Probability Distributions.- Linear Models for Regression.- Linear Models for Classification.- Neural Networks.- Kernel Methods.- Sparse Kernel Machines.- Graphical Models.- Mixture Models and EM.- Approximate Inference.- Sampling Methods.- Continuous Latent Variables.- Sequential Data.- Combining Models.

Pattern Recognition and Machine Learning

25. Multiple Imputation for Nonresponse in Surveys. By D. B. Rubin. ISBN 0 471 08705 X. Wiley, Chichester, 1987. 258 pp. £30.25.

Multiple Imputation for Nonresponse in Surveys

We explore the effect of dimensionality on the nearest neighbor problem. We show that under a broad set of conditions (much broader than independent and identically distributed dimensions), as dimensionality increases, the distance to the nearest data point approaches the distance to the farthest data point. To provide a practical perspective, we present empirical results on both real and synthetic data sets that demonstrate that this effect can occur for as few as 10-15 dimensions. These results should not be interpreted to mean that high-dimensional indexing is never meaningful; we illustrate this point by identifying some high-dimensional workloads for which this effect does not occur. However, our results do emphasize that the methodology used almost universally in the database literature to evaluate high-dimensional indexing techniques is flawed, and should be modified. In particular, most such techniques proposed in the literature are not evaluated versus simple linear scan, and are evaluated over workloads for which nearest neighbor is not meaningful. Often, even the reported experiments, when analyzed carefully, show that linear scan would outperform the techniques being proposed on the workloads studied in high (10-15) dimensionality!.

When is nearest neighbor meaningful

This paper presents the design of a read-optimized relational DBMS that contrasts sharply with most current systems, which are write-optimized. Among the many differences in its design are: storage of data by column rather than by row, careful coding and packing of objects into storage including main memory during query processing, storing an overlapping collection of column-oriented projections, rather than the current fare of tables and indexes, a non-traditional implementation of transactions which includes high availability and snapshot isolation for read-only transactions, and the extensive use of bitmap indexes to complement B-tree structures.We present preliminary performance data on a subset of TPC-H and show that the system we are building, C-Store, is substantially faster than popular commercial products. Hence, the architecture looks very encouraging.

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C-store: a column-oriented DBMS

コンピュータ・サイエンス : ACM computing surveys

Efficient processing of top-k queries is a crucial requirement in many interactive environments that involve massive amounts of data. In particular, efficient top-k processing in domains such as the Web, multimedia search, and distributed systems has shown a great impact on performance. In this survey, we describe and classify top-k processing techniques in relational databases. We discuss different design dimensions in the current techniques including query models, data access methods, implementation levels, data and query certainty, and supported scoring functions. We show the implications of each dimension on the design of the underlying techniques. We also discuss top-k queries in XML domain, and show their connections to relational approaches.

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A survey of top-k query processing techniques in relational database systems

Top-k processing in uncertain databases is semantically and computationally different from traditional top-k processing. The interplay between score and uncertainty makes traditional techniques inapplicable. We introduce new probabilistic formulations for top-k queries. Our formulations are based on "marriage" of traditional top-k semantics and possible worlds semantics. In the light of these formulations, we construct a framework that encapsulates a state space model and efficient query processing techniques to tackle the challenges of uncertain data settings. We prove that our techniques are optimal in terms of the number of accessed tuples and materialized search states. Our experiments show the efficiency of our techniques under different data distributions with orders of magnitude improvement over naive materialization of possible worlds.

/pdf/top-k-query-processing-in-uncertain-databases-2eajk65ijw.pdf

Top-k Query Processing in Uncertain Databases

Ranking queries, also known as top-k queries, produce results that are ordered on some computed score. Typically, these queries involve joins, where users are usually interested only in the top-k join results. Top-k queries are dominant in many emerging applications, e.g., multimedia retrieval by content, Web databases, data mining, middlewares, and most information retrieval applications. Current relational query processors do not handle ranking queries efficiently, especially when joins are involved. In this paper, we address supporting top-k join queries in relational query processors. We introduce a new rank-join algorithm that makes use of the individual orders of its inputs to produce join results ordered on a user-specified scoring function. The idea is to rank the join results progressively during the join operation. We introduce two physical query operators based on variants of ripple join that implement the rank-join algorithm. The operators are nonblocking and can be integrated into pipelined execution plans. We also propose an efficient heuristic designed to optimize a top-k join query by choosing the best join order. We address several practical issues and optimization heuristics to integrate the new join operators in practical query processors. We implement the new operators inside a prototype database engine based on PREDATOR. The experimental evaluation of our approach compares recent algorithms for joining ranked inputs and shows superior performance.

/pdf/supporting-top-k-join-queries-in-relational-databases-1xpj10acuh.pdf

Supporting top- k join queries in relational databases

We introduce HoloClean, a framework for holistic data repairing driven by probabilistic inference. HoloClean unifies qualitative data repairing, which relies on integrity constraints or external data sources, with quantitative data repairing methods, which leverage statistical properties of the input data. Given an inconsistent dataset as input, HoloClean automatically generates a probabilistic program that performs data repairing. Inspired by recent theoretical advances in probabilistic inference, we introduce a series of optimizations which ensure that inference over HoloClean's probabilistic model scales to instances with millions of tuples. We show that HoloClean finds data repairs with an average precision of ∼ 90% and an average recall of above ∼ 76% across a diverse array of datasets exhibiting different types of errors. This yields an average F1 improvement of more than 2× against state-of-the-art methods.

/pdf/holoclean-holistic-data-repairs-with-probabilistic-inference-528w5hw8xy.pdf

HoloClean: holistic data repairs with probabilistic inference

The rich dependency structure found in the columns of real-world relational databases can be exploited to great advantage, but can also cause query optimizers---which usually assume that columns are statistically independent---to underestimate the selectivities of conjunctive predicates by orders of magnitude. We introduce CORDS, an efficient and scalable tool for automatic discovery of correlations and soft functional dependencies between columns. CORDS searches for column pairs that might have interesting and useful dependency relations by systematically enumerating candidate pairs and simultaneously pruning unpromising candidates using a flexible set of heuristics. A robust chi-squared analysis is applied to a sample of column values in order to identify correlations, and the number of distinct values in the sampled columns is analyzed to detect soft functional dependencies. CORDS can be used as a data mining tool, producing dependency graphs that are of intrinsic interest. We focus primarily on the use of CORDS in query optimization. Specifically, CORDS recommends groups of columns on which to maintain certain simple joint statistics. These "column-group" statistics are then used by the optimizer to avoid naive selectivity estimates based on inappropriate independence assumptions. This approach, because of its simplicity and judicious use of sampling, is relatively easy to implement in existing commercial systems, has very low overhead, and scales well to the large numbers of columns and large table sizes found in real-world databases. Experiments with a prototype implementation show that the use of CORDS in query optimization can speed up query execution times by an order of magnitude. CORDS can be used in tandem with query feedback systems such as the LEO learning optimizer, leveraging the infrastructure of such systems to correct bad selectivity estimates and ameliorating the poor performance of feedback systems during slow learning phases.

/pdf/cords-automatic-discovery-of-correlations-and-soft-17d9bfgqsp.pdf

Ihab F. Ilyas

Papers

A survey of top-k query processing techniques in relational database systems

Top-k Query Processing in Uncertain Databases

Supporting top- k join queries in relational databases

HoloClean: holistic data repairs with probabilistic inference

CORDS: automatic discovery of correlations and soft functional dependencies