We address an approximation method for Gaussian process (GP) regression, where we approximate covariance by a block matrix such that diagonal blocks are calculated exactly while off-diagonal blocks are approximated. Partitioning input data points, we present a two-layer hierarchical model for GP regression, where prototypes of clusters in the upper layer are involved for coarse modeling by a GP...

using the mathematic techniques such as fuzzy approach has useful outcomes for production planning in different sources. in this paper lgp1 was used to model the objectives such as: avoidance of shortage or surplus of demand, access to maximum of income, using the normal capacity of production and organizing the inventory of warehouse, within the framework of goal constraints like balancing be...

The Hierarchical Dirichlet process is a discrete random measure serving as an important prior in Bayesian non-parametrics. It motivated with the study of groups clustered data. Each group modelled through level two and all share same base distribution which itself drawn from one process. has concentration parameters at each level. main results paper are law large numbers deviations for hierarch...

Optimal design problems of large-scale and complex engineering systems are typically decomposed into a number of smaller and tractable subproblems. Analytical target cascading (ATC) is a methodology for translating overall system design targets to individual specifications for the subsystems and components that make up the system based on a hierarchical partition. We propose to use the χ langua...

Optimal design problems of large-scale and complex engineering systems are typically decomposed into a number of smaller and tractable subproblems. Analytical target cascading (ATC) is a methodology for translating overall system design targets to individual specifications for the subsystems and components that make up the system based on a hierarchical partition. We propose to use the χ langua...

This article presents a hierarchy as an integral part of a data model. Placed in the context of a multidimensional database, this enables summarisation operators such as the CUBE to be extended with hierarchical paths for each dimension. For example, temporal aggregation could be composed of year, month, week, and daily intervals, whereas spatial aggregation could be based on a hierarchy of mul...