Subgroup discovery systems are concerned with finding interesting patterns in labeled data. How these systems deal with numeric and nominal data has a large impact on the quality of their results. In this paper, we consider two ways to extend the standard pattern language of subgroup discovery: using conditions that test for interval membership for numeric attributes, and value set membership for nominal attributes. We assume a greedy search setting, that is, iteratively refining a given subgroup, with respect to a (convex) quality measure. For numeric attributes, we propose an algorithm that finds the optimal interval in linear (rather than quadratic) time, with respect to the number of examples and split points. Similarly, for nominal attributes, we show that finding the optimal set of values can be achieved in linear (rather than exponential) time, with respect to the number of examples and the size of the domain of the attribute. These algorithms operate by only considering subgroup refinements that lie on a convex hull in ROC space, thus significantly narrowing down the search space. We further provide efficient algorithms specifically for the popular Weighted Relative Accuracy quality measure, taking advantage of some of its properties. Our algorithms are shown to perform well in practice, and furthermore provide additional expressive power leading to higher-quality results.

Knowledge discovery from data is an inherently iterative process. That is, what we know about the data greatly determines our expectations, and therefore, what results we would find interesting and/or surprising. Given new knowledge about the data, our expectations will change. Hence, in order to avoid redundant results, knowledge discovery algorithms ideally should follow such an iterative updating procedure. With this in mind, we introduce a well-founded approach for succinctly summarizing data with the most informative itemsets; using a probabilistic maximum entropy model, we iteratively find the itemset that provides us the most novel information—that is, for which the frequency in the data surprises us the most—and in turn we update our model accordingly. As we use the maximum entropy principle to obtain unbiased probabilistic models, and only include those itemsets that are most informative with regard to the current model, the summaries we construct are guaranteed to be both descriptive and nonredundant. The algorithm that we present, called mtv, can either discover the top- k most informative itemsets, or we can employ either the Bayesian Information Criterion (bic) or the Minimum Description Length (mdl) principle to automatically identify the set of itemsets that together summarize the data well. In other words, our method will “tell you what you need to know” about the data. Importantly, it is a one-phase algorithm: rather than picking itemsets from a user-provided candidate set, itemsets and their supports are mined on-the-fly. To further its applicability, we provide an efficient method to compute the maximum entropy distribution using Quick Inclusion-Exclusion. Experiments on our method, using synthetic, benchmark, and real data, show that the discovered summaries are succinct, and correctly identify the key patterns in the data. The models they form attain high likelihoods, and inspection shows that they summarize the data well with increasingly specific, yet nonredundant itemsets.

Data analysis is an inherently iterative process. That is, what we know about the data greatly determines our expectations, and hence, what result we would find the most interesting. With this in mind, we introduce a well-founded approach for succinctly summarizing data with a collection of itemsets; using a probabilistic maximum entropy model, we iteratively find the most interesting itemset, and in turn update our model of the data accordingly. As we only include itemsets that are surprising with regard to the current model, the summary is guaranteed to be both descriptive and non-redundant. The algorithm that we present can either mine the top-k most interesting itemsets, or use the Bayesian Information Criterion to automatically identify the model containing only the itemsets most important for describing the data. Or, in other words, it will 'tell you what you need to know'. Experiments on synthetic and benchmark data show that the discovered summaries are succinct, and correctly identify the key patterns in the data. The models they form attain high likelihoods, and inspection shows that they summarize the data well with increasingly specific, yet non-redundant itemsets.