Decision making under uncertainty often requires choosing packages , or bags of tuples, that collectively optimize expected outcomes while limiting risks. Processing Stochastic Package Queries (SPQs) involves solving very large optimization problems on uncertain data. Monte Carlo methods create numerous scenarios , or sample realizations of the stochastic attributes of all the tuples, and generate packages with optimal objective values across these scenarios. The number of scenarios needed for accurate approximation—and hence the size of the optimization problem when using prior methods—increases with variance in the data, and the search space of the optimization problem increases exponentially with the number of tuples in the relation. Existing solvers take hours to process SPQs on large relations containing stochastic attributes with high variance. Besides enriching the SPaQL language to capture a broader class of risk specifications, we make two fundamental contributions toward scalable SPQ processing. First, we propose risk-constraint linearization (RCL), which converts SPQs into Integer Linear Programs (ILPs) whose size is independent of the number of scenarios used. Solving these ILPs gives us feasible and near-optimal packages. Second, we propose Stochastic SketchRefine, a divide and conquer framework that breaks down a large stochastic optimization problem into subproblems involving smaller subsets of tuples. Our experiments show that, together, RCL and Stochastic SketchRefine produce high-quality packages in orders of magnitude lower runtime than the state of the art.

A package query returns a package---a multiset of tuples---that maximizes or minimizes a linear objective function subject to linear constraints, thereby enabling in-database decision support. Prior work has established the equivalence of package queries to Integer Linear Programs (ILPs) and developed the SketchRefine algorithm for package query processing. While this algorithm was an important first step toward supporting prescriptive analytics scalably inside a relational database, it struggles when the data size grows beyond a few hundred million tuples or when the constraints become very tight. In this paper, we present Progressive Shading, a novel algorithm for processing package queries that can scale efficiently to billions of tuples and gracefully handle tight constraints. Progressive Shading solves a sequence of optimization problems over a hierarchy of relations, each resulting from an ever-finer partitioning of the original tuples into homogeneous groups until the original relation is obtained. This strategy avoids the premature discarding of high-quality tuples that can occur with SketchRefine. Our novel partitioning scheme, Dynamic Low Variance, can handle very large relations with multiple attributes and can dynamically adapt to both concentrated and spread-out sets of attribute values, provably outperforming traditional partitioning schemes such as kd-tree. We further optimize our system by replacing our off-the-shelf optimization software with customized ILP and LP solvers, called Dual Reducer and Parallel Dual Simplex respectively, that are highly accurate and orders of magnitude faster.

We provide methods for in-database support of decision making under uncertainty. Many important decision problems correspond to selecting a "package" (bag of tuples in a relational database) that jointly satisfy a set of constraints while minimizing some overall "cost" function; in most real-world problems, the data is uncertain. We provide methods for specifying---via a SQL extension---and processing stochastic package queries (SPQS), in order to solve optimization problems over uncertain data, right where the data resides. Prior work in stochastic programming uses Monte Carlo methods where the original stochastic optimization problem is approximated by a large deterministic optimization problem that incorporates many "scenarios", i.e., sample realizations of the uncertain data values. For large database tables, however, a huge number of scenarios is required, leading to poor performance and, often, failure of the solver software. We therefore provide a novel ßs algorithm that, instead of trying to solve a large deterministic problem, seamlessly approximates it via a sequence of smaller problems defined over carefully crafted "summaries" of the scenarios that accelerate convergence to a feasible and near-optimal solution. Experimental results on our prototype system show that ßs can be orders of magnitude faster than prior methods at finding feasible and high-quality packages.

Everyone needs to make decisions under uncertainty and with limited resources, e.g., an investor who is building a stock portfolio subject to an investment budget and a bounded risk tolerance. Doing this with current technology is hard. There is a disconnect between software tools for data management, stochastic predictive modeling (e.g., simulation of future stock prices), and optimization; this leads to cumbersome analytical workflows. Moreover, current methods do not scale. To handle a broad class of uncertainty models, analysts approximate the original stochastic optimization problem by a large deterministic optimization problem that incorporates many "scenarios", i.e., sample realizations of the uncertain data values. For large problems, a huge number of scenarios is required, often causing the solver to fail. We demonstrate sPaQLTooLs, a system for in-database specification and scalable solution of constrained optimization problems. The key ingredients are (i) a database-oriented specification of constrained stochastic optimization problems as "stochastic package queries" (SPQs), (ii) use of a Monte Carlo database to incorporate stochastic predictive models, and (iii) a new SummarySearch algorithm for scalably solving SPQs with approximation guarantees. In this demonstration, the attendees will experience first-hand the difficulty of manually constructing feasible and high-quality portfolios, using real-world stock market data. We will then demonstrate how SummarySearch can easily and efficiently help them find very good portfolios, while being orders of magnitude faster than prior methods.

Text document summarization refers to the task of producing a brief representation of a document for easy human consumption. Existing text summarization techniques mostly focus on generic summarization, but users often require personalized summarization that targets their specific preferences and needs. However, precisely expressing preferences is challenging, and current methods are often ambiguous, outside the user's control, or require costly training data. We propose a novel and effective way to express summarization intent (preferences) via examples : the user provides a few example summaries for a small number of documents in a collection, and the system summarizes the rest. We demonstrate SuDocu, an example-based personalized Document Summarization system. Through a simple interface, SuDocu allows the users to provide example summaries, learns the summarization intent from the examples, and produces summaries for new documents that reflect the user's summarization intent. SuDocu further explains the captured summarization intent in the form of a package query , an extension of a traditional SQL query that handles complex constraints and preferences over answer sets. SuDocu combines topic modeling, semantic similarity discovery, and in-database optimization in a novel way to achieve example-driven document summarization. We demonstrate how SuDocu can detect complex summarization intents from a few example summaries and produce accurate summaries for new documents effectively and efficiently.

Efficiently computing linear algebra expressions is central to machine learning (ML) systems. Most systems support sparse formats and operations because sparse matrices are ubiquitous and their dense representation can cause prohibitive overheads. Estimating the sparsity of intermediates, however, remains a key challenge when generating execution plans or performing sparse operations. These sparsity estimates are used for cost and memory estimates, format decisions, and result allocation. Existing estimators tend to focus on matrix products only, and struggle to attain good accuracy with low estimation overhead. However, a key observation is that real-world sparse matrices commonly exhibit structural properties such as a single non-zero per row, or columns with varying sparsity. In this paper, we introduce MNC (Matrix Non-zero Count), a remarkably simple, count-based matrix synopsis that exploits these structural properties for efficient, accurate, and general sparsity estimation. We describe estimators and sketch propagation for realistic linear algebra expressions. Our experiments - on a new estimation benchmark called SparsEst - show that the MNC estimator yields good accuracy with very low overhead. This behavior makes MNC practical and broadly applicable in ML systems.

To maintain the accuracy of supervised learning models in the presence of evolving data streams, we provide temporally biased sampling schemes that weight recent data most heavily, with inclusion probabilities for a given data item decaying over time according to a specified “decay function.” We then periodically retrain the models on the current sample. This approach speeds up the training process relative to training on all of the data. Moreover, time-biasing lets the models adapt to recent changes in the data while—unlike in a sliding-window approach—still keeping some old data to ensure robustness in the face of temporary fluctuations and periodicities in the data values. In addition, the sampling-based approach allows existing analytic algorithms for static data to be applied to dynamic streaming data essentially without change. We provide and analyze both a simple sampling scheme (Targeted-Size Time-Biased Sampling (T-TBS)) that probabilistically maintains a target sample size and a novel reservoir-based scheme (Reservoir-Based Time-Biased Sampling (R-TBS)) that is the first to provide both control over the decay rate and a guaranteed upper bound on the sample size. If the decay function is exponential, then control over the decay rate is complete, and R-TBS maximizes both expected sample size and sample-size stability. For general decay functions, the actual item inclusion probabilities can be made arbitrarily close to the nominal probabilities, and we provide a scheme that allows a tradeoff between sample footprint and sample-size stability. R-TBS rests on the notion of a “fractional sample” and allows for data arrival rates that are unknown and time varying (unlike T-TBS). The R-TBS and T-TBS schemes are of independent interest, extending the known set of unequal-probability sampling schemes. We discuss distributed implementation strategies; experiments in Spark illuminate the performance and scalability of the algorithms, and show that our approach can increase machine learning robustness in the face of evolving data.

To maintain the accuracy of supervised learning models in the presence of evolving data streams, we provide temporally-biased sampling schemes that weight recent data most heavily, with inclusion probabilities for a given data item decaying exponentially over time. We then periodically retrain the models on the current sample. This approach speeds up the training process relative to training on all of the data. Moreover, time-biasing lets the models adapt to recent changes in the data while -- unlike in a sliding-window approach -- still keeping some old data to ensure robustness in the face of temporary fluctuations and periodicities in the data values. In addition, the sampling-based approach allows existing analytic algorithms for static data to be applied to dynamic streaming data essentially without change. We provide and analyze both a simple sampling scheme (T-TBS) that probabilistically maintains a target size and a novel reservoir-based scheme (R-TBS) that is the first to provide both complete control over the decay rate and a guaranteed upper bound on the size, while maximizing both expected size and sample-size stability. The latter scheme rests on the notion of a fractional sample and, unlike T-TBS, allows for data arrival rates that are unknown and time varying. R-TBS and T-TBS are of independent interest, extending the known set of unequal-probability sampling schemes. We discuss distributed implementation strategies; experiments in Spark illuminate the performance and scalability of the algorithms, and show that our approach can increase machine learning robustness in the face of evolving data.

Current tools for exploratory data analysis (EDA) require users to manually select data attributes, statistical computations and visual encodings. This can be daunting for large-scale, complex data. We introduce Foresight, a system that helps the user rapidly discover visual insights from large high-dimensional datasets. Formally, an "insight" is a strong manifestation of a statistical property of the data, e.g., high correlation between two attributes, high skewness or concentration about the mean of a single attribute, a strong clustering of values, and so on. For each insight type, Foresight initially presents visualizations of the top k instances in the data, based on an appropriate ranking metric. The user can then look at "nearby" insights by issuing "insight queries" containing constraints on insight strengths and data attributes. Thus the user can directly explore the space of insights, rather than the space of data dimensions and visual encodings as in other visual recommender systems. Foresight also provides "global" views of insight space to help orient the user and ensure a thorough exploration process. Furthermore, Foresight facilitates interactive exploration of large datasets through fast, approximate sketching.

Large-scale machine learning (ML) algorithms are often iterative, using repeated read-only data access and I/O-bound matrix-vector multiplications to converge to an optimal model. It is crucial for performance to fit the data into single-node or distributed main memory. General-purpose, heavy- and lightweight compression techniques struggle to achieve both good compression ratios and fast decompression speed to enable block-wise uncompressed operations. Hence, we initiate work on compressed linear algebra (CLA), in which lightweight database compression techniques are applied to matrices and then linear algebra operations such as matrix-vector multiplication are executed directly on the compressed representations. We contribute effective column compression schemes, cache-conscious operations, and an efficient sampling-based compression algorithm. Our experiments show that CLA achieves in-memory operations performance close to the uncompressed case and good compression ratios that allow us to fit larger datasets into available memory. We thereby obtain significant end-to-end performance improvements up to 26x or reduced memory requirements.

Shared-nothing systems such as Hadoop vastly simplify parallel programming when processing disk-resident data whose size exceeds aggregate cluster memory. Such systems incur a significant performance penalty, however, on the important class of “groupwise set-valued analytics” (GSVA) queries in which the data is dynamically partitioned into groups and then a set-valued synopsis is computed for some or all of the groups. Key examples of synopses include top-k sets, bottom-k sets, and uniform random samples. Applications of GSVA queries include micro-marketing, root-cause analysis for problem diagnosis, and fraud detection. A naive approach to executing GSVA queries first reshuffles all of the data so that all records in a group are at the same node and then computes the synopsis for the group. This approach can be extremely inefficient when, as is typical, only a very small fraction of the records in each group actually contribute to the final groupwise synopsis, so that most of the shuffling effort is wasted. We show how to significantly speed up GSVA queries by slightly modifying the shared-nothing environment to allow tasks to occasionally access a small, common data structure; we focus on the Hadoop setting and use the “Adaptive MapReduce” infrastructure of Vernica et al. to implement the data structure. Our approach retains most of the advantages of a system such as Hadoop while significantly improving GSVA query performance, and also allows for incremental updating of query results. Experiments show speedups of up to 5x. Importantly, our new technique can potentially be applied to other shared-nothing systems with disk-resident data.

A large scale network of social interactions, such as mentions in Twitter, can often be modeled as a “dynamic interaction graph” in which new interactions (edges) are continually added over time. Existing systems for extracting timely insights from such graphs are based on either a cumulative “snapshot” model or a “sliding window” model. The former model does not sufficiently emphasize recent interactions. The latter model abruptly forgets past interactions, leading to discontinuities in which, e.g., the graph analysis completely ignores historically important influencers who have temporarily gone dormant. We introduce TIDE, a distributed system for analyzing dynamic graphs that employs a new “probabilistic edge decay” (PED) model. In this model, the graph analysis algorithm of interest is applied at each time step to one or more graphs obtained as samples from the current “snapshot” graph that comprises all interactions that have occurred so far. The probability that a given edge of the snapshot graph is included in a sample decays over time according to a user specified decay function. The PED model allows controlled trade-offs between recency and continuity, and allows existing analysis algorithms for static graphs to be applied to dynamic graphs essentially without change. For the important class of exponential decay functions, we provide efficient methods that leverage past samples to incrementally generate new samples as time advances. We also exploit the large degree of overlap between samples to reduce memory consumption from O(N) to O(logN) when maintaining N sample graphs. Finally, we provide bulk-execution methods for applying graph algorithms to multiple sample graphs simultaneously without requiring any changes to existing graph-processing APIs. Experiments on a real Twitter dataset demonstrate the effectiveness and efficiency of our TIDE prototype, which is built on top of the Spark distributed computing framework.

We present KnIT, the Knowledge Integration Toolkit, a system for accelerating scientific discovery and predicting previously unknown protein-protein interactions. Such predictions enrich biological research and are pertinent to drug discovery and the understanding of disease. Unlike a prior study, KnIT is now fully automated and demonstrably scalable. It extracts information from the scientific literature, automatically identifying direct and indirect references to protein interactions, which is knowledge that can be represented in network form. It then reasons over this network with techniques such as matrix factorization and graph diffusion to predict new, previously unknown interactions. The accuracy and scope of KnIT's knowledge extractions are validated using comparisons to structured, manually curated data sources as well as by performing retrospective studies that predict subsequent literature discoveries using literature available prior to a given date. The KnIT methodology is a step towards automated hypothesis generation from text, with potential application to other scientific domains.

Keeping up with the ever-expanding flow of data and publications is untenable and poses a fundamental bottleneck to scientific progress. Current search technologies typically find many relevant documents, but they do not extract and organize the information content of these documents or suggest new scientific hypotheses based on this organized content. We present an initial case study on KnIT, a prototype system that mines the information contained in the scientific literature, represents it explicitly in a queriable network, and then further reasons upon these data to generate novel and experimentally testable hypotheses. KnIT combines entity detection with neighbor-text feature analysis and with graph-based diffusion of information to identify potential new properties of entities that are strongly implied by existing relationships. We discuss a successful application of our approach that mines the published literature to identify new protein kinases that phosphorylate the protein tumor suppressor p53. Retrospective analysis demonstrates the accuracy of this approach and ongoing laboratory experiments suggest that kinases identified by our system may indeed phosphorylate p53. These results establish proof of principle for automated hypothesis generation and discovery based on text mining of the scientific literature.

In the past few years, research around (big) data management has begun to intertwine with research around predictive modeling and simulation in novel and interesting ways. Driving this trend is an increasing recognition that information contained in real-world data must be combined with information from domain experts, as embodied in simulation models, in order to enable robust decision making under uncertainty. Simulation models of large, complex systems (traffic, biology, population well-being) consume and produce massive amounts of data and compound the challenges of traditional information management. We survey some challenges, mathematical tools, and future directions in the emerging research area of model-data ecosystems. Topics include (i) methods for enabling data-intensive simulation, (ii) simulation and information integration, and (iii) simulation metamodeling for guiding the generation of simulated data and the collection of real-world data.

An increasingly important analytics scenario for Hadoop involves multiple (often ad hoc) grouping and aggregation queries with selection predicates over a slowly changing dataset. These queries are typically expressed via high-level query languages such as Jaql, Pig, and Hive, and are used either directly for business-intelligence applications or to prepare the data for statistical model building and machine learning. In such scenarios it has been increasingly recognized that, as in classical databases, techniques for avoiding access to irrelevant data can dramatically improve query performance. Prior work on Hadoop, however, has simply ported classical techniques to the MapReduce setting, focusing on record-level indexing and key-based partition elimination. Unfortunately, record-level indexing only slightly improves overall query performance, because it does not minimize the number of mapper "waves", which is determined by the number of processed splits. Moreover, key-based partitioning requires data reorganization, which is usually impractical in Hadoop settings. We therefore need to re-envision how data access mechanisms are defined and implemented. To this end, we introduce the Eagle-Eyed Elephant (E3) framework for boosting the efficiency of query processing in Hadoop by avoiding accesses of data splits that are irrelevant to the query at hand. Using novel techniques involving inverted indexes over splits, domain segmentation, materialized views, and adaptive caching, E3 avoids accessing irrelevant splits even in the face of evolving workloads and data. Our experiments show that E3 can achieve up to 20x cost savings with small to moderate storage overheads.

This paper describes the SimSQL system, which allows for SQLbased specification, simulation, and querying of database-valued Markov chains, i.e., chains whose value at any time step comprises the contents of an entire database. SimSQL extends the earlier Monte Carlo database system (MCDB), which permitted Monte Carlo simulation of static database-valued random variables. Like MCDB, SimSQL uses user-specified "VG functions" to generate the simulated data values that are the building blocks of a simulated database. The enhanced functionality of SimSQL is enabled by the ability to parametrize VG functions using stochastic tables, so that one stochastic database can be used to parametrize the generation of another stochastic database, which can parametrize another, and so on. Other key extensions include the ability to explicitly define recursive versions of a stochastic table and the ability to execute the simulation in a MapReduce environment. We focus on applying SimSQL to Bayesian machine learning.

Virtually all work on topic modeling has assumed that the topics are to be learned over a text-based document corpus. However, there exist important applications where topic models must be learned over an audio corpus of spoken language. Unfortunately, speech-to-text programs can have very low accuracy. We therefore propose a novel topic model for spoken language that incorporates a statistical model of speech-to-text software behavior. Crucially, our model exploits the uncertainty numbers returned by the software. Our ideas apply to any domain in which it would be useful to build a topic model over data in which uncertainties are explicitly represented.

We provide a novel algorithm to approximately factor large matrices with millions of rows, millions of columns, and billions of nonzero elements. Our approach rests on stochastic gradient descent (SGD), an iterative stochastic optimization algorithm. We first develop a novel "stratified" SGD variant (SSGD) that applies to general loss-minimization problems in which the loss function can be expressed as a weighted sum of "stratum losses." We establish sufficient conditions for convergence of SSGD using results from stochastic approximation theory and regenerative process theory. We then specialize SSGD to obtain a new matrix-factorization algorithm, called DSGD, that can be fully distributed and run on web-scale datasets using, e.g., MapReduce. DSGD can handle a wide variety of matrix factorizations. We describe the practical techniques used to optimize performance in our DSGD implementation. Experiments suggest that DSGD converges significantly faster and has better scalability properties than alternative algorithms.

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.

Many modern enterprises are collecting data at the most detailed level possible, creating data repositories ranging from terabytes to petabytes in size. The ability to apply sophisticated statistical analysis methods to this data is becoming essential for marketplace competitiveness. This need to perform deep analysis over huge data repositories poses a significant challenge to existing statistical software and data management systems. On the one hand, statistical software provides rich functionality for data analysis and modeling, but can handle only limited amounts of data; e.g., popular packages like R and SPSS operate entirely in main memory. On the other hand, data management systems - such as MapReduce-based systems - can scale to petabytes of data, but provide insufficient analytical functionality. We report our experiences in building Ricardo, a scalable platform for deep analytics. Ricardo is part of the eXtreme Analytics Platform (XAP) project at the IBM Almaden Research Center, and rests on a decomposition of data-analysis algorithms into parts executed by the R statistical analysis system and parts handled by the Hadoop data management system. This decomposition attempts to minimize the transfer of data across system boundaries. Ricardo contrasts with previous approaches, which try to get along with only one type of system, and allows analysts to work on huge datasets from within a popular, well supported, and powerful analysis environment. Because our approach avoids the need to re-implement either statistical or data-management functionality, it can be used to solve complex problems right now.

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.

Entity uncertainty is an unavoidable problem in modern enterprise databases, resulting from integration of data over multiple sources. In traditional warehousing, the administrator, during an ETL process, manually and laboriously resolves inconsistent data records to discover "true'' entities(customers, products, etc.) and identify their "correct'' attribute values. At any time point, however, the current entity resolution is merely a best guess, and OLAP query results based on this resolution are inherently imprecise. We propose a new approach that maintains the data in an unresolved state, and dynamically deals with entity uncertainty at query time. We enhance the traditional OLAP model to return not a single query answer, but rather upper and lower bounds on each OLAP aggregate. This approach avoids expensive entity-resolution processing, and serves to identify potential risks when making business decisions based on the results of OLAP queries. By focusing on bounds, rather than probability distributions, we can easily and efficiently process roll-up and group-by aggregation queries over all of the core aggregation functions. Moreover, our approach can be readily implemented in an existing RDBMS using SQL queries, and does not require the user to specify explicit probabilities for alternative entity resolutions. Experiments show that the overhead of our new OLAP functionality is small over a wide range of scenarios.

Rule-based information extraction is a process by which structured objects are extracted from text based on user-defined rules. The compositional nature of rule-based information extraction also allows rules to be expressed over previously extracted objects. Such extraction is inherently uncertain, due to the varying precision associated with the rules used in a specific extraction task. Quantifying this uncertainty is crucial for querying the extracted objects in probabilistic databases, and for improving the recall of extraction tasks that use compositional rules. In this paper, we provide a probabilistic framework for handling the uncertainty in rule-based information extraction. Specifically, for each extraction task, we build a parametric exponential model of uncertainty that captures the interaction between the different rules, as well as the compositional nature of the rules; the exponential form of our model follows from maximum-entropy considerations. We also give model-decomposition techniques that make the learning algorithms scalable to large numbers of rules and constraints. Experiments over multiple real-world extraction tasks confirm that our approach yields accurate probability estimates with only a small performance overhead. Moreover, our framework supports incremental pay-as-you-go improvements in the accuracy of probability estimates as new rules, data, or constraints are added.

Modern enterprises must manage uncertain data for purposes of risk assessment and decisionmaking under uncertainty. The Monte Carlo approach embodied in the MCDB system of Jampani et al. is well suited for such a task. MCDB can support industrial strength business-intelligence queries over uncertain warehouse data. Moreover, MCDB's extensible approach to specifying uncertainty can also capture complex stochastic prediction models, allowing sophisticated ``what-if'' analyses within the DBMS. The MCDB computations can be highly CPU intensive, but offer the potential for massive parallelization. To realize this potential, we provide a new system, called MC3 (Monte Carlo Computation on a Cluster), that extends the MCDB approach to the map-reduce processing framework. MC3 can exploit the robustness and scalability of map-reduce, and can handle data stored in non-relational formats. We show how MCDB query plans over ``tuple bundles'' can be translated to sequences of map-reduce operations over nested data, and describe different parallelization schemes. We also provide and analyze several novel distributed algorithms for adding pseudorandom number seeds to tuple bundles. These algorithms ensure statistical correctness of the Monte-Carlo computations while minimizing the seed length. Our experiments show that MC3 can scale well for a variety of workloads.

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.

Computer architectures are increasingly based on multi-core CPUs and large memories. Memory bandwidth, which has riot kept pace with the increasing number of cores, has become the primary processing bottleneck, replacing disk I/O as the limiting factor. To address this challenge, we provide novel algorithms for increasing the throughput of Business Intelligence (BI) queries, as well as for ensuring fairness and avoiding starvation among a concurrent set of such queries. To maximize throughput, we propose a novel FullSharing scheme that allows all concurrent queries, when performing base-table I/O, to share the cache belonging to a given core. We then generalize this approach to a BatchSharing scheme that avoids thrashing on "agg-tables" ---hash tables that are used for aggregation processing---caused by execution of too many queries on a core. This scheme partitions queries into batches such that the working-set of agg-table entries for each batch can fit into a cache; an efficient sampling technique is used to estimate selectivities and working-set sizes for purposes of query partitioning. Finally, we use lottery-scheduling techniques to ensure fairness and impose a hard upper bound on staging time to avoid starvation. On our 8-core testbed, we were able to completely remove the memory I/O bottleneck, increasing throughput by a factor of 2 to 2.5, while also maintaining fairness and avoiding starvation.

Random sampling has become a crucial component of modern data management systems. Although the literature on database sampling is large, there has been relatively little work on the problem of maintaining a sample in the presence of arbitrary insertions and deletions to the underlying dataset. Most existing maintenance techniques apply either to the insert-only case or to datasets that do not contain duplicates. In this paper, we provide a scheme that maintains a Bernoulli sample of an underlying multiset in the presence of an arbitrary stream of updates, deletions, and insertions. Importantly, the scheme never needs to access the underlying multiset. Such Bernoulli samples are easy to manipulate, and are well suited to parallel processing environments. Our method can be viewed as an enhancement of the "counting sample" scheme developed by Gibbons and Matias for estimating the frequency of highly frequent items. We show how the "tracking counters" used by our maintenance scheme can be exploited to estimate population frequencies, sums, and averages in an unbiased manner, with lower variance than the usual estimators based on a Bernoulli sample. The number of distinct items in the multiset can also be estimated without bias. Finally, we discuss certain problems of subsampling and merging that a rise in systems with limited memory resources or distributed processing, respectively.

The task of estimating the number of distinct values (DVs) in a large dataset arises in a wide variety of settings in computer science and elsewhere. We provide DV estimation techniques that are designed for use within a flexible and scalable "synopsis warehouse" architecture. In this setting, incoming data is split into partitions and a synopsis is created for each partition; each synopsis can then be used to quickly estimate the number of DVs in its corresponding partition. By combining and extending a number of results in the literature, we obtain both appropriate synopses and novel DV estimators to use in conjunction with these synopses. Our synopses can be created in parallel, and can then be easily combined to yield synopses and DV estimates for arbitrary unions, intersections or differences of partitions. Our synopses can also handle deletions of individual partition elements. We use the theory of order statistics to show that our DV estimators are unbiased, and to establish moment formulas and sharp error bounds. Based on a novel limit theorem, we can exploit results due to Cohen in order to select synopsis sizes when initially designing the warehouse. Experiments and theory indicate that our synopses and estimators lead to lower computational costs and more accurate DV estimates than previous approaches.

We consider the problem of maintaining a warehouse of sampled data that "shadows" a full-scale data warehouse, in order to support quick approximate analytics and metadata discovery. The full-scale warehouse comprises many "data sets," where a data set is a bag of values; the data sets can vary enormously in size. The values constituting a data set can arrive in batch or stream form. We provide and compare several new algorithms for independent and parallel uniform random sampling of data-set partitions, where the partitions are created by dividing the batch or splitting the stream. We also provide novel methods for merging samples to create a uniform sample from an arbitrary union of data-set partitions. Our sampling/merge methods are the first to simultaneously support statistical uniformity, a priori bounds on the sample footprint, and concise sample storage. As partitions are rolled in and out of the warehouse, the corresponding samples are rolled in and out of the sample warehouse. In this manner our sampling methods approximate the behavior of more sophisticated stream-sampling methods, while also supporting parallel processing. Experiments indicate that our methods are efficient and scalable, and provide guidance for their application.

Database columns are often correlated, so that cardinality estimates computed by assuming independence often lead to a poor choice of query plan by the optimizer. Multidimensional histograms can help solve this problem, but the traditional approach of building such histograms using a data scan often scales poorly and does not always yield the best histogram for a given workload. An attractive alternative is to gather feedback from the query execution engine about the observed cardinality of predicates and use this feedback as the basis for a histogram. In this paper we describe ISOMER, a new feedback-based algorithm for collecting optimizer statistics by constructing and maintaining multidimensional histograms. ISOMER uses the maximumentropy principle to approximate the true data distribution by a histogram distribution that is as "simple"as possible while being consistent with the observed predicate cardinalities. ISOMER adapts readily to changes in the underlying data, automatically detecting and eliminating inconsistent feedback information in an efficient manner. The algorithm controls the size of the histogram by retaining only the most "important" feedback. Our experiments indicate that, unlike previous methods for feedback-driven histogram maintenance, ISOMER imposes little overhead, is extremely scalable, and yields highly accurate cardinality estimates while using only a modest amount of storage.

When comparing alternative query execution plans (QEPs), a cost-based query optimizer in a relational database management system needs to estimate the selectivity of conjunctive predicates. To avoid inaccurate independence assumptions, modern optimizers try to exploit multivariate statistics (MVS) that provide knowledge about joint frequencies in a table of a relation. Because the complete joint distribution is almost always too large to store, optimizers are given only partial knowledge about this distribution. As a result, there exist multiple, non-equivalent ways to estimate the selectivity of a conjunctive predicate. To consistently combine the partial knowledge during the estimation process, existing optimizers employ cumbersome ad hoc heuristics. These methods unjustifiably ignore valuable information, and the optimizer tends to favor QEPs for which the least information is available. This bias problem yields poor QEP quality and performance. We demonstrate MAXENT, a novel approach based on the maximum entropy principle, prototyped in IBM DB2 LUW. We illustrate MAXENT's ability to consistently estimate the selectivity of conjunctive predicates on a per-table basis. In contrast to the DB2 optimizer's current ad hoc methods, we show how MAXENT exploits all available information about the joint column distribution and thus avoids the bias problem. For some complex queries against a real-world database, we show that MAXENT improves selectivity estimates by orders of magnitude relative to the current DB2 optimizer, and also show how these improved estimate influence plan choices as well as query execution times.

If presented with inaccurate statistics, even the most sophisticated query optimizers make mistakes. They may wrongly estimate the output cardinality of a certain operation and thus make sub-optimal plan choices based on that cardinality. Maintaining accurate statistics is hard, both because each table may need a specifically parameterized set of statistics and because statistics get outdated as the database changes. Automated Statistic Collection (ASC) is a new component in IBM DB2 UDB that, without any DBA intervention, observes and analyzes the effects of faulty statistics and, in response, it triggers actions that continuously repair the latter. In this demonstration, we will show how ASC works to alleviate the DBA from the task of maintaining fresh, accurate statistics in several challenging scenarios. ASC is able to reconfigure the statistics collection parameters (e.g, number of frequent values for a column, or correlations between certain column pairs) on a per-table basis. ASC can also detect and guard against outdated statistics caused by high updates/inserts/deletes rates in volatile, dynamic databases. We will also show how ASC works from the inside: from how cardinality mis-estimations are introduced in different kind of operators, to how this error is propagated to later operations in the plan, to how this influences plan choices inside the optimizer.

Current database sampling methods give the user insufficient control when processing ISO-style sampling queries. To address this problem, we provide a bi-level Bernoulli sampling scheme that combines the row-level and page-level sampling methods currently used in most commercial systems. By adjusting the parameters of the method, the user can systematically trade off processing speed and statistical precision---the appropriate choice of parameter settings becomes a query optimization problem. We indicate the SQL extensions needed to support bi-level sampling and determine the optimal parameter settings for an important class of sampling queries with explicit time or accuracy constraints. As might be expected, row-level sampling is preferable when data values on each page are homogeneous, whereas page-level sampling should be used when data values on a page vary widely. Perhaps surprisingly, we show that in many cases the optimal sampling policy is of the "bang-bang" type: we identify a "page-heterogeneity index" (PHI) such that optimal sampling is as "row-like" as possible if the PHI is less than 1 and as "page-like" as possible otherwise. The PHI depends upon both the query and the data, and can be estimated by means of a pilot sample. Because pilot sampling can be nontrivial to implement in commercial database systems, we also give a heuristic method for setting the sampling parameters; the method avoids pilot sampling by using a small number of summary statistics that are maintained in the system catalog. Results from over 1100 experiments on 372 real and synthetic data sets show that the heuristic method performs optimally about half of the time, and yields sampling errors within a factor of 2.2 of optimal about 93% of the time. The heuristic method is stable over a wide range of sampling rates and performs best in the most critical cases, where the data is highly clustered or skewed.

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.

A variety of mining and analysis problems --- ranging from association-rule discovery to contingency table analysis to materialization of certain approximate datacubes --- involve the extraction of knowledge from a set of categorical count data. Such data can be viewed as a collection of "transactions," where a transaction is a fixed-length vector of counts. Classical algorithms for solving count-data problems require one or more computationally intensive passes over the entire database and can be prohibitively slow. One effective method for dealing with this ever-worsening scalability problem is to run the algorithms on a small sample of the data. We present a new data-reduction algorithm, called EASE, for producing such a sample. Like the FAST algorithm introduced by Chen et al., EASE is especially designed for count data applications. Both EASE and FAST take a relatively large initial random sample and then deterministically produce a subsample whose "distance" --- appropriately defined --- from the complete database is minimal. Unlike FAST, which obtains the final subsample by quasi-greedy descent, EASE uses epsilon-approximation methods to obtain the final subsample by a process of repeated halving. Experiments both in the context of association rule mining and classical χ2 contingency-table analysis show that EASE outperforms both FAST and simple random sampling, sometimes dramatically.

No abstract available.

We present FAST (finding associations from sampled transactions), a refined sampling-based mining algorithm that is distinguished from prior algorithms by its novel two-phase approach to sample collection. In phase I a large sample is collected to quickly and accurately estimate the support of each item in the database. In phase II, a small final sample is obtained by excluding "outlier" transactions in such a manner that the support of each item in the final sample is as close as possible to the estimated support of the item in the entire database. We propose two approaches to obtaining the final sample in phase II: trimming and growing. The trimming procedure starts from the large initial sample and removes outlier transactions until a specified stopping criterion is satisfied. In contrast, the growing procedure selects representative transactions from the initial sample and adds them to an initially empty data set.

This paper introduces FAST, a novel two-phase sampling-based algorithm for discovering association rules in large databases. In Phase I a large initial sample of transactions is collected and used to quickly and accurately estimate the support of each individual item in the database. In Phase II these estimated supports are used to either trim "outlier" transactions or select "representative" transactions from the initial sample, thereby forming a small final sample that more accurately reflects the statistical characteristics (i.e., itemset supports) of the entire database. The expensive operation of discovering association rules is then performed on the final sample. In an empirical study, FAST was able to achieve 90--95% accuracy using a final sample having a size of only 15--33% of that of a comparable random sample. This efficiency gain resulted in a speedup by roughly a factor of 10 over previous algorithms that require expensive processing of the entire database --- even efficient algorithms that exploit sampling. Our new sampling technique can be used in conjunction with almost any standard association-rule algorithm, and can potentially render scalable other algorithms that mine "count" data.

Recently, Haas and Hellerstein proposed the hash ripple join algorithm in the context of online aggregation. Although the algorithm rapidly gives a good estimate for many join-aggregate problem instances, the convergence can be slow if the number of tuples that satisfy the join predicate is small or if there are many groups in the output. Furthermore, if memory overflows (for example, because the user allows the algorithm to run to completion for an exact answer), the algorithm degenerates to block ripple join and performance suffers. In this paper, we build on the work of Haas and Hellerstein and propose a new algorithm that (a) combines parallelism with sampling to speed convergence, and (b) maintains good performance in the presence of memory overflow. Results from a prototype implementation in a parallel DBMS show that its rate of convergence scales with the number of processors, and that when allowed to run to completion, even in the presence of memory overflow, it is competitive with the traditional parallel hybrid hash join algorithm.

No abstract available.

We present a new family of join algorithms, called ripple joins, for online processing of multi-table aggregation queries in a relational database management system (DBMS). Such queries arise naturally in interactive exploratory decision-support applications.

Reviews techniques for exploring large object-relational scientific and statistical databases in an interactive online manner. The idea is to provide continuously updated running estimates of the final query results to the user, along with an indication of the precision of the estimates. The user can then halt the query as soon as the answer is sufficiently precise-the time required to obtain an acceptable approximate answer can be faster by orders of magnitude than the time needed to completely process the query. We describe methods for online processing of aggregation queries, online visualization and online display of a set of result records. We also describe methods that use precomputed results to rapidly obtain approximate query answers.

Aggregation in traditional database systems is performed in batch mode: a query is submitted, the system processes a large volume of data over a long period of time, and, eventually, the final answer is returned. This archaic approach is frustrating to users and has been abandoned in most other areas of computing. In this paper we propose a new online aggregation interface that permits users to both observe the progress of their aggregation queries and control execution on the fly. After outlining usability and performance requirements for a system supporting online aggregation, we present a suite of techniques that extend a database system to meet these requirements. These include methods for returning the output in random order, for providing control over the relative rate at which different aggregates are computed, and for computing running confidence intervals. Finally, we report on an initial implementation of online aggregation in POSTGRES.

The online aggregation system recently proposed by J.M. Hellerstein, et al. (1997) permits interactive exploration of large, complex datasets stored in relational database management systems. Running confidence intervals are an important component of an online aggregation system and indicate to the user the estimated proximity of each running aggregate to the corresponding final result. Large sample confidence intervals contain the final result with a prespecified probability and rest on central limit theorems, while deterministic confidence intervals contain the final query result with probability 1. We show how new and existing central limit theorems, simple bounding arguments, and the delta method can be used to derive formulas for both large sample and deterministic confidence intervals. To illustrate these techniques, we obtain formulas for running confidence intervals in the case of single table and multi table AVG, COUNT, SUM, VARIANCE, and STDEV queries with join and selection predicates. Duplicate elimination and GROUP-BY operations are also considered. We then provide numerically stable algorithms for computing the confidence intervals and analyzing the complexity of these algorithms.

Many commercial database systems maintain histograms to summarize the contents of relations and permit efficient estimation of query result sizes and access plan costs. Although several types of histograms have been proposed in the past, there has never been a systematic study of all histogram aspects, the available choices for each aspect, and the impact of such choices on histogram effectiveness. In this paper, we provide a taxonomy of histograms that captures all previously proposed histogram types and indicates many new possibilities. We introduce novel choices for several of the taxonomy dimensions, and derive new histogram types by combining choices in effective ways. We also show how sampling techniques can be used to reduce the cost of histogram construction. Finally, we present results from an empirical study of the proposed histogram types used in selectivity estimation of range predicates and identify the histogram types that have the best overall performance. 1 Introduction...

We compare empirically the cost of estimating the selectivity of a star join using the sampling-based t-cross procedure to the cost of computing the join and obtaining the exact answer. The relative cost of sampling can be excessive when a join attribute value exhibits "heterogeneous skew." To alleviate this problem, we propose Algorithm TCM, a modified version of t-cross that incorporates "augmented frequent value" (AFV) statistics. We provide a sampling-based method for estimating AFV statistics that does not require indexes on attribute values, requires only one pass though each relation, and uses an amount of memory much smaller than the size of a relation. Our experiments show that the use of estimated AFV statistics can reduce the relative cost of sampling by orders of magnitude. We also show that use of estimated AFV statistics can reduce the relative error of the classical System R selectivity formula.>

We compare the cost of estimating the selectivity of a “star join” using sampling procedure t-cross to the cost of simply computing the join and obtaining the exact answer. Our bounds and approximations for the relative cost of sampling show how this cost depends on the size of the input relations, the number of input relations, and the precision criterion used by the estimation procedure. We also demonstrate the deleterious effect of dangling tuples and the mixed effect of data skew on the relative cost of sampling. These results provide insight into when sampling should or should not be used for join selectivity estimation.

We compare the performance of sampling-based procedures for estimation of the selectivity of an equijoin. While some of the procedures have been proposed in the database sampling literature, their relative performance has never been analyzed. A main result of this paper is a partial ordering that compares the variability of the estimators for the different procedures after an arbitrary fixed number of sampling steps. Prior to the current work, it was also unknown whether these fixed-step estimation procedures can be extended to asymptotically efficient fixed-precision estimation procedures. Our second main result is a general method for such an extension and a proof that the method is valid for all the estimation procedures under consideration. Finally, we show that, under reasonable assumptions on sampling costs, the partial ordering on the variability of the fixed-step estimation procedures implies a partial ordering on the cost of the corresponding fixed-precision estimation procedures. These results lead to a new algorithm for fixed-precision estimation of the selectivity of an equijoin. The algorithm appears to be the best available when there are no indices on the join key. Our results can be extended to general select-join queries.

We provide a procedure, based on random sampling, for estimation of the size of a query result. The procedure is sequential in that sampling terminates after a random number of steps according to a stopping rule that depends upon the observations obtained so far. Enough observations are obtained so that, with a pre-specified probability, the estimate differs from the true size of the query result by no more than a prespecified amount. Unlike previous sequential estimation procedures for queries, our procedure is asymptotically efficient and requires no ad hoc pilot sample or a a priori assumptions about data characteristics. In addition to establishing the asymptotic properties of the estimation procedure, we provide techniques for reducing undercoverage at small sample sizes and show that the sampling cost of the procedure can be reduced through stratified sampling techniques.