Showing papers on "Uncertain data published in 1997"

A generalized version space learning algorithm for noisy and uncertain data

Abstract: This paper generalizes the learning strategy of version space to manage noisy and uncertain training data. A new learning algorithm is proposed that consists of two main phases: searching and pruning. The searching phase generates and collects possible candidates into a large set; the pruning then prunes this set according to various criteria to find a maximally consistent version space. When the training instances cannot completely be classified, the proposed learning algorithm can make a trade-off between including positive training instances and excluding negative ones according to the requirements of different application domains. Furthermore, suitable pruning parameters are chosen according to a given time limit, so the algorithm can also make a trade-off between time complexity and accuracy. The proposed learning algorithm is then a flexible and efficient induction method that makes the version space learning strategy more practical.

Assigning uncertainties to scientific data

Abstract: Long-standing problems of assigning uncertainties to scientific data became apparent in recent years when uncertainty information (covariance files) had to be added to applications-oriented large libraries of evaluated nuclear data such as ENDF and JEF. Questions arose about the best way to express uncertainties, the meaning of statistical and systematic errors, the origin of correlations and the construction of covariance matrices, the combination of uncertain data from different sources, the general usefulness of results that are strictly valid only for Gaussians or only for linear statistical models, and so forth. Conventional statistical theory is often unable to give unambiguous answers and tends to fail when statistics are poor, making prior information crucial. Modern probability theory, on the other hand, incorporating results from information, decision, and group theory, is shown to provide straight and unique answers to such questions and to deal easily with prior information and small samples.

Parameter estimation in the presence of bounded modeling errors

Abstract: We formulate and solve a new parameter estimation problem in the presence of bounded data uncertainties. The new method is suitable when a priori bounds on the uncertain data are available; its solution guarantees that the effect of the uncertainties will never be unnecessarily overestimated beyond what is reasonably assumed by the a priori bounds.

Uncertain, Incomplete, and Inconsistent Data in Scientific and Statistical Databases

Abstract: This chapter is a survey of several issues and applications in uncertain, inconsistent, and incomplete data in scientific and statistical databases (SSDBs).

Stochastic Programming and Robust Optimization

Abstract: Earlier chapters dealt with problems arising from data uncertainty by examining the sensitivity of the model’s recommendations with respect to changes in the data. This chapter presents prescriptive approaches to problems of sensitivity analysis and parametric programming. It provides an introduction to stochastic programming and robust optimization models. Such models deal, in a constructive manner, with noisy, incomplete or uncertain data. Information about possible values of the problem data is incorporated in the model, and the model generates solutions that are less sensitive to data uncertainty. Stochastic linear programming and robust optimization models are introduced and applications are presented, with emphasis on financial planning problems.

Fitting Uncertain Data with NURBS

Abstract: Fitting of uncertain data, that is, tting of data points that are subject to some error, has important applications for example in statistics and for the evaluation of results from physical experiments. Fitting in these problem domains is usually achieved with polynomial approximation, which involves the minimization of an error at discrete data points. Norms typically used for this minimization include the l1, l2 and l1 norms, which are chosen depending on the problem domain and the expected type of error on the data points. In this paper we describe how the l1 and l1 norms can be applied to integral and rational B-spline tting as a linear programming problem. This allows for the use of B-splines and NURBS for the tting of uncertain data.

Worst-case parameter estimation with bounded model uncertainties

Abstract: We formulate and solve a new parameter estimation problem in the presence of bounded model uncertainties. The new method is suitable when a priori bounds on the uncertain data are available, and its solution guarantees that the effect of the uncertainties will never be unnecessarily over-estimated beyond what is reasonably assumed by the a priori bounds. This is in contrast to other methods, such as total least-squares and robust estimation that do not incorporate explicit bounds on the size of the uncertainties. A geometric interpretation of the solution of the new problem is provided, along with a closed form expression for it. We also consider the case in which only selected columns of the coefficient matrix are subject to perturbations.

Learning Flexible Concepts from Uncertain Data

Abstract: Learning from examples consists of knowledge induction from training examples using an inductive learning algorithm. In practice, a preprocessing phase is necessary to transform numerical attributes into intervals (discretization), to deal with missing values, noisy data, and so forth. The major part of research efforts has proposed methods for data pre-processing but no special attention has been devoted to model and to handle the uncertainty inherent in real-world data. In this paper we introduce a preprocessing task to model uncertainty which is considered during all the learning process. In this context we formalize a notion of flexible concepts in contrast with “sharp” concepts usually represented by crisp sets. Next, we discuss an inductive learning approach based on rough set theory and we propose a method which allows the user to control both the granularity of knowledge resulting from the partition of the universe and the consistency of rules to be learned. Our proposed method is at the basis of the system Alpha which is run on real-world datasets.

The least squares fit of a hyperplane to uncertain data

Abstract: Sensor based robotic systems are an important emerging technology. When robots are working in unknown or partially known environments, they need range sensors that will measure the Cartesian coordinates of surfaces of objects in their environment. Like any sensor, range sensors must be calibrated. The range sensors can be calibrated by comparing a measured surface shape to a known surface shape. The most simple surface is a plane and many physical objects have planar surfaces. Thus, an important problem in the calibration of range sensors is to find the best (least squares) fit of a plane to a set of 3D points. We have formulated a constrained optimization problem to determine the least squares fit of a hyperplane to uncertain data. The first order necessary conditions require the solution of an eigenvalue problem. We have shown that the solution satisfies the second order conditions (the Hessian matrix is positive definite). Thus, our solution satisfies the sufficient conditions for a local minimum. We have performed numerical experiments that demonstrate that our solution is superior to alternative methods.

The combinatorial structure of fuzzy functional dependencies

Abstract: We investigate the underlying combinatorial structure of fuzzy functional dependencies. This leads to an interesting connection between models of imprecise or uncertain data and a model of changing databases.

Extended SQL Support for Uncertain Data

Abstract: Although the relational model for databases provides a great range of advantages over other data models, it lacks a comprehensive way for handling uncertain data. Uncertainty in data values, however, is pervasive in all real world environments and has received some attention in the literature. Several methods have been proposed for incorporating uncertain data into relational databases; however, these approaches have many shortcomings. In this paper, we discuss a probabilistic extension of the relational model and propose a query language for creation, modification, and retrieval of uncertain data.

Extended SQL support for uncertain data

Abstract: Although the relational model for databases provides a great range of advantages over other data models, it lacks a comprehensive way for handling uncertain data. Uncertainty in data values, however, is pervasive in all real world environments and has received some attention in the literature. Several methods have been proposed for incorporating uncertain data into relational databases; however, these approaches have many shortcomings. In this paper, we discuss a probabilistic extension of the relational model and propose a query language for creation, modification, and retrieval of uncertain data.

LogiCook and QUESTAR: two case studies in successful technology transfer

Abstract: Neural networks are ideally suited to the processing of noisy or uncertain data as they operate within a probabilistic framework. They produce probability estimates at their output and so allowance must be made for this. This is a very important consideration in the context of industrial applications and the author illustrates how this issue was addressed in the Sharp LogiCook (a neural network microwave oven) and in Oxford Medical's QUESTAR (a neural network system for the analysis of sleep disorders).

A Combined Approach to Uncertain Data Analysis

Abstract: In the real world, various kinds of uncertain information are very popular in decision making. It is highly desirable to represent them in a database form. We develop a new uncertain relational database model that includes using possibility distributions as values of attributes along with probabilities associated with tuples. This new model can represent all kinds of uncertainty by providing rich structure to support realistic uncertain data manipulation more completely. Relational algebra based on the new uncertain database model is introduced and a query processing example is presented.

Fuzzy set theory for dynamic analysis with uncertain design data

Abstract: In this paper, theories of possibility and fuzzy sets are used for dynamic analysis of simple structures. The potentialities of possibility theory for analysis and design of engineering problems with uncertain data are first discussed. Possibility theory and fuzzy numbers are used to obtain upper and lower bounds for probability distributions and other statistical quantities, such as mean value intervals and upper and lower percentiles. The method is used to obtain the natural frequency of a simple structural system constituted by the principal structure (frames, shear walls) and a number of nonstructural elements and infrastructures which are considered uncertainly defined and represented through fuzzy numbers. The aim of the study is to propose a technique to evaluate the influence of nonstructural elements on the dynamic response of multistorey buildings.