Machine learning models and algorithms are used in a number of systems that affect our daily life. Thus, in some settings, methods that are easy to explain or interpret may be highly desirable. The price of explainability can be thought of as the loss in terms of quality that is unavoidable if we restrict these systems to use explainablemethods. We study the price of explainability, under a theoretical perspective, for clustering tasks .  We provide upper and lower bounds on this price as well as efficient algorithms to build explainable clustering for the k-means, k-medians, k-center and the maximum-spacing problems in a natural model in which explainability is achieved via decision trees  ]  .
 The price of explainability for a clustering task can be defined as the unavoidable loss, in terms of the objective function, if we force the final partition to be explainable . Here, we study this price for the following clustering problems: k-means, k-medians, k-centers and maximum-spacing. We provide upper and lower bounds for a natural model where explainability is achieved via decision trees . For the k-means and k-medians problems our upper bounds improve those obtained by Moshkovitz et. al, ICML 20] for low dimensions. Another contribution is a simple and efficient algorithm for building explainable clusterings for the k-means problem. We provide empirical evidence that its performance is better than the current state of the art for decision-tree based explainable clustering .
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Machine learning models and algorithms are used in a number of systems that affect our daily life. Thus, in some settings, methods that are easy to explain or interpret may be highly desirable.
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can be thought of as the loss
for a clustering task can be defined as the unavoidable loss,
R
quality that is unavoidable if we restrict these systems to use explainablemethods. We study the price of explainability, under a theoretical perspective, for clustering tasks
the objective function, if we force the final partition to be explainable
A
Here, we study this price for the following clustering problems: k-means, k-medians, k-centers and maximum-spacing.
R
on this price as well as efficient algorithms to build explainable clustering for the k-means, k-medians, k-center and the maximum-spacing problems in
for
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in which
where
A
. For the k-means and k-medians problems our upper bounds improve those obtained by
A
Moshkovitz et. al, ICML 20
A
for low dimensions. Another contribution is a simple and efficient algorithm for building explainable clusterings for the k-means problem. We provide empirical evidence that its performance is better than the current state of the art for decision-tree based explainable clustering