No abstract

Sequential pattern mining is a fundamental data mining task with application in several domains. We study two variants of this task—the first is the extraction of frequent sequential patterns, whose frequency in a dataset of sequential transactions is higher than a user-provided threshold; the second is the mining of true frequent sequential patterns, which appear with probability above a user-defined threshold in transactions drawn from the generative process underlying the data. We present the first sampling-based algorithm to mine, with high confidence, a rigorous approximation of the frequent sequential patterns from massive datasets. We also present the first algorithms to mine approximations of the true frequent sequential patterns with rigorous guarantees on the quality of the output. Our algorithms are based on novel applications of Vapnik-Chervonenkis dimension and Rademacher complexity, advanced tools from statistical learning theory, to sequential pattern mining. Our extensive experimental evaluation shows that our algorithms provide high-quality approximations for both problems we consider.

No abstract

The mining of time series data has applications in several domains, and in many cases the data are generated by networks, with time series representing paths on such networks. In this work, we consider the scenario in which the dataset, i.e., a collection of time series, is generated by an unknown underlying network, and we study the problem of mining statistically significant paths, which are paths whose number of observed occurrences in the dataset is unexpected given the distribution defined by some features of the underlying network. A major challenge in such a problem is that the underlying network is unknown, and, thus, one cannot directly identify such paths. We then propose caSPiTa, an algorithm to mine statistically significant paths in time series data generated by an unknown and underlying network that considers a generative null model based on meaningful characteristics of the observed dataset, while providing guarantees in terms of false discoveries. Our extensive evaluation on pseudo-artificial and real data shows that caSPiTa is able to efficiently mine large sets of significant paths, while providing guarantees on the false positives.

Pattern mining is a fundamental data mining task with applications in several domains. In this work, we consider the scenario in which we have a sequence of datasets generated by potentially different underlying generative processes, and we study the problem of mining statistically robust patterns, which are patterns whose probabilities of appearing in transactions drawn from such generative processes respect well-defined conditions. Such conditions define the patterns of interest, describing the evolution of their probabilities through the datasets in the sequence, which may, for example, increase, decrease, or stay stable, through the sequence. Due to the stochastic nature of the data, one cannot identify the exact set of the statistically robust patterns by analyzing a sequence of samples, i.e., the datasets, taken from the generative processes, and has to resort to approximations. We then propose gRosSo, an algorithm to find rigorous approximations of the statistically robust patterns that do not contain false positives or false negatives with high probability. We apply our framework to the mining of statistically robust sequential patterns and statistically robust itemsets. Our extensive evaluation on pseudo-artificial and real data shows that gRosSo provides high-quality approximations for the problem of mining statistically robust sequential patterns and statistically robust itemsets.