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Visual representations of data (visualizations) are tools of great importance and widespread use in data analytics as they provide users visual insight to patterns in the observed data in a simple and effective way. However, since visualizations tools are applied to sample data, there is a a risk of visualizing random fluctuations in the sample rather than a true pattern in the data. This problem is even more significant when visualization is used to identify interesting patterns among many possible possibilities, or to identify an interesting deviation in a pair of observations among many possible pairs, as commonly done in visual recommendation systems. We present VizRec, a framework for improving the performance of visual recommendation systems by quantifying the statistical significance of recommended visualizations. The proposed methodology allows to control the probability of misleading visual recommendations using both classical statistical testing procedures and a novel application of the Vapnik Chervonenkis (VC) dimension method which is a fundamental concept in statistical learning theory.

Recent tools for interactive data exploration significantly increase the chance that users make false discoveries. The crux is that these tools implicitly allow the user to test a large body of different hypotheses with just a few clicks thus incurring in the issue commonly known in statistics as the multiple hypothesis testing error. In this paper, we propose solutions to integrate multiple hypothesis testing control into interactive data exploration tools. A key insight is that existing methods for controlling the false discovery rate (such as FDR) are not directly applicable for interactive data exploration. We therefore discuss a set of new control procedures that are better suited and integrated them in our system called Aware. By means of extensive experiments using both real-world and synthetic data sets we demonstrate how Aware can help experts and novice users alike to efficiently control false discoveries.

We present TRI\`EST, a suite of one-pass streaming algorithms to compute unbiased, low-variance, high-quality approximations of the global and local (i.e., incident to each vertex) number of triangles in a fully-dynamic graph represented as an adversarial stream of edge insertions and deletions. Our algorithms use reservoir sampling and its variants to exploit the user-specified memory space at all times. This is in contrast with previous approaches which use hard-to-choose parameters (e.g., a fixed sampling probability) and offer no guarantees on the amount of memory they will use. We show a full analysis of the variance of the estimations and novel concentration bounds for these quantities. Our experimental results on very large graphs show that TRI\`EST outperforms state-of-the-art approaches in accuracy and exhibits a small update time., Comment: 49 pages, 7 figures, extended version of the paper appeared at ACM KDD'16

The tasks of extracting (top-$K$) Frequent Itemsets (FI's) and Association Rules (AR's) are fundamental primitives in data mining and database applications. Exact algorithms for these problems exist and are widely used, but their running time is hindered by the need of scanning the entire dataset, possibly multiple times. High quality approximations of FI's and AR's are sufficient for most practical uses, and a number of recent works explored the application of sampling for fast discovery of approximate solutions to the problems. However, these works do not provide satisfactory performance guarantees on the quality of the approximation, due to the difficulty of bounding the probability of under- or over-sampling any one of an unknown number of frequent itemsets. In this work we circumvent this issue by applying the statistical concept of \emph{Vapnik-Chervonenkis (VC) dimension} to develop a novel technique for providing tight bounds on the sample size that guarantees approximation within user-specified parameters. Our technique applies both to absolute and to relative approximations of (top-$K$) FI's and AR's. The resulting sample size is linearly dependent on the VC-dimension of a range space associated with the dataset to be mined. The main theoretical contribution of this work is a proof that the VC-dimension of this range space is upper bounded by an easy-to-compute characteristic quantity of the dataset which we call \emph{d-index}, and is the maximum integer $d$ such that the dataset contains at least $d$ transactions of length at least $d$ such that no one of them is a superset of or equal to another. We show that this bound is strict for a large class of datasets., Comment: 19 pages, 7 figures. A shorter version of this paper appeared in the proceedings of ECML PKDD 2012

We develop a novel method, based on the statistical concept of the Vapnik-Chervonenkis dimension, to evaluate the selectivity (output cardinality) of SQL queries - a crucial step in optimizing the execution of large scale database and data-mining operations. The major theoretical contribution of this work, which is of independent interest, is an explicit bound to the VC-dimension of a range space defined by all possible outcomes of a collection (class) of queries. We prove that the VC-dimension is a function of the maximum number of Boolean operations in the selection predicate and of the maximum number of select and join operations in any individual query in the collection, but it is neither a function of the number of queries in the collection nor of the size (number of tuples) of the database. We leverage on this result and develop a method that, given a class of queries, builds a concise random sample of a database, such that with high probability the execution of any query in the class on the sample provides an accurate estimate for the selectivity of the query on the original large database. The error probability holds simultaneously for the selectivity estimates of all queries in the collection, thus the same sample can be used to evaluate the selectivity of multiple queries, and the sample needs to be refreshed only following major changes in the database. The sample representation computed by our method is typically sufficiently small to be stored in main memory. We present extensive experimental results, validating our theoretical analysis and demonstrating the advantage of our technique when compared to complex selectivity estimation techniques used in PostgreSQL and the Microsoft SQL Server., Comment: 20 pages, 3 figures

As advances in technology allow for the collection, storage, and analysis of vast amounts of data, the task of screening and assessing the significance of discovered patterns is becoming a major challenge in data mining applications. In this work, we address significance in the context of frequent itemset mining. Specifically, we develop a novel methodology to identify a meaningful support threshold s* for a dataset, such that the number of itemsets with support at least s* represents a substantial deviation from what would be expected in a random dataset with the same number of transactions and the same individual item frequencies. These itemsets can then be flagged as statistically significant with a small false discovery rate. We present extensive experimental results to substantiate the effectiveness of our methodology., Comment: A preliminary version of this work was presented in ACM PODS 2009. 20 pages, 0 figures