Reynold Cheng

Evaluating probabilistic queries over imprecise data

Many applications employ sensors for monitoring entities such as temperature and wind speed. A centralized database tracks these entities to enable query processing. Due to continuous changes in these values and limited resources (e.g., network bandwidth and battery power), it is often infeasible to store the exact values at all times. A similar situation exists for moving object environments that track the constantly changing locations of objects. In this environment, it is possible for database queries to produce incorrect or invalid results based upon old data. However, if the degree of error (or uncertainty) between the actual value and the database value is controlled, one can place more confidence in the answers to queries. More generally, query answers can be augmented with probabilistic estimates of the validity of the answers. In this paper we study probabilistic query evaluation based upon uncertain data. A classification of queries is made based upon the nature of the result set. For each class, we develop algorithms for computing probabilistic answers. We address the important issue of measuring the quality of the answers to these queries, and provide algorithms for efficiently pulling data from relevant sensors or moving objects in order to improve the quality of the executing queries. Extensive experiments are performed to examine the effectiveness of several data update policies.

Querying imprecise data in moving object environments

In moving object environments, it is infeasible for the database tracking the movement of objects to store the exact locations of objects at all times. Typically, the location of an object is known with certainty only at the time of the update. The uncertainty in its location increases until the next update. In this environment, it is possible for queries to produce incorrect results based upon old data. However, if the degree of uncertainty is controlled, then the error of the answers to queries can be reduced. More generally, query answers can be augmented with probabilistic estimates of the validity of the answer. We study the execution of probabilistic range and nearest-neighbor queries. The imprecision in answers to queries is an inherent property of these applications due to uncertainty in data, unlike the techniques for approximate nearest-neighbor processing that trade accuracy for performance. Algorithms for computing these queries are presented for a generic object movement model and detailed solutions are discussed for two common models of uncertainty in moving object databases. We study the performance of these queries through extensive simulations.

Efficient indexing methods for probabilistic threshold queries over uncertain data

It is infeasible for a sensor database to contain the exact value of each sensor at all points in time. This uncertainty is inherent in these systems due to measurement and sampling errors, and resource limitations. In order to avoid drawing erroneous conclusions based upon stale data, the use of uncertainty intervals that model each data item as a range and associated probability density function (pdf) rather than a single value has recently been proposed. Querying these uncertain data introduces imprecision into answers, in the form of probability values that specify the likeliness the answer satisfies the query. These queries are more expensive to evaluate than their traditional counterparts but are guaranteed to be correct and more informative due to the probabilities accompanying the answers. Although the answer probabilities are useful, for many applications, it is only necessary to know whether the probability exceeds a given threshold - we term these Probabilistic Threshold Queries (PTQ). In this paper we address the efficient computation of these types of queries. In particular, we develop two index structures and associated algorithms to efficiently answer PTQs. The first index scheme is based on the idea of augmenting uncertainty information to an R-tree. We establish the difficulty of this problem by mapping one-dimensional intervals to a two-dimensional space, and show that the problem of interval indexing with probabilities is significantly harder than interval indexing which is considered a well-studied problem. To overcome the limitations of this R-tree based structure, we apply a technique we call variance-based clustering, where data points with similar degrees of uncertainty are clustered together. Our extensive index structure can answer the queries for various kinds of uncertainty pdfs, in an almost optimal sense. We conduct experiments to validate the superior performance of both indexing schemes.

Probabilistic Verifiers: Evaluating Constrained Nearest-Neighbor Queries over Uncertain Data

In applications like location-based services, sensor monitoring and biological databases, the values of the database items are inherently uncertain in nature. An important query for uncertain objects is the probabilistic nearest-neighbor query (PNN), which computes the probability of each object for being the nearest neighbor of a query point. Evaluating this query is computationally expensive, since it needs to consider the relationship among uncertain objects, and requires the use of numerical integration or Monte-Carlo methods. Sometimes, a query user may not be concerned about the exact probability values. For example, he may only need answers that have sufficiently high confidence. We thus propose the constrained nearest-neighbor query (C-PNN), which returns the IDs of objects whose probabilities are higher than some threshold, with a given error bound in the answers. The C-PNN can be answered efficiently with probabilistic verifiers. These are methods that derive the lower and upper bounds of answer probabilities, so that an object can be quickly decided on whether it should be included in the answer. We have developed three probabilistic verifiers, which can be used on uncertain data with arbitrary probability density functions. Extensive experiments were performed to examine the effectiveness of these approaches.

Range search on multidimensional uncertain data

In an uncertain database, every object <i>o</i> is associated with a probability density function, which describes the likelihood that <i>o</i> appears at each position in a multidimensional workspace. This article studies two types of range retrieval fundamental to many analytical tasks. Specifically, a nonfuzzy query returns all the objects that appear in a search region <i>r</i>_<i>q</i> with at least a certain probability <i>t</i>_<i>q</i>. On the other hand, given an uncertain object <i>q</i>, fuzzy search retrieves the set of objects that are within distance ϵ_<i>q</i> from <i>q</i> with no less than probability <i>t</i>_<i>q</i>. The core of our methodology is a novel concept of “probabilistically constrained rectangle”, which permits effective pruning/validation of nonqualifying/qualifying data. We develop a new index structure called the U-tree for minimizing the query overhead. Our algorithmic findings are accompanied with a thorough theoretical analysis, which reveals valuable insight into the problem characteristics, and mathematically confirms the efficiency of our solutions. We verify the effectiveness of the proposed techniques with extensive experiments.

Mining uncertain data with probabilistic guarantees

Data uncertainty is inherent in applications such as sensor monitoring systems, location-based services, and biological databases. To manage this vast amount of imprecise information, probabilistic databases have been recently developed. In this paper, we study the discovery of frequent patterns and association rules from probabilistic data under the Possible World Semantics. This is technically challenging, since a probabilistic database can have an exponential number of possible worlds. We propose two effcient algorithms, which discover frequent patterns in bottom-up and top-down manners. Both algorithms can be easily extended to discover maximal frequent patterns. We also explain how to use these patterns to generate association rules. Extensive experiments, using real and synthetic datasets, were conducted to validate the performance of our methods.

Efficient join processing over uncertain data

In many applications data values are inherently uncertain. This includes moving-objects, sensors and biological databases. There has been recent interest in the development of database management systems that can handle uncertain data. Some proposals for such systems include attribute values that are uncertain. In particular, an attribute value can be modeled as a range of possible values, associated with a probability density function. Previous efforts for this type of data have only addressed simple queries such as range and nearest-neighbor queries. Queries that join multiple relations have not been addressed in earlier work despite the significance of joins in databases. In this paper we address join queries over uncertain data. We propose a semantics for the join operation, define probabilistic operators over uncertain data, and propose join algorithms that provide efficient execution of probabilistic joins. The paper focuses on an important class of joins termed probabilistic threshold joins that avoid some of the semantic complexities of dealing with uncertain data. For this class of joins we develop three sets of optimization techniques: item-level, page-level, and index-level pruning. These techniques facilitate pruning with little space and time overhead, and are easily adapted to most join algorithms. We verify the performance of these techniques experimentally.

Database Support for Probabilistic Attributes and Tuples

The inherent uncertainty of data present in numerous applications such as sensor databases, text annotations, and information retrieval motivate the need to handle imprecise data at the database level. Uncertainty can be at the attribute or tuple level and is present in both continuous and discrete data domains. This paper presents a model for handling arbitrary probabilistic uncertain data (both discrete and continuous) natively at the database level. Our approach leads to a natural and efficient representation for probabilistic data. We develop a model that is consistent with possible worlds semantics and closed under basic relational operators. This is the first model that accurately and efficiently handles both continuous and discrete uncertainty. The model is implemented in a real database system (PostgreSQL) and the effectiveness and efficiency of our approach is validated experimentally.

Uncertain data mining: an example in clustering location data

Data uncertainty is an inherent property in various applications due to reasons such as outdated sources or imprecise measurement. When data mining techniques are applied to these data, their uncertainty has to be considered to obtain high quality results. We present UK-means clustering, an algorithm that enhances the K-means algorithm to handle data uncertainty. We apply UK-means to the particular pattern of moving-object uncertainty. Experimental results show that by considering uncertainty, a clustering algorithm can produce more accurate results.

Naive Bayes Classification of Uncertain Data

Traditional machine learning algorithms assume that data are exact or precise. However, this assumption may not hold in some situations because of data uncertainty arising from measurement errors, data staleness, and repeated measurements, etc. With uncertainty, the value of each data item is represented by a probability distribution function (pdf). In this paper, we propose a novel naive Bayes classification algorithm for uncertain data with a pdf. Our key solution is to extend the class conditional probability estimation in the Bayes model to handle pdf’s. Extensive experiments on UCI datasets show that the accuracy of naive Bayes model can be improved by taking into account the uncertainty information.