Gradual semantics within abstract argumentation associate a numeric score
with every argument in a system, which represents the level of acceptability of
this argument, and from which a preference ordering over arguments can be
derived. While some semantics operate over standard argumentation frameworks,
many utilise a weighted framework, where a numeric initial weight is associated
with each argument. Recent work has examined the inverse problem within gradual
semantics. Rather than determining a preference ordering given an argumentation
framework and a semantics, the inverse problem takes an argumentation
framework, a gradual semantics, and a preference ordering as inputs, and
identifies what weights are needed to over arguments in the framework to obtain
the desired preference ordering. Existing work has attacked the inverse problem
numerically, using a root finding algorithm (the bisection method) to identify
appropriate initial weights. In this paper we demonstrate that for a class of
gradual semantics, an analytical approach can be used to solve the inverse
problem. Unlike the current state-of-the-art, such an analytic approach can
rapidly find a solution, and is guaranteed to do so. In obtaining this result,
we are able to prove several important properties which previous work had posed
as conjectures.

本文讲述了针对逐渐语义中的反问题，使用解析方法而非当前数值方法来识别权重分配问题，从而使得问题可迅速寻找解决方案且具有保证性。同时，本文也证明了几个在前人猜测中重要的性质。

渐进语义内的反问题的解析解

Analytical Solutions for the Inverse Problem within Gradual Semantics

Designing adaptive classifiers for an evolving data stream is a challenging
task due to the data size and its dynamically changing nature. Combining
individual classifiers in an online setting, the ensemble approach, is a
well-known solution. It is possible that a subset of classifiers in the
ensemble outperforms others in a time-varying fashion. However, optimum weight
assignment for component classifiers is a problem which is not yet fully
addressed in online evolving environments. We propose a novel data stream
ensemble classifier, called Geometrically Optimum and Online-Weighted Ensemble
(GOOWE), which assigns optimum weights to the component classifiers using a
sliding window containing the most recent data instances. We map vote scores of
individual classifiers and true class labels into a spatial environment. Based
on the Euclidean distance between vote scores and ideal-points, and using the
linear least squares (LSQ) solution, we present a novel, dynamic, and online
weighting approach. While LSQ is used for batch mode ensemble classifiers, it
is the first time that we adapt and use it for online environments by providing
a spatial modeling of online ensembles. In order to show the robustness of the
proposed algorithm, we use real-world datasets and synthetic data generators
using the MOA libraries. First, we analyze the impact of our weighting system
on prediction accuracy through two scenarios. Second, we compare GOOWE with 8
state-of-the-art ensemble classifiers in a comprehensive experimental
environment. Our experiments show that GOOWE provides improved reactions to
different types of concept drift compared to our baselines. The statistical
tests indicate a significant improvement in accuracy, with conservative time
and memory requirements.

本文介绍了一种新的数据流集成分类器，Geometrically Optimum and Online-Weighted Ensemble (GOOWE)。GOOWE 通过使用包含最近数据实例的滑动窗口，为组成分类器分配最优权重。作者在真实世界数据集和 MOA 库的合成数据生成器中使用 GOOWE，通过两个情景分析了该权重系统对预测准确性的影响，并将其与 8 种其他集成分类器进行了比较。实验结果表明，与基线相比，GOOWE 在不同类型的概念漂移下提供了更好的反应，并且具有保守的时间和内存要求。