Explaining Algorithmic Fairness Through Fairness-Aware Causal Path Decomposition
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Algorithmic fairness has aroused considerable interests in data mining and machine learning communities recently. So far the existing research has been mostly focusing on the development of quantitative metrics to measure algorithm disparities across different protected groups, and approaches for adjusting the algorithm output to reduce such disparities. In this paper, we propose to study the problem of identification of the source of model disparities. Unlike existing interpretation methods which typically learn feature importance, we consider the causal relationships among feature variables and propose a novel framework to decompose the disparity into the sum of contributions from fairness-aware causal paths, which are paths linking the sensitive attribute and the final predictions, on the graph. We also consider the scenario when the directions on certain edges within those paths cannot be determined. Our framework is also model agnostic and applicable to a variety of quantitative disparity measures. Empirical evaluations on both synthetic and real-world data sets are provided to show that our method can provide precise and comprehensive explanations to the model disparities.Keywords:
Identification
Feature (linguistics)
Causal model
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Journal Article Measure for measure,' II Get access F. Adams F. Adams Search for other works by this author on: Oxford Academic Google Scholar Notes and Queries, Volume s8-VII, Issue 168, 16 March 1895, Page 203, https://doi.org/10.1093/nq/s8-VII.168.203b Published: 16 March 1895
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In the process of machining, it is very important to measure the machining spare parts accurately. It is very necessary to analyze every element that influences the measure results completely, induding the changing temperature, the size of measure force, the contact area of measure, measure principle, etc. The paper analyses the effects of measure accuracy on them and points out the methods of decreasing measure error to get qualified products in practice.
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“Measure for measure.” Get access F. J. Furnivall F. J. Furnivall Search for other works by this author on: Oxford Academic Google Scholar Notes and Queries, Volume s5-I, Issue 16, 18 April 1874, Page 304, https://doi.org/10.1093/nq/s5-I.16.304a Published: 18 April 1874
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Summary In our previous article [22], we showed complete additivity as a condition for extension of a measure. However, this condition premised the existence of a σ -field and the measure on it. In general, the existence of the measure on σ -field is not obvious. On the other hand, the proof of existence of a measure on a semialgebra is easier than in the case of a σ -field. Therefore, in this article we define a measure ( pre-measure ) on a semialgebra and extend it to a measure on a σ -field. Furthermore, we give a σ -measure as an extension of the measure on a σ -field. We follow [24], [10], and [31].
σ-finite measure
Discrete measure
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