Uncertain Data

It is generally accepted that data production has experienced spectacular growth for several years due to the proliferation of new technologies such as new mobile devices, smart meters, social networks, cloud computing and sensors. In fact, this data explosion should continue and even accelerate. To find all of the documents responding to a request, any information search system develops a methodology to confirm whether or not the terms of each document correspond to those of the user's request. Most systems are based on the assumption that the terms extracted from the documents have been certain and precise. However, there are data in which this assumption is difficult to apply. The main objective of the work carried out within the framework of this article is to propose a new model of data service indexing in an uncertain environment, meaning that the data they contain can be untrustworthy, or they can be contradictory to another data source, due to failure in collection or in...

Engineering economics deals with the investment decisions based on the time value of money. In the real life conditions, the exact estimations of investment parameters are almost impossible. Probabilistic analyses are preferred when sufficient data are available for the estimation of these parameters. Possibilistic analyses should be used when insufficient data exist for the estimation. This paper develops both fuzzy present worth and annual worth analyses using the extensions of fuzzy sets, which are namely intuitionistics fuzzy sets and hesitant fuzzy sets. Each of these extended fuzzy sets is also divided into four subtitles with respect to the types of the data in these economic analyses: Triangular hesitant fuzzy data, triangular intuitionistic fuzzy data, interval-valued hesitant data, and interval-valued intuitionistic fuzzy data. The numerical examples illustrate the applications of the developed analyses.

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.

Generally, users often have vague or imprecise ideas when searching databases and thus may not know how to use traditional structured query language to precisely formulate queries that lead to satisfactory answers. Also, the user searching criteria may depend on the current state of the data stored in the searched database. This paper presents a more flexible fuzzy set-based approach for human-like querying of relational databases. Such approach supports queries that can use both of stationary fuzzy sets with fixed definition and non-stationary
fuzzy sets or data-sensitive fuzzy sets with dynamic definitions. Based on fuzzy set theory and data-sensitive fuzzy sets, this paper proposes a fuzzy query approach supporting data-sensitive fuzzy queries in which the definition of a fuzzy set can be dynamic and depend on some data in the current database state. Also, the proposed approach allows fuzzy joining of database relations. Such fuzzy join makes a query statement much closed to human querying behaviors. On the other hand, many other query structures like nested, complex and correlated fuzzy queries are supported by the proposed approach.

The present state of the art in analytics requires high upfront investment of human effort and computational resources to curate datasets, even before the first query is posed. So-called pay-as-you-go data curation techniques allow these high costs to be spread out, first by enabling queries over uncertain and incomplete data, and then by assessing the quality of the query results. We describe the design of a system, called Mimir, around a recently introduced class of probabilistic pay-as-you-go data cleaning operators called Lenses. Mimir wraps around any deterministic database engine using JDBC, extending it with support for probabilistic query processing. Queries processed through Mimir produce uncertainty-annotated result cursors that allow client applications to quickly assess result quality and provenance. We also present a GUI that provides analysts with an interactive tool for exploring the uncertainty exposed by the system. Finally, we present optimizations that make Lenses...

Solving complex decision problems requires the usage of information from different sources. Usually this information is uncertain and statistical or probabilistic methods are needed for its processing. However, in many cases a decision maker faces not only uncertainty of a random nature but also imprecision in the description of input data that is rather of linguistic nature. Therefore, there is a need to merge uncertainties of both types into one mathematical model. In the paper we present methodology of merging information from imprecisely reported statistical data and imprecisely formulated fuzzy prior information. Moreover, we also consider the case of imprecisely defined loss functions. The proposed methodology may be considered as the application of fuzzy statistical methods for the decision making in the systems analysis.

Frequent itemset mining in uncertain transaction databases semantically and computationally diers from traditional techniques applied on standard (certain) transaction databases. Uncertain transaction databases consist of sets of existentially uncertain items. The uncertainty of items in transactions makes traditional techniques inapplicable. In this paper, we tackle the problem of nding probabilistic frequent itemsets based on possible world semantics. In this context, an itemset X is called frequent if the probability that X occurs in at least minSup transactions is above a given threshold τ. We make the following contributions: We propose the rst probabilistic FP-Growth algorithm (ProFP-Growth) and associated probabilistic FP-Tree (ProFP-Tree), which we use to mine all probabilistic frequent itemsets in uncertain transaction databases without candidate generation. In addition, we propose an ecient technique to compute the support probability distribution of an itemset in linear time using the concept of generating functions. An extensive experimental section evaluates the our proposed techniques and shows that our ProFP-Growth approach is signicantly faster than the current state-ofthe-art algorithm.

In many application domains, e.g. sensor databases, traffic management or recognition systems, objects have to be compared based on positionally and existentially uncertain data. Feature databases with uncertain data require special methods for effective similarity search. In this paper, we propose a probabilistic similarity ranking algorithm which computes the results dynamically based on the complete information given by inexact object representations. Hence, this can be performed in an effective and efficient way. We assume that the objects are given by a set of points in a vector space with confidence values following the discrete uncertainty model. Based on this representation, we introduce a probabilistic ranking algorithm that is able to reduce significantly the computational complexity of the computation of the probability that an object is at a certain ranking position. In a detailed experimental evaluation, we demonstrate the benefits of this approach compared to several competitors. The experiments show that, in addition to the gain of efficiency, we can achieve convenient query results of high quality.

This paper introduces a scalable approach for probabilistic top-k similarity ranking on uncertain vector data. Each uncertain object is represented by a set of vector instances that are assumed to be mutually-exclusive. The objective is to rank the uncertain data according to their distance to a reference object. We propose a framework that incrementally computes for each object instance and ranking position, the probability of the object falling at that ranking position. The resulting rank probability distribution can serve as input for several state-of-the-art probabilistic ranking models. Existing approaches compute this probability distribution by applying a dynamic programming approach of quadratic complexity. In this paper we theoretically as well as experimentally show that our framework reduces this to a linear-time complexity while having the same memory requirements, facilitated by incremental accessing of the uncertain vector instances in increasing order of their distance to the reference object. Furthermore, we show how the output of our method can be used to apply probabilistic top-k ranking for the objects, according to different state-of-the-art definitions. We conduct an experimental evaluation on synthetic and real data, which demonstrates the efficiency of our approach.

Abstract: The sample selection model is studied in the context of semi-parametric methods. The issue of uncertainty and ambiguity are still major problems and the modelling of a semi-parametric sample selection model as well as its parametric. The best approach of ...

While an increasing number of human activities are studied using data produced by individuals' ICT devices, there have been relatively few contributions investigating the robustness of results against fluctuations of data characteristics. In particular, when ICT data contain spatial information, they represent an invaluable new source for analyzing urban phenomena. Here, we present a stability analysis of higher-level information extracted from mobile phone metadata passively produced during an entire year by 9 million individuals in Senegal. We focus on two specific information-retrieval tasks: (a) the identification of land use in the region of Dakar by analyzing the temporal rhythms of the communication activity; (b) the identification of home and work locations of anonymized individuals, allowing for the construction of the Origin-Destination (OD) matrices for commuting flows. Our analysis reveals that the spatial distributions of land use computed for different samples are remarkably robust, with on average 80% of shared surface area between the different spatial partitions. The OD matrix is less stable with a share of about 70% of commuters in common when considering all types of flows. Better results can be obtained at larger levels of aggregation. These different results confirm that ICT data are mostly a very useful source for the spatial analysis of urban systems, but that their reliability should be tested more thoroughly.

This thesis presents and demonstrates ideas for improved robustness in diagnostic prol)lem solving of complex physical systems in operation, or operative diagnosis. The first idea is that graceful degradation can be viewed as reasoning at higher levels of

In this paper, a guaranteed equilibrated error estimator is proposed for the harmonic magnetodynamic formulation of the Maxwell's system. This system is recast in two classical potential formulations, which are solved by a Finite Element method. The equilibrated estimator is built starting from these dual problems and is consequently available to estimate the error of both numerical resolutions. The estimator reliability and efficiency without generic constants are established. Then, numerical tests are performed, allowing to illustrate the obtained theoretical results.

The core contribution of this study is to develop a novel generalized idea of q-rung orthopair probabilistic hesitant fuzzy rough set (q-ROPHFRS) which is hybrid structure of the q-rung orthopair fuzzy set, probabilistic hesitant fuzzy set, and rough set. The q-ROPHFRS covers the positive and negative membership grades in the form of probabilistic hesitant fuzzy rough information to address the uncertainties in real-world decision-making problems. This paper proposes a list of novel q-rung orthopair probabilistic hesitant fuzzy rough averaging/geometric aggregation operators to handle the uncertainty effectively and reliably to aggregate the uncertain information under q-ROPHFRSs. Several interesting elementary properties have been investigated. Furthermore, a novel multi-attribute decision-making approach based on the proposed aggregation information is presented. Finally, a numerical application regarding selecting a medical oxygen supplier to the hospital is presented to illustrate the consistency of the developed decision-making technique. The comparison of the proposed technique with B Noor Rehman

Large databases with uncertainty became more common in many applications.In many modern applications, there are no exact values available to describe the data objects. Instead, the feature values are considered to be uncertain. This uncertainty is modeled by probability distributions instead of exact feature values and that are assumed to be mutually-exclusive. A typical application of such an uncertainty model are moving objects where the exact position of each object can be determined only at discrete time intervals. The objective is to rank the uncertain data according to their distance to a reference object. In the existing system, a framework is used for efficient computation of probabilistic similarity ranking queries in uncertain vector databases, each object is ranked in object instance wise and it is clustered and again ranking to the objects is performed, which results in log-linear i.e, O(nlogn). In this paper, we propose the Radix algorithm in order to increase the performance to O(n).we theoretically as well as experimentally show that it reduces this to a linear-time complexity while having the same memory requirements, facilitated by incremental accessing of the uncertain vector instances in increasing order of their distance to the reference object.

Frequent pattern mining is the extraction of interested collection of items from dataset. Frequent Itemset mining plays an important role in the mining of various patterns and is in demand in many real life applications. When handling uncertain data U-Apriori, UF-growth, UFP-growth and PUF-growth are examples of well-known mining algorithms, which use the UF-tree, the UFP-tree and the PUF-tree respectively. However, these trees can be large, and thus degrade the mining performance. The researchers have proposed various algorithms like U-Apriori, UF-growth, UH-mine, PUF-growth etc. In this paper, we are presenting depth analysis of algorithms of mining frequent patterns from uncertain datasets and discuss some problems associated with these algorithms in transactional databases.

It is generally assumed in the traditional formulation of supervised learning that only the outputs data are uncertain. However, this assumption might be too strong for some learning tasks. This paper investigates the use of Gaussian Process prior to infer consistent models given uncertain data. By assuming a Gaussian distribution with known variances over the inputs and a Gaussian covariance function, it is possible to marginalize out the inputs' uncertainty and keep an analytical posterior distribution over functions. We demonstrated the properties of the method on a synthetic problem and on a more realistic one, which consist in learning the dynamics of the well-known cart-pole problem and compare the performance versus a classic Gaussian Process. A large improvement of the mean squared error is presented as well as the consistency of the result of the regression.

In real-world problems, input data may be pervaded with uncertainty. In this paper, we investigate the behavior of naive possibilistic classifiers, as a counterpart to naive Bayesian ones, for dealing with classification tasks in presence of uncertainty. For this purpose, we extend possibilistic classifiers, which have been recently adapted to numerical data, in order to cope with uncertainty in data representation. Here the possibility distributions that are used are supposed to encode the family of Gaussian probabilistic distributions that are compatible with the considered data set. We consider two types of uncertainty: i) the uncertainty associated with the class in the training set, which is modeled by a possibility distribution over class labels, and ii) the imprecision pervading attribute values in the testing set represented under the form of intervals for continuous data. Moreover, the approach takes into account the uncertainty about the estimation of the Gaussian distribution parameters due to the limited amount of data available. We first adapt the possibilistic classification model, previously proposed for the certain case, in order to accommodate the uncertainty about class labels. Then, we propose an algorithm based on the extension principle to deal with imprecise attribute values. The experiments reported show the interest of possibilistic classifiers for handling uncertainty in data. In particular, the probability-to-possibility transform-based classifier shows a robust behavior when dealing with imperfect data.

As the remnants of the post-Roman world transformed into the early Medieval period, there is observable significant and evident reuse of acontemporaneous, “antique” material culture together with the adoption of “anachronistic” mortuary practices. Roman culture lingered, continuing to reverberate into the future in medieval communities that had not been part of the original multi-scalar empire, nor had maintained a direct connection to the land throughout the previous empire. Early medieval mortuary practices of the central Balkans clearly demonstrate interconnections in social and cultural construction in a time of crisis, building upon the remains of "the shoulders of giants”. Cemeteries and individual graves from the 9th to 11th century around the Danubian limes (located in modern-day Serbia) are most recognizable. The phenomenon of reuse may be more concretely labelled the “percolation of time” i.e., how the link to the past could be used to justify the present by newly-settled small communities of Slavs and Avars in the Early Middle Ages.
The key takeaway is that the dissemination of material culture and ideas need not merely be derived directly from the centre to the periphery and in reverse, but may trickle out locally beyond assumed boundaries of time. New communities continue to be shaped from the past, selecting and augmenting to the original meanings of the material culture of the past while assigning ones of their own.

Origin-destination (O-D) matrix estimation methods based on traffic counts have been largely discussed and investigated. The most used methods are based on Generalised Least Square estimators (GLS) that use as input data a starting O-D matrix and a set of traffic counts. In addition to traffic counts, the analysts could know other general information about travel demand or link flows, based on their experience, or spot data, but few works deal with the matter of including effectively these sources of information. This paper proposes a Fuzzy-GLS estimation method that allows to improve the estimation performances of classic GLS estimator by including, in addition to traffic counts, uncertain information about starting O-D demand (i.e. outdated estimates, spot data, expert knowledge, etc.). The methods explicitly take into account the relevant level of uncertainty by taking as much advantage as possible from the few vague available data. The method is developed using fuzzy sets theory and fuzzy programming that seems to be a convenient theoretical framework to represent uncertainty in the available data. A solution algorithm for the proposed problem is also presented. The method has been tested by numerical applications and then compared to the classical GLS method under different sets of constraints to the problem.

There are numerous data mining applications working in metric spaces. In the following we will exemplarily sketch three main topics in this area: the impact of metric similarity functions on data mining, data mining in uncertain data and mining high-dimensional data.

This paper extends the decision tree technique to an uncertain environment where the uncertainty is represented by belief functions as interpreted in the Transferable Belief Model (TBM). This so-called belief decision tree is a new classification method adapted to uncertain data. We will be concerned with the construction of the belief decision tree from a training set where the knowledge about the instances' classes is represented by belief functions, and its use for the classification of new instances where the knowledge about the attributes' values is represented by belief functions.

Complexity and, by implication, change and uncertainty, are inherent features of ecosystems. In managing ecosystems, or linked social-ecological systems, decisions are often based on insufficient or uncertain data and information. Appropriate and sufficient knowledge, which essentially resides in people, is a critical factor for making informed decisions under such circumstances. Informed action is a function of what we know, and our knowledge is a product of what and how we have learned. Because of the central importance of learning, this chapter proposes that the development of an appropriate learning capability should not be left to chance but should be the result of deliberate intervention to establish the conditions for an organisation to operate in a learning mode. Focusing on organisations or agencies with mandates for ecosystem governance, the chapter sets out to identify the principles that will enable the creation of such learning environments. Firstly, the key concepts of knowledge, learning and ecosystem governance are defined. Secondly, the chapter identifies main issues of concern regarding (a) the type of knowledge that needs to be created for good ecosystem governance; (b) the desirable processes for learning or knowledge creation; and (c) the characteristics of good learners. Thirdly, these main issues (10 in all) form the basis for formulating nine principles intended to enable the setting up of appropriate learning environments for ecosystem governance. The proposed principles are summarised as follows. Good ecosystem governance requires positively persistent and adaptive people with a culture of empathy for other knowledge systems and levels. Their knowledge must be trans-disciplinary, moulded by a common future focus, acquired by patiently engaging their prior knowledge and learning by doing, in an environment of social knowledge sharing. It is concluded that good learning practice would promote the achievement of some of the principles underlying the practice of good ecosystem governance, notably effective stakeholder engagement, adaptability and transformability. The proposed learning principles could be used as a framework to assess the learning proficiency of ecosystem management agencies and to develop learning strategies for such agencies.

Crisp input and output data are fundamentally indispensable in traditional data envelopment analysis (DEA). However, the input and output data in real-world problems are often imprecise or ambiguous. Some researchers have proposed interval DEA (IDEA) and fuzzy DEA (FDEA) to deal with imprecise and ambiguous data in DEA. Nevertheless, many real-life problems use linguistic data that cannot be used as interval data and a large number of input variables in fuzzy logic could result in a significant number of rules that are needed to specify a dynamic model. In this paper, we propose an adaptation of the standard DEA under conditions of uncertainty. The proposed approach is based on a robust optimization model in which the input and output parameters are constrained to be within an uncertainty set with additional constraints based on the worst case solution with respect to the uncertainty set. Our robust DEA (RDEA) model seeks to maximize efficiency (similar to standard DEA) but under the assumption of a worst case efficiency defied by the uncertainty set and it's supporting constraint. A Monte-Carlo simulation is used to compute the conformity of the rankings in the RDEA model. The contribution of this paper is fourfold: (1) we consider ambiguous, uncertain and imprecise input and output data in DEA; (2) we address the gap in the imprecise DEA literature for problems not suitable or difficult to model with interval or fuzzy representations; (3) we propose a robust optimization model in which the input and output parameters are constrained to be within an uncertainty set with additional constraints based on the worst case solution with respect to the uncertainty set; and (4) we use Monte-Carlo simulation to specify a range of Gamma in which the rankings of the DMUs occur with high probability.

We study the convex-hull problem in a probabilistic setting, motivated by the need to handle data uncertainty inherent in many applications, including sensor databases, location-based services and computer vision. In our framework, the uncertainty of each input point is described by a probability distribution over a finite number of possible locations including a null location to account for non-existence of the point. Our results include both exact and approximation algorithms for computing the probability of a query point lying inside the convex hull of the input, time-space tradeo↵s for the membership queries, a connection between Tukey depth and membership queries, as well as a new notion of-hull that may be a useful representation of uncertain hulls.

In this paper, we consider the following degenerate/singular parabolic equation ut − (x α ux)x − µ x 2−α u = 0, x ∈ (0, 1), t ∈ (0, T), where 0 ≤ α < 1 and µ ≤ (1 − α) 2 /4 are two real parameters. We prove the boundary null controllability by means of a H 1 (0, T) control acting either at x = 1 or at the point of degeneracy and singularity x = 0. Besides we give sharp estimates of the cost of controllability in both cases in terms of the parameters α and µ. The proofs are based on the classical moment method by Fattorini and Russell and on recent results on biorthogonal sequences.

In this paper we study a geometric partial differential equation including a forcing term. This equation defines a hypersurface evolution that we use for level set regularization. We study the shape of the radial solutions of the equation and some qualitative properties about the level set propagations. We show that under a suitable choice of the forcing term, the geometric equation has nontrivial asymptotic states and it represents a model for level set regularization. We show that by using a forcing term which is merely a bounded Hölder continuous function, we can obtain finite time stabilization of the solutions. We introduce an explicit finite difference scheme to compute numerically the solution of the equation and we present some applications of the model to nonlinear two-dimensional image filtering and three-dimensional segmentation in the context of medical imaging.

It is standard to perform classification tasks under the assumption that class labels are deterministic. In this context, the F-measure is an increasingly popular measure of performance for a classifier, and expresses a flexible trade-off between precision and recall. However, it may just as easily be advisable to remove this assumption and consider instances as belonging to each class with given probabilities. The presence of uncertainty in a training set may be due to subjectivity of a classification task or noise introduced during data collection. In this paper, we adapt the classical F-measure to the uncertain context and present an efficient, easy-to-implement algorithm for the optimization of this new “noisy ” F-measure within the maximum entropy modeling framework. We provide comprehensive theoretical justification along with numerical experiments that demon-strate the novelty and effectiveness of this approach.

We link the weighted maximum entropy and the optimization of the expected F measure, by viewing them in the framework of a general common multi-criteria optimization problem. As a result, each solution of the expectedF -measure maximization can be realized as a weighted maximum likelihood solution - a well understood and behaved problem. The specific structure of maximum entropy models allows us to approximate this characterization via the much simpler class-wise weighted maximum likelihood. Our approach reveals any probabilistic learning scheme as a specific trade-off between different objectives and provides the framework to link it to the expectedF -measure.

We link the weighted maximum entropy and the optimization of the expected F βmeasure, by viewing them in the framework of a general common multi-criteria optimization problem. As a result, each solution of the expected F β-measure maximization can be realized as a weighted maximum likelihood solution-a well understood and behaved problem. The specific structure of maximum entropy models allows us to approximate this characterization via the much simpler class-wise weighted maximum likelihood. Our approach reveals any probabilistic learning scheme as a specific trade-off between different objectives and provides the framework to link it to the expected F β-measure.

Increasing use of computers, leads to accumulation of data of an organization, demanding the need of sophisticated data handling techniques. Many data handling concepts have evolved that support data analysis, and knowledge discovery. Data warehouse and Data mining techniques are playing an important role in the area of data analysis for knowledge discovery. These techniques typically address the four basic applications such as data classification, data clustering, association between data and finding sequential patterns between the data. Various algorithms that address to classification on large data sets have proved to be efficient in classifying the variables of known or certain characteristics. However they are less effective when applied to the analysis of variable of unknown or uncertain characteristics and creating classes by combining multiple correlated variables in real world. A methodology presented in the paper that addresses two major issues of data classification using decision tree, 1) classification of variables of unknown or uncertain characteristics, 2) creating classification by combining multiple correlated variables.

We consider linear programs with uncertain parameters, lying in some prescribed uncertainty set, where part of the variables must be determined before the realization of the uncertain parameters ("nonadjustable variables"), while the other part are variables that can be chosen after the realization ("adjustable variables"). We extend the Robust Optimization methodology ([1, 3-6, 9, 13, 14]) to this situation by introducing the Adjustable Robust Counterpart (ARC) associated with an LP of the above structure. Often the ARC is significantly less conservative than the usual Robust Counterpart (RC), however, in most cases the ARC is computationally intractable (NP-hard). This difficulty is addressed by restricting the adjustable variables to be affine functions of the uncertain data. The ensuing Affinely Adjustable Robust Counterpart (AARC) problem is then shown to be, in certain important cases, equivalent to a tractable optimization problem (typically an LP or a Semidefinite problem), and in other cases, having a tight approximation which is tractable. The AARC approach is illustrated by applying it to a multi-stage inventory management problem.

Robust Optimization is a rapidly developing methodology for handling optimization problems affected by non-stochastic "uncertain-butbounded" data perturbations. In this paper, we overview several selected topics in this popular area, specifically, (1) recent extensions of the basic concept of robust counterpart of an optimization problem with uncertain data, (2) tractability of robust counterparts, (3) links between RO and traditional chance constrained settings of problems with stochastic data, and (4) a novel generic application of the RO methodology in Robust Linear Control.

In this paper, we propose a new methodology for handling optimization problems with uncertain data. With the usual Robust Optimization paradigm, one looks for the decisions ensuring a required performance for all realizations of the data from a given bounded uncertainty set, whereas with the proposed approach, we require also a controlled deterioration in performance when the data is outside the uncertainty set. The extension of Robust Optimization methodology developed in this paper opens up new possibilities to solve efficiently multi-stage finite-horizon uncertain optimization problems, in particular, to analyze and to synthesize linear controllers for discrete time dynamical systems.

This paper studies the problem of constructing robust classifiers when the training is plagued with uncertainty. The problem is posed as a Chance-Constrained Program (CCP) which ensures that the uncertain datapoints are classified correctly with high probability. Unfortunately such a CCP turns out to be intractable. The key novelty is in employing Bernstein bounding schemes to relax the CCP as a convex second order cone program whose solution is guaranteed to satisfy the probabilistic constraint. Prior to this work, only the Chebyshev based relaxations were exploited in learning algorithms. Bernstein bounds employ richer partial information and hence can be far less conservative than Chebyshev bounds. Due to this efficient modeling of uncertainty, the resulting classifiers achieve higher classification margins and hence better generalization. Methodologies for classifying uncertain test datapoints and error measures for evaluating classifiers robust to uncertain data are discussed. Experimental results on synthetic and real-world datasets show that the proposed classifiers are better equipped to handle data uncertainty and outperform state-of-the-art in many cases.

We consider linear programs with uncertain parameters, lying in some prescribed uncertainty set, where part of the variables must be determined before the realization of the uncertain parameters ("nonadjustable variables"), while the other part are variables that can be chosen after the realization ("adjustable variables"). We extend the Robust Optimization methodology ([1, 3-6, 9, 13, 14]) to this situation by introducing the Adjustable Robust Counterpart (ARC) associated with an LP of the above structure. Often the ARC is significantly less conservative than the usual Robust Counterpart (RC), however, in most cases the ARC is computationally intractable (NP-hard). This difficulty is addressed by restricting the adjustable variables to be affine functions of the uncertain data. The ensuing Affinely Adjustable Robust Counterpart (AARC) problem is then shown to be, in certain important cases, equivalent to a tractable optimization problem (typically an LP or a Semidefinite problem), and in other cases, having a tight approximation which is tractable. The AARC approach is illustrated by applying it to a multi-stage inventory management problem.

Optimal solutions of Linear Programming problems may become severely infeasible if the nominal data is slightly perturbed. We demonstrate this phenomenon by studying 90 LPs from the well-known NETLIB collection. We then apply the Robust Optimization methodology (Ben-Tal and Nemirovski [1-3]; El Ghaoui et al. [5,6]) to produce "robust" solutions of the above LPs which are in a sense immuned against uncertainty. Surprisingly, for the NETLIB problems these robust solutions nearly lose nothing in optimality.

In this paper, we consider second-order evolution equations with unbounded dynamic feedbacks. Under a regularity assumption, we show that observability properties for the undamped problem imply decay estimates for the damped problem. We consider both uniform and non-uniform decay properties.

This paper presents a new selforganiz ing type RBF neural network and introduces the Geometric Algebra framework in the neurocomputing eld. Real valued neural nets for function approximation require feature enhancement, dilation and rotation operations and are limited by the Euclidean metric. The authors believe that more general and exible neural networks should be designed in order to capture important geometric characteristics of the manifolds. This is an important goal overlooked ever since. Geometric algebra is a system which allows the design of neural networks in a coordinate-free framework to process patterns between layers using di erent dimensions and desired metric. The potential of such nets working in a Cli ord algebra C(V p;q) is shown by a simple application of frame coordination in robotics.

The sample selection model studied in the context of semi-parametric methods. With the deficiency of the parametric model, such as inconsistent estimators etc, the semi-parametric estimation methods provide the best alternative to handle this deficiency. Semi-parametric of a sample selection model is an econometric model has been found interesting application in empirical studies. The issue of uncertainty and ambiguity still become are major problem and complicated in the modeling of semi-parametric sample selection model as well as its parametric. In this study, we will focus in the context of fuzzy concept as a hybrid to the semi-parametric sample selection model. The best approach of accounting for uncertainty and ambiguity is to take advantage of the tools provided by the theory of fuzzy sets. It seems particularly appropriate for modeling vague concepts. Fuzzy sets theory and its properties through the concept of fuzzy number provide an ideal framework in order to solve the problem of uncertainty data. In this paper, we introduce a fuzzy membership function for solving uncertainty data of a semi-parametric sample selection model.

In a possibly multiply-connected three dimensional bounded domain, we prove in the L p theory the existence and uniqueness of vector potentials, associated with a divergence-free function and satisfying non homogeneous boundary conditions. Furthermore, we consider the stationary Stokes equations with nonstandard boundary conditions of the form u • n = g and curl u × n = h × n on the boundary Γ. We prove the existence and uniqueness of weak, strong and very weak solutions. Our proofs are mainly based on In f − Sup conditions.

Regularity results for minimal configurations of variational problems involving both bulk and surface energies and subject to a volume constraint are established. The bulk energies are convex functions with p-power growth, but are otherwise not subjected to any further structure conditions. For a minimal configuration (u, E), Hölder continuity of the function u is proved as well as partial regularity of the boundary of the minimal set E. Moreover, full regularity of the boundary of the minimal set is obtained under suitable closeness assumptions on the eigenvalues of the bulk energies.

Uncertain data streams are increasingly common in real-world deployments and monitoring applications require the evaluation of complex queries on such streams. In this paper, we consider complex queries involving conditioning (e.g., selections and group by&#39;s) and aggregation operations on uncertain data streams. To characterize the uncertainty of answers to these queries, one generally has to compute the full probability distribution of each operation used in the query. Computing distributions of aggregates given conditioned tuple distributions is a hard, unsolved problem. Our work employs a new evaluation framework that includes a general data model, approximation metrics, and approximate representations. Within this framework we design fast data-stream algorithms, both deterministic and randomized, for returning approximate distributions with bounded errors as answers to those complex queries. Our experimental results demonstrate the accuracy and efficiency of our approximatio...