Related papers: Efficient Discovery of Association Rules and Frequ…
Frequent pattern (itemset) mining in transactional databases is one of the most well-studied problems in data mining. One obstacle that limits the practical usage of frequent pattern mining is the extremely large number of patterns…
We study the use of sampling for efficiently mining the top-K frequent itemsets of cardinality at most w. To this purpose, we define an approximation to the top-K frequent itemsets to be a family of itemsets which includes (resp., excludes)…
Frequent Itemsets (FIs) mining is a fundamental primitive in data mining. It requires to identify all itemsets appearing in at least a fraction $\theta$ of a transactional dataset $\mathcal{D}$. Often though, the ultimate goal of mining…
In this paper we present a new error bound on sampling algorithms for frequent itemsets mining. We show that the new bound is asymptotically tighter than the state-of-art bounds, i.e., given the chosen samples, for small enough error…
Data mining is the practice to search large amount of data to discover data patterns. Data mining uses mathematical algorithms to group the data and evaluate the future events. Association rule is a research area in the field of knowledge…
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…
Association rules mining (ARM) is one of the most important problems in knowledge discovery and data mining. Given a transaction database that has a large number of transactions and items, the task of ARM is to acquire consumption habits of…
We present algorithms for estimating the forward reachable set of a dynamical system using only a finite collection of independent and identically distributed samples. The produced estimate is the sublevel set of a function called an…
Here, we present a novel algorithm for frequent itemset mining for streaming data (FIM-SD). For the past decade, various FIM-SD methods in one-pass approximation settings have been developed to approximate the frequency of each itemset.…
We investigate the feasibility of sample average approximation (SAA) for general stochastic optimization problems, including two-stage stochastic programming without the relatively complete recourse assumption. Instead of analyzing problems…
We design new algorithms for the combinatorial pure exploration problem in the multi-arm bandit framework. In this problem, we are given $K$ distributions and a collection of subsets $\mathcal{V} \subset 2^{[K]}$ of these distributions, and…
Given a domain $X$ and a collection $\mathcal{H}$ of functions $h:X\to \{0,1\}$, the Vapnik-Chervonenkis (VC) dimension of $\mathcal{H}$ measures its complexity in an appropriate sense. In particular, the fundamental theorem of statistical…
Finding frequent itemsets in a data source is a fundamental operation behind Association Rule Mining. Generally, many algorithms use either the bottom-up or top-down approaches for finding these frequent itemsets. When the length of…
Mining association rules is a task of data mining, which extracts knowledge in the form of significant implication relation of useful items (objects) from a database. Mining multilevel association rules uses concept hierarchies, also called…
Apriori Algorithm is one of the most important algorithm which is used to extract frequent itemsets from large database and get the association rule for discovering the knowledge. It basically requires two important things: minimum support…
We study the complexity of the maximum coverage problem, restricted to set systems of bounded VC-dimension. Our main result is a fixed-parameter tractable approximation scheme: an algorithm that outputs a $(1-\eps)$-approximation to the…
The VC-dimension is a well-studied and fundamental complexity measure of a set system (or hypergraph) that is central to many areas of machine learning. We establish several new results on the complexity of computing the VC-dimension. In…
We study range spaces, where the ground set consists of either polygonal curves in $\mathbb{R}^d$ or polygonal regions in the plane that may contain holes and the ranges are balls defined by an elastic distance measure, such as the…
In this dissertation, I derive a new method to estimate the Vapnik-Chervonenkis Dimension (VCD) for the class of linear functions. This method is inspired by the technique developed by Vapnik et al. Vapnik et al. (1994). My contribution…
A data sketch algorithm scans a big data set, collecting a small amount of data -- the sketch, which can be used to statistically infer properties of the big data set. Some data sketch algorithms take a fixed-size random sample of a big…