In this work, we propose a family of novel quantum kernels, namely the
Hierarchical Aligned Quantum Jensen-Shannon Kernels (HAQJSK), for un-attributed
graphs. Different from most existing classical graph kernels, the proposed
HAQJSK kernels can incorporate hierarchical aligned structure information
between graphs and transform graphs of random sizes into fixed-sized aligned
graph structures, i.e., the Hierarchical Transitive Aligned Adjacency Matrix of
vertices and the Hierarchical Transitive Aligned Density Matrix of the
Continuous-Time Quantum Walk (CTQW). For a pair of graphs to hand, the
resulting HAQJSK kernels are defined by measuring the Quantum Jensen-Shannon
Divergence (QJSD) between their transitive aligned graph structures. We show
that the proposed HAQJSK kernels not only reflect richer intrinsic global graph
characteristics in terms of the CTQW, but also address the drawback of
neglecting structural correspondence information arising in most existing
R-convolution kernels. Furthermore, unlike the previous Quantum Jensen-Shannon
Kernels associated with the QJSD and the CTQW, the proposed HAQJSK kernels can
simultaneously guarantee the properties of permutation invariant and positive
definiteness, explaining the theoretical advantages of the HAQJSK kernels.
Experiments indicate the effectiveness of the proposed kernels.

该研究提出了一种基于 Hierarchical Aligned Quantum Jensen-Shannon Kernels 的新型量子核，利用 Hierarchical Transitive Aligned Adjacency Matrix 和 Hierarchical Transitive Aligned Density Matrix 处理无标记图形的层次对齐结构信息，并简化了原本大小随机的图形结构，同时保证了置换不变性和正定性。实验证明了这种方法的有效性。

HAQJSK: 分层对齐的量子 Jensen-Shannon 核用于图分类

HAQJSK: Hierarchical-Aligned Quantum Jensen-Shannon Kernels for Graph Classification

We introduce an acceleration for covariance matrix adaptation evolution
strategies (CMA-ES) by means of adaptive diagonal decoding (dd-CMA). This
diagonal acceleration endows the default CMA-ES with the advantages of
separable CMA-ES without inheriting its drawbacks. Technically, we introduce a
diagonal matrix D that expresses coordinate-wise variances of the sampling
distribution in DCD form. The diagonal matrix can learn a rescaling of the
problem in the coordinates within linear number of function evaluations.
Diagonal decoding can also exploit separability of the problem, but, crucially,
does not compromise the performance on non-separable problems. The latter is
accomplished by modulating the learning rate for the diagonal matrix based on
the condition number of the underlying correlation matrix. dd-CMA-ES not only
combines the advantages of default and separable CMA-ES, but may achieve
overadditive speedup: it improves the performance, and even the scaling, of the
better of default and separable CMA-ES on classes of non-separable test
functions that reflect, arguably, a landscape feature commonly observed in
practice.
The paper makes two further secondary contributions: we introduce two
different approaches to guarantee positive definiteness of the covariance
matrix with active CMA, which is valuable in particular with large population
size; we revise the default parameter setting in CMA-ES, proposing accelerated
settings in particular for large dimension.
All our contributions can be viewed as independent improvements of CMA-ES,
yet they are also complementary and can be seamlessly combined. In numerical
experiments with dd-CMA-ES up to dimension 5120, we observe remarkable
improvements over the original covariance matrix adaptation on functions with
coordinate-wise ill-conditioning. The improvement is observed also for large
population sizes up to about dimension squared.

介绍了对协方差矩阵适应进化策略（CMA-ES）的加速技术 - 自适应对角解码（dd-CMA）。通过为采样分布引入表达坐标方差的对角矩阵来实现对称 CMA-ES 的重要优势，还可以利用可分离性，而不会损害非可分离问题的性能。我们还引入了两种保证协方差矩阵正定性的方法，并修订了 CMA-ES 的默认参数设置。在数值实验中，我们观察到 dd-CMA-ES 在存在坐标病态性的函数上表现出显着的性能提高，并且在大规模问题中也表现出了改进的效果。

协方差矩阵适应进化策略的对角加速

Diagonal Acceleration for Covariance Matrix Adaptation Evolution  Strategies

With the advent of kernel methods, automating the task of specifying a
suitable kernel has become increasingly important. In this context, the
Multiple Kernel Learning (MKL) problem of finding a combination of
pre-specified base kernels that is suitable for the task at hand has received
significant attention from researchers. In this paper we show that Multiple
Kernel Learning can be framed as a standard binary classification problem with
additional constraints that ensure the positive definiteness of the learned
kernel. Framing MKL in this way has the distinct advantage that it makes it
easy to leverage the extensive research in binary classification to develop
better performing and more scalable MKL algorithms that are conceptually
simpler, and, arguably, more accessible to practitioners. Experiments on nine
data sets from different domains show that, despite its simplicity, the
proposed technique compares favorably with current leading MKL approaches.

本文将 Multiple Kernel Learning 问题表述为标准的二分类问题，并在保持学习内核正定性的附加约束条件下进行处理，从而使得更好、更可扩展的 MKL 算法能够更容易地利用二分类研究，从而在各个领域中取得更好的性能，并且易于在实践中操作。进行的实验结果表明，所提出的技术虽然简单，但相比于目前的领先 MKL 方法具有明显的优势。