Mining Sequential Patterns with VC-Dimension and Rademacher Complexity

Santoro, Diego; Tonon, Andrea; Vandin, Fabio

doi:10.3390/a13050123

Cited by 13 publications

(5 citation statements)

References 30 publications

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“…The following theorem is a generalization of a result for sequential patterns appearing in [22]. Here, we provide it for a general pattern mining task.…”

Section: Range Space Of Patternsmentioning

confidence: 89%

“…In this work, we propose a tighter upper bound on the capacity of a sequence to compute it and we apply it in a different scenario. More recently, Santoro et al [22] provide a sampling-based algorithm to compute approximations for the frequent sequential patterns problem, based on an upper bound on the VC-dimension of sequential patterns. They are also the first who consider the problem of mining true frequent sequential patterns, that are frequent sequential patterns w.r.t.…”

Section: Related Workmentioning

confidence: 99%

“…They propose two approaches to compute approximations of such a problem: one based on the empirical VC-dimension and the other based on the Rademacher complexity. While we use a general framework similar to the one proposed by [22], we consider the problem of mining statistically robust patterns in a sequence of datasets, that is a different task. Riondato and Upfal [23] are the first who apply the VC-dimension to itemsets, providing a samplingbased algorithm to compute approximations for the frequent itemsets problem.…”

Section: Related Workmentioning

confidence: 99%

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gRosSo: mining statistically robust patterns from a sequence of datasets

Tonon

Vandin

2022

Knowl Inf Syst

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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.

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“…The following theorem is a generalization of a result for sequential patterns appearing in [22]. Here, we provide it for a general pattern mining task.…”

Section: Range Space Of Patternsmentioning

confidence: 89%

Section: Related Workmentioning

confidence: 99%

Section: Related Workmentioning

confidence: 99%

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gRosSo: mining statistically robust patterns from a sequence of datasets

Tonon

Vandin

2022

Knowl Inf Syst

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“…Diego Santoro [18] have introduced a samplingbased algorithm to mine the frequent items from huge databases. The introduced sampling algorithm utilized the ideology of VC-dimension which helps in approximating the frequent sequential pattern.…”

Section: Related Workmentioning

confidence: 99%

A Progressive Sampling and RadeMacher Average for an Effective Frequent Pattern Mining in Big Data Environment

2023

IJIES

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Big data refers to the large amount of information that is collected from different areas and shared on the internet. However, this development has led to difficulties in using frequent itemset mining applications. To overcome the issue of frequent data mining, this research has introduced an empirical sampling algorithm using RadeMacher average (ESA-RMA). When considering the size of the initial sample and scheduling the samples, the ESA utilizes the RadeMacher average to bound the samples. Initially, the data is obtained from the dataset of the human activity recognition (HAR) and real time datasets from smartphone gyroscope and accelerometer, then obtained data is pre-processed using the data normalization technique. Then, the ESA is used to select the labelled data and RMA is used to bound the samples. This bounding process defines the upper limit of the input data which helps in the effective mining of frequent item sets. Thus, the data with redundant items are mined out using the proposed ESA-RMA method. The experimental results show that the proposed ESA-RMA has taken a minimum run time of 212 ms for data obtained from smartphone accelerometer which is comparatively lower than the existing Scalable Simple Random Sampling (ScaSRS) with processing time of 362 ms. Similarly, for HAR dataset, the proposed method took processing time of 5.43 s whereas the existing vertical frequent time interval-related pattern (VertTIRP) mining approach took processing time of 7.82 s.

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“…MCRapper instead computes the exact n-MCERA of the family of interest on the observed sample, without having to consider the worst case. For other kinds of patterns, Riondato and Vandin [20] studied the pseudodimension of subgroups, while Servan-Schreiber et al [22] and Santoro et al [21] considered the (empirical) VC-dimension and Rademacher averages for sequential patterns. MCRapper can be applied in all these cases, and obtains better bounds because it uses the sample-and-distribution-dependent n-MCERA, rather than a worst case dataset-dependent bound.…”

Section: Related Workmentioning

confidence: 99%

MCRapper: Monte-Carlo Rademacher Averages for Poset Families and Approximate Pattern Mining

Pellegrina

Cousins

Vandin

et al. 2020

Proceedings of the 26th ACM SIGKDD International Conference on Knowledge Discovery &Amp; Data Mining

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We present MCRapper, an algorithm for efficient computation of Monte-Carlo Empirical Rademacher Averages (MCERA) for families of functions exhibiting poset (e.g., lattice) structure, such as those that arise in many pattern mining tasks. The MCERA allows us to compute upper bounds to the maximum deviation of sample means from their expectations, thus it can be used to find both statisticallysignificant functions (i.e., patterns) when the available data is seen as a sample from an unknown distribution, and approximations of collections of high-expectation functions (e.g., frequent patterns) when the available data is a small sample from a large dataset. This feature is a strong improvement over previously proposed solutions that could only achieve one of the two. MCRapper uses upper bounds to the discrepancy of the functions to efficiently explore and prune the search space, a technique borrowed from pattern mining itself. To show the practical use of MCRapper, we employ it to develop an algorithm TFP-R for the task of True Frequent Pattern (TFP) mining. TFP-R gives guarantees on the probability of including any false positives (precision) and exhibits higher statistical power (recall) than existing methods offering the same guarantees. We evaluate MCRapper and TFP-R and show that they outperform the state-of-the-art for their respective tasks.

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Mining Sequential Patterns with VC-Dimension and Rademacher Complexity

Cited by 13 publications

References 30 publications

gRosSo: mining statistically robust patterns from a sequence of datasets

gRosSo: mining statistically robust patterns from a sequence of datasets

A Progressive Sampling and RadeMacher Average for an Effective Frequent Pattern Mining in Big Data Environment

MCRapper: Monte-Carlo Rademacher Averages for Poset Families and Approximate Pattern Mining

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