Approximating Representations For Large Numerical Databases

The paper introduces a notion of support for real-valued functions. It is shown how to approximate supports of a large class of functions based on supports of so called polynomial itemsets, which can efficiently be mined using an Apriori-style algorithm. An upper bound for the error of such an approximation can be reliably computed. The concept of an approximating representation was introduced, which extends the idea of concise representations to numerical data. It has been shown that many standard statistical modelling tasks such as nonlinear regression and least squares curve fitting can efficiently be solved using only the approximating representation, without accessing the original data at all. Since many of those methods traditionally require several passes over the data, our approach makes it possible to use such methods with huge datasets and data streams where several repeated scans are very costly or outright impossible.