## Discovering significant patterns (2007)

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Citations: | 46 - 3 self |

### BibTeX

@MISC{Webb07discoveringsignificant,

author = {Geoffrey I. Webb},

title = {Discovering significant patterns},

year = {2007}

}

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### Abstract

Pattern discovery techniques, such as association rule discovery, explore large search spaces of potential patterns to find those that satisfy some user-specified constraints. Due to the large number of patterns considered, they suffer from an extreme risk of type-1 error, that is, of finding patterns that appear due to chance alone to satisfy the constraints on the sample data. This paper proposes techniques to overcome this problem by applying well-established statistical practices. These allow the user to enforce a strict upper limit on the risk of experimentwise error. Empirical studies demonstrate that standard pattern discovery techniques can discover numerous spurious patterns when applied to random data and when applied to real-world data result in large numbers of patterns that are rejected when subjected to sound statistical evaluation. They also reveal that a number of pragmatic choices about how such tests are performed can greatly affect their power.

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Citation Context ...ques perform on real-world data. The same seven treatments were used as for Experiment 1. Experiments were conducted using eight of the largest attribute-value datasets from the UCI machine learning (=-=Newman, Hettich, Blake, & Merz, 2006-=-) and KDD (Hettich & Bay, 2006) repositories together with the BMS-WebView-1 (Zheng, Kohavi, & Mason, 2001) and Retail (Brijs, Swinnen, Vanhoof, & Wets, 1999) datasets. These datasets are described in... |

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Citation Context ...iscovery (Agrawal, Imielinski, & Swami, 1993), k-optimal or ktop rule discovery (Webb, 1995; Scheffer & Wrobel, 2002; Webb & Zhang, 2005), contrast or emerging pattern discovery (Bay & Pazzani, 2001; =-=Dong & Li, 1999-=-), subgroup discovery (Klösgen, 1996), interesting itemset discovery (Jaroszewicz & Simovici, 2004) and impact or quantitative rule discovery (Aumann & Lindell, 1999; Webb, 2001; Zhang, Padmanabhan, &... |

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Citation Context ...as a minimum support (Agrawal et al., 1993), together with other constraints, if desired, such as minimum confidence (Agrawal et al., 1993), lift (International Business Machines, 1996), or leverage (=-=Piatetsky-Shapiro, 1991-=-). These terms are defined with respect to a rule X → y and dataset D as follows: • coverage(X → y) is |{R ∈ D : X ⊆ R}|; • support(X → y) is |{R ∈ D : X ∪ {y} ⊆ R}|; • confidence(X → y) = support(X →... |

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Citation Context ...o screen individual patterns in the context of discovering large numbers of patterns from a single set of data. This problem arises in pattern discovery, as exemplified by association rule discovery (=-=Agrawal, Imielinski, & Swami, 1993-=-), k-optimal or ktop rule discovery (Webb, 1995; Scheffer & Wrobel, 2002; Webb & Zhang, 2005), contrast or emerging pattern discovery (Bay & Pazzani, 2001; Dong & Li, 1999), subgroup discovery (Klösge... |

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Citation Context ...ed using eight of the largest attribute-value datasets from the UCI machine learning (Newman, Hettich, Blake, & Merz, 2006) and KDD (Hettich & Bay, 2006) repositories together with the BMS-WebView-1 (=-=Zheng, Kohavi, & Mason, 2001-=-) and Retail (Brijs, Swinnen, Vanhoof, & Wets, 1999) datasets. These datasets are described in Table 2. We first found for each dataset the minimum even value for minimum-support that produced fewer t... |

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Citation Context ...) and improvement (Bayardo, Agrawal, & Gunopulos, 2000). They also include the identification and rejection of redundant (Bastide, Pasquier, Taouil, Stumme, & Lakhal, 2000; Zaki, 2000) and derivable (=-=Calders & Goethals, 2002-=-) rules. Redundant rules are those such as {pregnant,female} → oedema that include items in the antecedent that are entailed by the other elements of the antecedent, as is the case with pregnant entai... |

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Citation Context ...g pattern discovery (Bay & Pazzani, 2001; Dong & Li, 1999), subgroup discovery (Klösgen, 1996), interesting itemset discovery (Jaroszewicz & Simovici, 2004) and impact or quantitative rule discovery (=-=Aumann & Lindell, 1999-=-; Webb, 2001; Zhang, Padmanabhan, & Tuzhilin, 2004). All these techniques search large spaces of possible patterns P and return all patterns that satisfy user-defined constraints. Such a process entai... |

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Citation Context ..., which, for even relatively small values of κ and n, rapidly approaches 1.0. This problem is closely related to the multiple comparisons problem (Jensen & Cohen, 2000) and the problem of oversearch (=-=Quinlan & Cameron-Jones, 1995-=-). Most pattern discovery systems do little to control this risk. While a number of approaches to controlling this risk have been developed (for example, Megiddo & Srikant, 1998; Bay & Pazzani, 2001; ... |

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Citation Context ...lift (International Business Machines, 1996) leverage (Piatetsky-Shapiro, 1991) and improvement (Bayardo, Agrawal, & Gunopulos, 2000). They also include the identification and rejection of redundant (=-=Bastide, Pasquier, Taouil, Stumme, & Lakhal, 2000-=-; Zaki, 2000) and derivable (Calders & Goethals, 2002) rules. Redundant rules are those such as {pregnant,female} → oedema that include items in the antecedent that are entailed by the other elements ... |

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Citation Context ...by association rule discovery (Agrawal, Imielinski, & Swami, 1993), k-optimal or ktop rule discovery (Webb, 1995; Scheffer & Wrobel, 2002; Webb & Zhang, 2005), contrast or emerging pattern discovery (=-=Bay & Pazzani, 2001-=-; Dong & Li, 1999), subgroup discovery (Klösgen, 1996), interesting itemset discovery (Jaroszewicz & Simovici, 2004) and impact or quantitative rule discovery (Aumann & Lindell, 1999; Webb, 2001; Zhan... |

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Citation Context ...ast one erroneous pattern by chance is 1 − (1 − κ) n , which, for even relatively small values of κ and n, rapidly approaches 1.0. This problem is closely related to the multiple comparisons problem (=-=Jensen & Cohen, 2000-=-) and the problem of oversearch (Quinlan & Cameron-Jones, 1995). Most pattern discovery systems do little to control this risk. While a number of approaches to controlling this risk have been develope... |

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Citation Context ...s of patterns from a single set of data. This problem arises in pattern discovery, as exemplified by association rule discovery (Agrawal, Imielinski, & Swami, 1993), k-optimal or ktop rule discovery (=-=Webb, 1995-=-; Scheffer & Wrobel, 2002; Webb & Zhang, 2005), contrast or emerging pattern discovery (Bay & Pazzani, 2001; Dong & Li, 1999), subgroup discovery (Klösgen, 1996), interesting itemset discovery (Jarosz... |

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Citation Context ...lue datasets from the UCI machine learning (Newman, Hettich, Blake, & Merz, 2006) and KDD (Hettich & Bay, 2006) repositories together with the BMS-WebView-1 (Zheng, Kohavi, & Mason, 2001) and Retail (=-=Brijs, Swinnen, Vanhoof, & Wets, 1999-=-) datasets. These datasets are described in Table 2. We first found for each dataset the minimum even value for minimum-support that produced fewer than 10,000 productive rules when applied with respe... |

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Citation Context ...s limitations as detailed in Section 4. The current paper investigates two approaches to applying statistical tests in pattern discovery. The first applies a Bonferroni correction for multiple tests (=-=Shaffer, 1995-=-), dividing the global significance level α by the number of patterns in the search space in order to obtain the critical value κ. The second divides the available data into exploratory and holdout se... |

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Citation Context ...m of oversearch (Quinlan & Cameron-Jones, 1995). Most pattern discovery systems do little to control this risk. While a number of approaches to controlling this risk have been developed (for example, =-=Megiddo & Srikant, 1998-=-; Bay & Pazzani, 2001; Webb, 2002), each has limitations as detailed in Section 4. The current paper investigates two approaches to applying statistical tests in pattern discovery. The first applies a... |

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Citation Context ... & Pazzani, 2001; Dong & Li, 1999), subgroup discovery (Klösgen, 1996), interesting itemset discovery (Jaroszewicz & Simovici, 2004) and impact or quantitative rule discovery (Aumann & Lindell, 1999; =-=Webb, 2001-=-; Zhang, Padmanabhan, & Tuzhilin, 2004). All these techniques search large spaces of possible patterns P and return all patterns that satisfy user-defined constraints. Such a process entails evaluatin... |

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Citation Context ..., 1995; Scheffer & Wrobel, 2002; Webb & Zhang, 2005), contrast or emerging pattern discovery (Bay & Pazzani, 2001; Dong & Li, 1999), subgroup discovery (Klösgen, 1996), interesting itemset discovery (=-=Jaroszewicz & Simovici, 2004-=-) and impact or quantitative rule discovery (Aumann & Lindell, 1999; Webb, 2001; Zhang, Padmanabhan, & Tuzhilin, 2004). All these techniques search large spaces of possible patterns P and return all p... |

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Citation Context ...s from a single set of data. This problem arises in pattern discovery, as exemplified by association rule discovery (Agrawal, Imielinski, & Swami, 1993), k-optimal or ktop rule discovery (Webb, 1995; =-=Scheffer & Wrobel, 2002-=-; Webb & Zhang, 2005), contrast or emerging pattern discovery (Bay & Pazzani, 2001; Dong & Li, 1999), subgroup discovery (Klösgen, 1996), interesting itemset discovery (Jaroszewicz & Simovici, 2004) a... |

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Citation Context ...ta. This problem arises in pattern discovery, as exemplified by association rule discovery (Agrawal, Imielinski, & Swami, 1993), k-optimal or ktop rule discovery (Webb, 1995; Scheffer & Wrobel, 2002; =-=Webb & Zhang, 2005-=-), contrast or emerging pattern discovery (Bay & Pazzani, 2001; Dong & Li, 1999), subgroup discovery (Klösgen, 1996), interesting itemset discovery (Jaroszewicz & Simovici, 2004) and impact or quantit... |

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(Show Context)
Citation Context ...2001; Dong & Li, 1999), subgroup discovery (Klösgen, 1996), interesting itemset discovery (Jaroszewicz & Simovici, 2004) and impact or quantitative rule discovery (Aumann & Lindell, 1999; Webb, 2001; =-=Zhang, Padmanabhan, & Tuzhilin, 2004-=-). All these techniques search large spaces of possible patterns P and return all patterns that satisfy user-defined constraints. Such a process entails evaluating numerous patterns ρ ∈ P against a se... |

16 |
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(Show Context)
Citation Context ...is a promising issue for further investigation. It is worth noting that an advantage of the holdout approach relative to direct-adjustment is that it can support controls on the false discovery rate (=-=Benjamini & Hochberg, 1995-=-) instead of the experimentwise error rate. If this is to be done, a technique that accommodates correlations between the hypothesis tests should be employed (Benjamini & Yekutieli, 2001). An advantag... |

4 |
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(Show Context)
Citation Context ... treatments were used as for Experiment 1. Experiments were conducted using eight of the largest attribute-value datasets from the UCI machine learning (Newman, Hettich, Blake, & Merz, 2006) and KDD (=-=Hettich & Bay, 2006-=-) repositories together with the BMS-WebView-1 (Zheng, Kohavi, & Mason, 2001) and Retail (Brijs, Swinnen, Vanhoof, & Wets, 1999) datasets. These datasets are described in Table 2. We first found for e... |

4 |
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Citation Context ...). Most pattern discovery systems do little to control this risk. While a number of approaches to controlling this risk have been developed (for example, Megiddo & Srikant, 1998; Bay & Pazzani, 2001; =-=Webb, 2002-=-), each has limitations as detailed in Section 4. The current paper investigates two approaches to applying statistical tests in pattern discovery. The first applies a Bonferroni correction for multip... |

3 | Preliminary investigations into statistically valid exploratory rule discovery - Webb - 2003 |

1 |
Magnum Opus Version 3.0.1
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(Show Context)
Citation Context ... conservative estimates of the true probability of a conjunction of conditions. Examples of this approach include DuMouchel and Pregibon’s (2001) Empirical Bayes Screening, Magnum Opus’s m-estimates (=-=Webb, 2005-=-) and Scheffer’s (1995) Bayesian Frequency Correction. These approaches can be very effective at reducing the overestimates of measures such as support or confidence that can occur for rules with low ... |