scholarly journals Conditional Deep Gaussian Processes: Multi-Fidelity Kernel Learning

Entropy ◽  
2021 ◽  
Vol 23 (11) ◽  
pp. 1545
Author(s):  
Chi-Ken Lu ◽  
Patrick Shafto
Keyword(s):  
Gaussian Processes ◽  
Marginal Likelihood ◽  
High Dimensional ◽  
Moment Matching ◽  
Implicit Functions ◽  
Matching Method ◽  
Regression Methods ◽  
The Hierarchical Structure ◽  
Comparable Performance ◽  
The Moment

Deep Gaussian Processes (DGPs) were proposed as an expressive Bayesian model capable of a mathematically grounded estimation of uncertainty. The expressivity of DPGs results from not only the compositional character but the distribution propagation within the hierarchy. Recently, it was pointed out that the hierarchical structure of DGP well suited modeling the multi-fidelity regression, in which one is provided sparse observations with high precision and plenty of low fidelity observations. We propose the conditional DGP model in which the latent GPs are directly supported by the fixed lower fidelity data. Then the moment matching method is applied to approximate the marginal prior of conditional DGP with a GP. The obtained effective kernels are implicit functions of the lower-fidelity data, manifesting the expressivity contributed by distribution propagation within the hierarchy. The hyperparameters are learned via optimizing the approximate marginal likelihood. Experiments with synthetic and high dimensional data show comparable performance against other multi-fidelity regression methods, variational inference, and multi-output GP. We conclude that, with the low fidelity data and the hierarchical DGP structure, the effective kernel encodes the inductive bias for true function allowing the compositional freedom.

scholarly journals Computing Expectiles Using k-Nearest Neighbours Approach

Symmetry ◽  
2021 ◽  
Vol 13 (4) ◽  
pp. 645
Author(s):  
Muhammad Farooq ◽  
Sehrish Sarfraz ◽  
Christophe Chesneau ◽  
Mahmood Ul Hassan ◽  
Muhammad Ali Raza ◽  
...  
Keyword(s):  
Computational Cost ◽  
Real Life ◽  
Distance Measures ◽  
Computational Time ◽  
High Dimensional ◽  
Test Error ◽  
Nearest Neighbours ◽  
Comparable Performance ◽  
Asymmetric Least Squares ◽  
Low Computational Cost

Expectiles have gained considerable attention in recent years due to wide applications in many areas. In this study, the k-nearest neighbours approach, together with the asymmetric least squares loss function, called ex-kNN, is proposed for computing expectiles. Firstly, the effect of various distance measures on ex-kNN in terms of test error and computational time is evaluated. It is found that Canberra, Lorentzian, and Soergel distance measures lead to minimum test error, whereas Euclidean, Canberra, and Average of (L1,L∞) lead to a low computational cost. Secondly, the performance of ex-kNN is compared with existing packages er-boost and ex-svm for computing expectiles that are based on nine real life examples. Depending on the nature of data, the ex-kNN showed two to 10 times better performance than er-boost and comparable performance with ex-svm regarding test error. Computationally, the ex-kNN is found two to five times faster than ex-svm and much faster than er-boost, particularly, in the case of high dimensional data.

scholarly journals Gaussian Processes Proxy Model with Latent Variable Models and Variogram-Based Sensitivity Analysis for Assisted History Matching

Energies ◽  
2020 ◽  
Vol 13 (17) ◽  
pp. 4290
Author(s):  
Dongmei Zhang ◽  
Yuyang Zhang ◽  
Bohou Jiang ◽  
Xinwei Jiang ◽  
Zhijiang Kang
Keyword(s):  
Sensitivity Analysis ◽  
Gaussian Processes ◽  
Latent Variable ◽  
History Matching ◽  
Latent Variable Models ◽  
High Dimensional ◽  
Model Parameters ◽  
Variable Model ◽  
Assisted History Matching ◽  
Proxy Models

Reservoir history matching is a well-known inverse problem for production prediction where enormous uncertain reservoir parameters of a reservoir numerical model are optimized by minimizing the misfit between the simulated and history production data. Gaussian Process (GP) has shown promising performance for assisted history matching due to the efficient nonparametric and nonlinear model with few model parameters to be tuned automatically. Recently introduced Gaussian Processes proxy models and Variogram Analysis of Response Surface-based sensitivity analysis (GP-VARS) uses forward and inverse Gaussian Processes (GP) based proxy models with the VARS-based sensitivity analysis to optimize the high-dimensional reservoir parameters. However, the inverse GP solution (GPIS) in GP-VARS are unsatisfactory especially for enormous reservoir parameters where the mapping from low-dimensional misfits to high-dimensional uncertain reservoir parameters could be poorly modeled by GP. To improve the performance of GP-VARS, in this paper we propose the Gaussian Processes proxy models with Latent Variable Models and VARS-based sensitivity analysis (GPLVM-VARS) where Gaussian Processes Latent Variable Model (GPLVM)-based inverse solution (GPLVMIS) instead of GP-based GPIS is provided with the inputs and outputs of GPIS reversed. The experimental results demonstrate the effectiveness of the proposed GPLVM-VARS in terms of accuracy and complexity. The source code of the proposed GPLVM-VARS is available at https://github.com/XinweiJiang/GPLVM-VARS.

Probabilistic Optimal Design Using Successive Surrogate Probability Density Functions

1990 ◽  
Author(s):  
R. J. Eggert ◽  
R. W. Mayne
Keyword(s):  
Probability Density ◽  
Optimization Method ◽  
Probability Density Functions ◽  
Density Functions ◽  
Matching Method ◽  
Design Constraint ◽  
New Approach ◽  
Function Formulation ◽  
The Moment ◽  
Theoretical Considerations

Abstract Probabilistic optimization using the moment matching method and the simulation optimization method are discussed and compared to conventional deterministic optimization. A new approach based on successively approximating probability density functions, using recursive quadratic programming for the optimization process, is described. This approach incorporates the speed and robustness of analytical probability density functions and improves accuracy by considering simulation results. Theoretical considerations and an example problem illustrate the features of the approach. The paper closes with a discussion of an objective function formulation which includes the expected cost of design constraint failure.

scholarly journals SEMANTIC DESCRIPTION FOR THE TAXONOMY OF THE GEOSPATIAL SERVICES

2015 ◽  
Vol 21 (3) ◽  
pp. 515-531 ◽  
Author(s):  
Hao Li ◽  
Yandong Wang ◽  
Penggen Cheng
Keyword(s):  
Information System ◽  
World Wide ◽  
Geospatial Data ◽  
Semantic Description ◽  
Matching Method ◽  
The World ◽  
The Hierarchical Structure ◽  
Description Framework ◽  
Geospatial Services ◽  
Readable Format

Abstract:With the advances in the World Wide Web and Geographic Information System, geospatial services have progressively developed to provide geospatial data and processing functions online. In order to efficiently discover and manage the large amount of geospatial services, these services are registered with semantic descriptions and categorized into classes according to certain taxonomies. Most taxonomies for geospatial services are only provided in the human readable format. The lack of semantic description for taxonomies limits the semantic-based discovery of geospatial services. The objectives of this paper are proposing an approach to semantically describe the taxonomy of geospatial services and using the semantic descriptions for taxonomy to improve the discovery of geospatial services. A semantic description framework is introduced for geospatial service taxonomy to describe not only the hierarchical structure of classes but also the definitions for all classes. The semantic description of taxonomy base on this framework is further used to simplify the semantic description and registration of geospatial services and enhance the semantic-based service matching method.

scholarly journals Criminal community: crimonological approach

2020 ◽  
Vol 4 (2) ◽  
pp. 109-116
Author(s):  
Margarita G. Kozlovskaya
Keyword(s):  
Criminal Group ◽  
Criminal Organization ◽  
Point Of View ◽  
Community Members ◽  
External Relations ◽  
The Hierarchical Structure ◽  
Internal Interaction ◽  
Scope Of Application ◽  
The Subject ◽  
The Moment

The subject of the research is the criminal community, its characteristics, and features within the framework of criminology. The purpose of the research is to confirm or disprove hypothesis that a criminal community as a criminological phenomenon is nor equal to a criminal organization or an organized criminal group Methodology. The author uses general theoretical methods (comparative analysis, generalization, deduction) and specific methods (formal legal interpretation of legal acts, questionnaires). The main results, scope of application. A criminal organization and a criminal community are different criminological phenomena that differ from each other in significant ways. The differences are both in the degree of criminal organization, and the complexity of the structure of internal and external interaction. From the point of view of a systematic approach, a criminal community is not only a more complex system compared to a criminal organization. It is characterized by an improved structure of internal interaction, in which the hierarchical structure is either complicated, or replaced or supplemented by a network structure. The peculiarity is to complement the system approach with a synergistic one: in the criminal community, the pooling of criminal efforts is carried out more effectively, mainly in the sphere of external relations. The criminal community is a more open system compared to the criminal organization. Certain features can be identified in the contacts of criminal community members with the external environment. The most important feature is a symbiosis of criminal and legal practices that affects the life of entire regions or relatively large masses of the population. The criminal community is a purposeful system with its own specifics. And this specificity is seen in the fact that the criminal community pursues (secretly or openly, at the moment or in the foreseeable future) the achievement of political goals, namely: the possession of power, infiltration into power, undermining power, its capture and retention. It is power, not wealth, that is the real goal of the criminal community, and not just because it is easily converted into wealth. Power is valuable in itself, because it also gives a lot of other advantages. Conclusions. A criminal community cannot be reduced to a criminal organization, much less – to an organized criminal group, and this conclusion requires to be included into legislation.

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