164 research outputs found
Pointwise consistency of the kriging predictor with known mean and covariance functions
This paper deals with several issues related to the pointwise consistency of
the kriging predictor when the mean and the covariance functions are known.
These questions are of general importance in the context of computer
experiments. The analysis is based on the properties of approximations in
reproducing kernel Hilbert spaces. We fix an erroneous claim of Yakowitz and
Szidarovszky (J. Multivariate Analysis, 1985) that the kriging predictor is
pointwise consistent for all continuous sample paths under some assumptions.Comment: Submitted to mODa9 (the Model-Oriented Data Analysis and Optimum
Design Conference), 14th-19th June 2010, Bertinoro, Ital
Solving Support Vector Machines in Reproducing Kernel Banach Spaces with Positive Definite Functions
In this paper we solve support vector machines in reproducing kernel Banach
spaces with reproducing kernels defined on nonsymmetric domains instead of the
traditional methods in reproducing kernel Hilbert spaces. Using the
orthogonality of semi-inner-products, we can obtain the explicit
representations of the dual (normalized-duality-mapping) elements of support
vector machine solutions. In addition, we can introduce the reproduction
property in a generalized native space by Fourier transform techniques such
that it becomes a reproducing kernel Banach space, which can be even embedded
into Sobolev spaces, and its reproducing kernel is set up by the related
positive definite function. The representations of the optimal solutions of
support vector machines (regularized empirical risks) in these reproducing
kernel Banach spaces are formulated explicitly in terms of positive definite
functions, and their finite numbers of coefficients can be computed by fixed
point iteration. We also give some typical examples of reproducing kernel
Banach spaces induced by Mat\'ern functions (Sobolev splines) so that their
support vector machine solutions are well computable as the classical
algorithms. Moreover, each of their reproducing bases includes information from
multiple training data points. The concept of reproducing kernel Banach spaces
offers us a new numerical tool for solving support vector machines.Comment: 26 page
Singular Value Decomposition of Operators on Reproducing Kernel Hilbert Spaces
Reproducing kernel Hilbert spaces (RKHSs) play an important role in many
statistics and machine learning applications ranging from support vector
machines to Gaussian processes and kernel embeddings of distributions.
Operators acting on such spaces are, for instance, required to embed
conditional probability distributions in order to implement the kernel Bayes
rule and build sequential data models. It was recently shown that transfer
operators such as the Perron-Frobenius or Koopman operator can also be
approximated in a similar fashion using covariance and cross-covariance
operators and that eigenfunctions of these operators can be obtained by solving
associated matrix eigenvalue problems. The goal of this paper is to provide a
solid functional analytic foundation for the eigenvalue decomposition of RKHS
operators and to extend the approach to the singular value decomposition. The
results are illustrated with simple guiding examples
Improving SIEM for critical SCADA water infrastructures using machine learning
Network Control Systems (NAC) have been used in many industrial processes. They aim to reduce the human factor burden and efficiently handle the complex process and communication of those systems. Supervisory control and data acquisition (SCADA) systems are used in industrial, infrastructure and facility processes (e.g. manufacturing, fabrication, oil and water pipelines, building ventilation, etc.) Like other Internet of Things (IoT) implementations, SCADA systems are vulnerable to cyber-attacks, therefore, a robust anomaly detection is a major requirement. However, having an accurate anomaly detection system is not an easy task, due to the difficulty to differentiate between cyber-attacks and system internal failures (e.g. hardware failures). In this paper, we present a model that detects anomaly events in a water system controlled by SCADA. Six Machine Learning techniques have been used in building and evaluating the model. The model classifies different anomaly events including hardware failures (e.g. sensor failures), sabotage and cyber-attacks (e.g. DoS and Spoofing). Unlike other detection systems, our proposed work helps in accelerating the mitigation process by notifying the operator with additional information when an anomaly occurs. This additional information includes the probability and confidence level of event(s) occurring. The model is trained and tested using a real-world dataset
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An Overview of the Use of Neural Networks for Data Mining Tasks
In the recent years the area of data mining has experienced a considerable demand for technologies that extract knowledge from large and complex data sources. There is a substantial commercial interest as well as research investigations in the area that aim to develop new and improved approaches for extracting information, relationships, and patterns from datasets. Artificial Neural Networks (NN) are popular biologically inspired intelligent methodologies, whose classification, prediction and pattern recognition capabilities have been utilised successfully in many areas, including science, engineering, medicine, business, banking, telecommunication, and many other fields. This paper highlights from a data mining perspective the implementation of NN, using supervised and unsupervised learning, for pattern recognition, classification, prediction and cluster analysis, and focuses the discussion on their usage in bioinformatics and financial data analysis tasks
Analysis causes of the incidence and compare social, economic, physical characteristics of informal settlements, case study: city of Marivan in Kurdistan province
Informal settlements are one of the problems of urban management in developing countries. Various theories about the causes and management of these settlements have been proposed. The most important of these theories, new socialist, liberal and dependency can be noted. The theory that argues for mandatory clearing informal settlement is not logical. Empowerment approach to be interested by countries and international organizations, and successful examples of this approach, with emphasis on the internal dynamics of these communities has been experienced. This paper tries to analyze the causes of marginalization and social, economic and spatial characteristics of informal settlement of Marivan city in Kurdistan province. Research areas consist of 4 region of Marivan informal settlement (Kosar,tape Mosk, sardoshiha, Tefine) sample size based on Cochran formula is 320 samples that Randomly and in four districts have been selected. Reasons for residents that they living in such places and social, economic characteristics of marginalized communities collected and entered into SPSS software and have been analyzed. The results show that more than 50 percent of residents in informal settlement areas of the city have come to this neighborhood. The main factor in the development of these four areas is not rural migrants. The highest levels of rural migrants from the neighborhood Tefin are that only 47% of residents are immigrants. The results suggest the great differences in social, economic and physical characteristics of slums. Among neighborhoods communities tapa Mosk and Tefini in the index close to each other and compare to two other neighborhoods are poor
MiL Testing of Highly Configurable Continuous Controllers: Scalable Search Using Surrogate Models
Continuous controllers have been widely used in automotive do- main to monitor and control physical components. These con- trollers are subject to three rounds of testing: Model-in-the-Loop (MiL), Software-in-the-Loop and Hardware-in-the-Loop. In our earlier work, we used meta-heuristic search to automate MiL test- ing of fixed configurations of continuous controllers. In this paper, we extend our work to support MiL testing of all feasible configura- tions of continuous controllers. Specifically, we use a combination of dimensionality reduction and surrogate modeling techniques to scale our earlier MiL testing approach to large, multi-dimensional input spaces formed by configuration parameters. We evaluated our approach by applying it to a complex, industrial continuous controller. Our experiment shows that our approach identifies test cases indicating requirements violations. Further, we demonstrate that dimensionally reduction helps generate surrogate models with higher prediction accuracy. Finally, we show that combining our search algorithm with surrogate modelling improves its efficiency for two out of three requirements
Bayesian Probabilistic Numerical Methods in Time-Dependent State Estimation for Industrial Hydrocyclone Equipment
The use of high-power industrial equipment, such as large-scale mixing equipment or a hydrocyclone for separation of particles in liquid suspension, demands careful monitoring to ensure correct operation. The fundamental task of state-estimation for the liquid suspension can be posed as a time-evolving inverse problem and solved with Bayesian statistical methods. In this article, we extend Bayesian methods to incorporate statistical models for the error that is incurred in the numerical solution of the physical governing equations. This enables full uncertainty quantification within a principled computation-precision trade-off, in contrast to the over-confident inferences that are obtained when all sources of numerical error are ignored. The method is cast within a sequential Monte Carlo framework and an optimized implementation is provided in Python
Convergence acceleration for multiobjective sparse reconstruction via knowledge transfer
© Springer Nature Switzerland AG 2019. Multiobjective sparse reconstruction (MOSR) methods can potentially obtain superior reconstruction performance. However, they suffer from high computational cost, especially in high-dimensional reconstruction. Furthermore, they are generally implemented independently without reusing prior knowledge from past experiences, leading to unnecessary computational consumption due to the re-exploration of similar search spaces. To address these problems, we propose a sparse-constraint knowledge transfer operator to accelerate the convergence of MOSR solvers by reusing the knowledge from past problem-solving experiences. Firstly, we introduce the deep nonlinear feature coding method to extract the feature mapping between the search of the current problem and a previously solved MOSR problem. Through this mapping, we learn a set of knowledge-induced solutions which contain the search experience of the past problem. Thereafter, we develop and apply a sparse-constraint strategy to refine these learned solutions to guarantee their sparse characteristics. Finally, we inject the refined solutions into the iteration of the current problem to facilitate the convergence. To validate the efficiency of the proposed operator, comprehensive studies on extensive simulated signal reconstruction are conducted
Rademacher chaos complexities for learning the kernel problem
Copyright © 2010 The MIT PressCopyright © 2010 Massachusetts Institute of TechnologyWe develop a novel generalization bound for learning the kernel problem. First, we show that the generalization analysis of the kernel learning problem reduces to investigation of the suprema of the Rademacher chaos process of order 2 over candidate kernels, which we refer to as Rademacher chaos complexity. Next, we show how to estimate the empirical Rademacher chaos complexity by well-established metric entropy integrals and pseudo-dimension of the set of candidate kernels. Our new methodology mainly depends on the principal theory of U-processes and entropy integrals. Finally, we establish satisfactory excess generalization bounds and misclassification error rates for learning gaussian kernels and general radial basis kernels
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