= p_b（y）$; $ x $的仿射转换，使所有分布等效。我们提出了一种方法，通过（1）将域将域投射到每个域的经验协方差矩阵的特征向量中，将源和目标域投射到一个较低的公共空间中，然后（2）找到一个正交矩阵，以最小化两个域之间的最大平均差异。对于任意的仿射转换，执行无监督的域适应性时存在固有的不可识别性问题，可以在半监督的情况下得到缓解。我们在模拟数据和二进制数字分类任务中显示了方法的有效性，在校正数据中的域移动时，可以获得高达48％的精度的改进。
A predictor, $f_A : X \to Y$, learned with data from a source domain (A) might not be accurate on a target domain (B) when their distributions are different. Domain adaptation aims to reduce the negative effects of this distribution mismatch. Here, we analyze the case where $P_A(Y\ |\ X) \neq P_B(Y\ |\ X)$, $P_A(X) \neq P_B(X)$ but $P_A(Y) = P_B(Y)$; where there are affine transformations of $X$ that makes all distributions equivalent. We propose an approach to project the source and target domains into a lower-dimensional, common space, by (1) projecting the domains into the eigenvectors of the empirical covariance matrices of each domain, then (2) finding an orthogonal matrix that minimizes the maximum mean discrepancy between the projections of both domains. For arbitrary affine transformations, there is an inherent unidentifiability problem when performing unsupervised domain adaptation that can be alleviated in the semi-supervised case. We show the effectiveness of our approach in simulated data and in binary digit classification tasks, obtaining improvements up to 48% accuracy when correcting for the domain shift in the data.
