This paper presents a kernelized version of the t-SNE algorithm, capable of
mapping high-dimensional data to a low-dimensional space while preserving the
pairwise distances between the data points in a non-Euclidean metric. This can
be achieved using a kernel trick only in the high dimensional space or in both
spaces, leading to an end-to-end kernelized version. The proposed kernelized
version of the t-SNE algorithm can offer new views on the relationships between
data points, which can improve performance and accuracy in particular
applications, such as classification problems involving kernel methods. The
differences between t-SNE and its kernelized version are illustrated for
several datasets, showing a neater clustering of points belonging to different
classes.

本文介绍了 t-SNE 算法的核化版本，能够将高维数据映射到低维空间并在非欧几里德度量下保留数据点之间的成对距离，可以通过仅在高维空间或在两个空间中使用核技巧来实现，提供了数据点之间关系的新视角，改进了包括使用核方法的分类问题的性能和准确性，并利用多个数据集阐明了 t-SNE 和其核化版本之间的区别，展示了不同类别点的更整洁的聚类。

核 t 分布随机邻域嵌入

Kernel t-distributed stochastic neighbor embedding

We propose and analyze a kernelized version of Q-learning. Although a kernel
space is typically infinite-dimensional, extensive study has shown that
generalization is only affected by the effective dimension of the data. We
incorporate such ideas into the Q-learning framework and derive regret bounds
for arbitrary kernels. In particular, we provide concrete bounds for linear
kernels and Gaussian RBF kernels; notably, the latter bound looks almost
identical to the former, only that the actual dimension is replaced by a
different notion of dimensionality. Finally, we test our algorithm on a suite
of classic control tasks; remarkably, under the Gaussian RBF kernel, it
achieves reasonably good performance after only 1000 environmental steps, while
its neural network counterpart, deep Q-learning, still struggles.

在 Q-learning 框架下，我们提出并分析了核化 Q-learning。该方法在任意核函数下可以导出遗憾界，并且在经典控制任务的测试中，与深度 Q-learning 相比，使用高斯 RBF 核函数的核化 Q-learning 在较少步数内就能取得理想成果。

可证明有效的核化 Q 学习

Provably Efficient Kernelized Q-Learning

Bolukbasi et al. (2016) presents one of the first gender bias mitigation
techniques for word embeddings. Their method takes pre-trained word embeddings
as input and attempts to isolate a linear subspace that captures most of the
gender bias in the embeddings. As judged by an analogical evaluation task,
their method virtually eliminates gender bias in the embeddings. However, an
implicit and untested assumption of their method is that the bias sub-space is
actually linear. In this work, we generalize their method to a kernelized,
non-linear version. We take inspiration from kernel principal component
analysis and derive a non-linear bias isolation technique. We discuss and
overcome some of the practical drawbacks of our method for non-linear gender
bias mitigation in word embeddings and analyze empirically whether the bias
subspace is actually linear. Our analysis shows that gender bias is in fact
well captured by a linear subspace, justifying the assumption of Bolukbasi et
al. (2016).

该研究针对词嵌入中的性别偏见进行了研究，通过构建线性子空间的方法来消除偏见，而我们则提出了基于核函数的非线性方法，并分析了线性子空间偏见消除的合理性。