We describe a data-driven discovery method that leverages Simpson's paradox to uncover interesting patterns in behavioral data. Our method systematically disaggregates data to identify subgroups within a population whose behavior deviates significantly from the rest of the population. Given an outcome of interest and a set of covariates, the method follows three steps. First, it disaggregates data into subgroups, by conditioning on a particular covariate, so as minimize the variation of the outcome within the subgroups. Next, it models the outcome as a linear function of another covariate, both in the subgroups and in the aggregate data. Finally, it compares trends to identify disaggregations that produce subgroups with different behaviors from the aggregate. We illustrate the method by applying it to three real-world behavioral datasets, including Q &A site Stack Exchange and online learning platforms Khan Academy and Duolingo.
The idea for using Simpson's paradox to uncover interesting patterns in data was explored by researchers in the past @cite_5 . Our work extends previous research in new directions. We not only provide a principled way to disaggregate data, but also introduce a novel measure that allows us to quantify how interesting or surprising an instance of Simpson's paradox is. As we demonstrate in the results, this provides a novel tool for studying behavioral data.
@cite_5
37107183 2077947412 1586011174 2950812595
This paper addresses the discovery of surprising patterns. Recently, several authors have addressed the task of discovering surprising prediction rules. However, we do not focus on prediction rules, but rather on a quite different kind of pattern, namely the occurrence of Simpson’s paradox. Intuitively, the fact that this is a paradox suggests that it has a great potential to be a surprising pattern for the user. With this motivation, we make the detection of Simpson’s paradox the central goal of a data mining algorithm explicitly designed to discover surprising patterns. We present computational results showing surprising occurrences of the paradox in some public-domain data sets. In addition, we propose a method for ranking the discovered instances of the paradox in decreasing order of estimated degree of surprisingness. Discovering the most interesting patterns is the key problem in the field of pattern mining. While ranking or selecting patterns is well-studied for itemsets it is surprisingly under-researched for other, more complex, pattern types. In this paper we propose a new quality measure for episodes. An episode is essentially a set of events with possible restrictions on the order of events. We say that an episode is significant if its occurrence is abnormally compact, that is, only few gap events occur between the actual episode events, when compared to the expected length according to the independence model. We can apply this measure as a post-pruning step by first discovering frequent episodes and then rank them according to this measure. In order to compute the score we will need to compute the mean and the variance according to the independence model. As a main technical contribution we introduce a technique that allows us to compute these values. Such a task is surprisingly complex and in order to solve it we develop intricate finite state machines that allow us to compute the needed statistics. We also show that asymptotically our score can be interpreted as a @math P value. In our experiments we demonstrate that despite its intricacy our ranking is fast: we can rank tens of thousands episodes in seconds. Our experiments with text data demonstrate that our measure ranks interpretable episodes high. An apparent paradox in classical statistical physics is the mechanism by which conservative, time-reversible microscopic dynamics, can give rise to seemingly dissipative behavior. In this paper we use system theoretic tools to show that dissipation can arise as an artifact of incomplete observations over a finite horizon. In addition, this approach allows us to obtain finite-time, low order, approximations of systems with moderate size and to establish how the approach to the thermodynamic limit depends on the different physical parameters. This paper presents a framework for exact discovery of the top-k sequential patterns under Leverage. It combines (1) a novel definition of the expected support for a sequential pattern - a concept on which most interestingness measures directly rely - with (2) SkOPUS: a new branch-and-bound algorithm for the exact discovery of top-k sequential patterns under a given measure of interest. Our interestingness measure employs the partition approach. A pattern is interesting to the extent that it is more frequent than can be explained by assuming independence between any of the pairs of patterns from which it can be composed. The larger the support compared to the expectation under independence, the more interesting is the pattern. We build on these two elements to exactly extract the k sequential patterns with highest leverage, consistent with our definition of expected support. We conduct experiments on both synthetic data with known patterns and real-world datasets; both experiments confirm the consistency and relevance of our approach with regard to the state of the art. This article was published in Data Mining and Knowledge Discovery and is accessible at this http URL