Unsupervised anomaly detection (AD) is critical for a wide range of practical
applications, from network security to health and medical tools. Due to the
diversity of problems, no single algorithm has been found to be superior for
all AD tasks. Choosing an algorithm, otherwise known as the Algorithm Selection
Problem (ASP), has been extensively examined in supervised classification
problems, through the use of meta-learning and AutoML, however, it has received
little attention in unsupervised AD tasks. This research proposes a new
meta-learning approach that identifies an appropriate unsupervised AD algorithm
given a set of meta-features generated from the unlabelled input dataset. The
performance of the proposed meta-learner is superior to the current state of
the art solution. In addition, a mixed model statistical analysis has been
conducted to examine the impact of the meta-learner components: the meta-model,
meta-features, and the base set of AD algorithms, on the overall performance of
the meta-learner. The analysis was conducted using more than 10,000 datasets,
which is significantly larger than previous studies. Results indicate that a
relatively small number of meta-features can be used to identify an appropriate
AD algorithm, but the choice of a meta-model in the meta-learner has a
considerable impact.

该研究提出了一种新的元学习方法，通过使用从未标记的输入数据集生成的元特征，识别出适当的无监督异常检测算法。该方法的性能优于现有的解决方案，并使用超过 10000 个数据集进行了混合模型统计分析，结果表明相对较少的元特征就足以识别合适的无监督异常检测算法，但在元学习器中选择元模型具有相当大的影响。

构建无监督异常检测的元学习器

Constructing a meta-learner for unsupervised anomaly detection

Even though it is well known that for most relevant computational problems
different algorithms may perform better on different classes of problem
instances, most researchers still focus on determining a single best
algorithmic configuration based on aggregate results such as the average. In
this paper, we propose Integer Programming based approaches to build decision
trees for the Algorithm Selection Problem. These techniques allow automate
three crucial decisions: (i) discerning the most important problem features to
determine problem classes; (ii) grouping the problems into classes and (iii)
select the best algorithm configuration for each class. To evaluate this new
approach, extensive computational experiments were executed using the linear
programming algorithms implemented in the COIN-OR Branch & Cut solver across a
comprehensive set of instances, including all MIPLIB benchmark instances. The
results exceeded our expectations. While selecting the single best parameter
setting across all instances decreased the total running time by 22%, our
approach decreased the total running time by 40% on average across 10-fold
cross validation experiments. These results indicate that our method
generalizes quite well and does not overfit.

本文提出了基于整数规划的方法来构建用于算法选择问题的决策树，并使用 COIN-OR Branch & Cut solver 实现的线性规划算法进行了实验。实验结果表明，该方法具有很好的泛化性能且未过度拟合。