Sampling Reloaded

Sampling methods are integral to the design of surveys and experiments, to the validity of results, and thus to the study of statistics, social science, and a variety other disciplines that use statistical data. Many probabilistic sampling methods have been proposed in the literature for capturing large amounts of data succinctly. Such methods are bound by the space & time constraint and find direct applications in approximate query answering systems, where the main objective is to provide a quick but approximate answer to a user query, providing error guarantees.The main principle behind the design of such systems is that for a very large data sets on which execution of complex queries is time consuming, it is much better to provide an approximate answer.Here we present a comprehensive survey of the various sampling methods and categorize them on the basis of their underlying algorithms. We present a detailed comparative analysis of various techniques and validate our observations through extensive simulations. All major queries on data streams can be categorized into (1) Count Distinct: Estimating the number of distinct value in the data stream. (2) Frequency Estimation: Estimating the approximate frequencies of elements. We study the efficiency of various schemes in answering these fundamental queries. We have analyzed the effects of probability, space and error bounds on the efficiency of various schemes. On the basis of our experimental results, we also present some heuristics for approximating count and count distinct in various scenarios.