A novel ordinal regression algorithm, called moving window regression (MWR),
is proposed in this paper. First, we propose the notion of relative rank
($\rho$-rank), which is a new order representation scheme for input and
reference instances. Second, we develop global and local relative regressors
($\rho$-regressors) to predict $\rho$-ranks within entire and specific rank
ranges, respectively. Third, we refine an initial rank estimate iteratively by
selecting two reference instances to form a search window and then estimating
the $\rho$-rank within the window. Extensive experiments results show that the
proposed algorithm achieves the state-of-the-art performances on various
benchmark datasets for facial age estimation and historical color image
classification. The codes are available at this https URL

本文提出了一种新的序数回归算法 —— 移动窗口回归 (MWR)。在算法中，我们设计了基于相对排序的表示模式、全局与局部相对回归模型以及迭代式的排名估计方法。实验结果表明，该算法在面部年龄估计和彩色图像分类等多个数据集上均取得了最先进的表现。

移动窗口回归：一种新的序回归方法

Moving Window Regression: A Novel Approach to Ordinal Regression

We demonstrate an equivalence between reproducing kernel Hilbert space (RKHS)
embeddings of conditional distributions and vector-valued regressors. This
connection introduces a natural regularized loss function which the RKHS
embeddings minimise, providing an intuitive understanding of the embeddings and
a justification for their use. Furthermore, the equivalence allows the
application of vector-valued regression methods and results to the problem of
learning conditional distributions. Using this link we derive a sparse version
of the embedding by considering alternative formulations. Further, by applying
convergence results for vector-valued regression to the embedding problem we
derive minimax convergence rates which are O(\log(n)/n) -- compared to current
state of the art rates of O(n^{-1/4}) -- and are valid under milder and more
intuitive assumptions. These minimax upper rates coincide with lower rates up
to a logarithmic factor, showing that the embedding method achieves nearly
optimal rates. We study our sparse embedding algorithm in a reinforcement
learning task where the algorithm shows significant improvement in sparsity
over an incomplete Cholesky decomposition.

本文介绍了使用 reproducing kernel Hilbert space embeddings of conditional distributions 与 vector-valued regressors 之间的等价关系，从而引入了一个自然的正则化损失函数以更好地理解和使用这种嵌入方法，并且通过向量回归方法的应用和导出推导生成了嵌入算法的最小一致收敛率 O (log (n)/n)，并在强化学习任务中得出了一个稀疏嵌入算法。