The application of stochastic models and analysis techniques to large datasets is now commonplace. Unfortunately, in practice this usually means extracting data from a database system into an external tool (such as SAS, R, Arena, or Matlab), and then running the analysis there. This extract-and-model paradigm is typically error-prone, slow, does not support fine-grained modeling, and discourages what-if and sensitivity analyses. In this article we describe MCDB, a database system that permits a wide spectrum of stochastic models to be used in conjunction with the data stored in a large database, without ever extracting the data. MCDB facilitates in-database execution of tasks such as risk assessment, prediction, and imputation of missing data, as well as management of errors due to data integration, information extraction, and privacy-preserving data anonymization. MCDB allows a user to define “random” relations whose contents are determined by stochastic models. The models can then be queried using standard SQL. Monte Carlo techniques are used to analyze the probability distribution of the result of an SQL query over random relations. Novel “tuple-bundle” processing techniques can effectively control the Monte Carlo overhead, as shown in our experiments.

We consider the problem of similarity search in applications where the cost of computing the similarity between two records is very expensive, and the similarity measure is not a metric. In such applications, comparing even a tiny fraction of the database records to a single query record can be orders of magnitude slower than reading the entire database from disk, and indexing is often not possible. We develop a general-purpose, statistical framework for answering top-k queries in such databases, when the database administrator is able to supply an inexpensive surrogate ranking function that substitutes for the actual similarity measure. We develop a robust method that learns the relationship between the surrogate function and the similarity measure. Given a query, we use Bayesian statistics to update the model by taking into account the observed partial results. Using the updated model, we construct bounds on the accuracy of the result set obtained via the surrogate ranking. Our experiments show that our models can produce useful bounds for several real-life applications.

Enterprises often need to assess and manage the risk arising from uncertainty in their data. Such uncertainty is typically modeled as a probability distribution over the uncertain data values, specified by means of a complex (often predictive) stochastic model. The probability distribution over data values leads to a probability distribution over database query results, and risk assessment amounts to exploration of the upper or lower tail of a query-result distribution. In this paper, we extend the Monte Carlo Database System to efficiently obtain a set of samples from the tail of a query-result distribution by adapting recent "Gibbs cloning" ideas from the simulation literature to a database setting.

To deal with data uncertainty, existing probabilistic database systems augment tuples with attribute-level or tuple-level probability values, which are loaded into the database along with the data itself. This approach can severely limit the system's ability to gracefully handle complex or unforeseen types of uncertainty, and does not permit the uncertainty model to be dynamically parameterized according to the current state of the database. We introduce MCDB, a system for managing uncertain data that is based on a Monte Carlo approach. MCDB represents uncertainty via "VG functions," which are used to pseudorandomly generate realized values for uncertain attributes. VG functions can be parameterized on the results of SQL queries over "parameter tables" that are stored in the database, facilitating what-if analyses. By storing parameters, and not probabilities, and by estimating, rather than exactly computing, the probability distribution over possible query answers, MCDB avoids many of the limitations of prior systems. For example, MCDB can easily handle arbitrary joint probability distributions over discrete or continuous attributes, arbitrarily complex SQL queries, and arbitrary functionals of the query-result distribution such as means, variances, and quantiles. To achieve good performance, MCDB uses novel query processing techniques, executing a query plan exactly once, but over "tuple bundles" instead of ordinary tuples. Experiments indicate that our enhanced functionality can be obtained with acceptable overheads relative to traditional systems.

We demonstrate our prototype of the DBO database system. DBO is designed to facilitate scalable analytic processing over large data archives. DBO's analytic processing performance is competitive with other database systems; however, unlike any other existing research or industrial system, DBO maintains a statistically meaningful guess to the final answer to a query from start to finish during query processing. This guess may be quite accurate after only a few seconds or minutes, while answering a query exactly may take hours. This can result in significant savings in both user and computer time, since a user can abort a query as soon as he or she is happy with the guess' accuracy.