Regression problems on massive data sets are ubiquitous in many application domains including the Internet, earth and space sciences, and finances. In many cases, regression algorithms such as linear regression or neural networks attempt to fit the target variable as a function of the input variables without regard to the underlying joint distribution of the variables. As a result, these global models are not sensitive to variations in the local structure of the input space. Several algorithms, including the mixture of experts model, classification and regression trees (CART), and others have been developed, motivated by the fact that a variability in the local distribution of inputs may be reflective of a significant change in the target variable. While these methods can handle the non-stationarity in the relationships to varying degrees, they are often not scalable and, therefore, not used in large scale data mining applications. In this paper we develop Block-GP, a Gaussian Process regression framework for multimodal data, that can be an order of magnitude more scalable than existing state-of-the-art nonlinear regression algorithms. The framework builds local Gaussian Processes on semantically meaningful partitions of the data and provides higher prediction accuracy than a single global model with very high confidence. The method relies on approximating the covariance matrix of the entire input space by smaller covariance matrices that can be modeled independently, and can therefore be parallelized for faster execution. Theoretical analysis and empirical studies on various synthetic and real data sets show high accuracy and scalability of Block-GP compared to existing nonlinear regression techniques.

The use of Gaussian processes can be an effective approach to prediction in a supervised learning environment. For large data sets, the standard Gaussian process approach requires solving very large systems of linear equations and approximations are required for the calculations to be practical. We will focus on the subset of regressors approximation technique. We will demonstrate that there can be numerical instabilities in a well known implementation of the technique. We discuss alternate implementations that have better numerical stability properties and can lead to better predictions. Our results will be illustrated by looking at an application involving prediction of galaxy redshift from broadband spectrum data.

The Geometry Manipulation Protocol (GMP) is a library which serializes datatypes between XML and ANSI C data structures to support CFD applications. This library currently provides a description of geometric configurations, general moving-body scenarios (prescribed and/or 6-DOF), and control surface settings.

One of the key problems that arises in many areas is to estimate a potentially nonlinear function [tex] G(x, \theta)[/tex] given input and output samples [tex] ( X,y ) [/tex] so that [tex]y approx G(x, \theta)[/tex]. There are many approaches to addressing this regression problem. Neural networks, regression trees, and many other methods have been developed to estimate [tex]$G$[/tex] given the input output pair [tex] ( X,y ) [/tex]. One method that I have worked with is called Gaussian process regression. There many good texts and papers on the subject. For more technical information on the method and its applications see: http://www.gaussianprocess.org/ A key problem that arises in developing these models on very large data sets is that it ends up requiring an [tex]O(N^3)[/tex] computation where N is the number of data points and the training sample. Obviously this becomes very problematic when N is large. I discussed this problem with Leslie Foster, a mathematics professor at San Jose State University. He, along with some of his students, developed a method to address this problem based on Cholesky decomposition and pivoting. He also shows that this leads to a numerically stable result. If ou're interested in some light reading, I’d suggest you take a look at his [recent paper]( ) (which was accepted in the Journal of Machine Learning Research) posted on dashlink. We've also posted code for you to try it out. Let us know how it goes. If you are interested in applications of this method in the area of prognostics, check out our [new paper](/dashlink/resources/51/) on the subject which was published in IEEE Transactions on Systems, Man, and Cybernetics.

SPATIALLY ADAPTIVE SEMI-SUPERVISED LEARNING WITH GAUSSIAN PROCESSES FOR HYPERSPECTRAL DATA ANALYSIS GOO JUN * AND JOYDEEP GHOSH* Abstract. A semi-supervised learning algorithm for the classification of hyperspectral data, Gaussian process expectation maximization (GP-EM), is proposed. Model parameters for each land cover class is first estimated by a supervised algorithm using Gaussian process regressions to find spatially adaptive parameters, and the estimated parameters are then used to initialize a spatially adaptive mixture-of-Gaussians model. The mixture model is updated by expectationmaximization iterations using the unlabeled data, and the spatially adaptive parameters for unlabeled instances are obtained by Gaussian process regressions with soft assignments. Two sets of hyperspectral data taken from the Botswana area by the NASA EO-1 satellite are used for experiments. Empirical evaluations show that the proposed framework performs significantly better than baseline algorithms that do not use spatial information, and the results are also better than any previously reported results by other algorithms on the same data.

The 2023 cartographic boundary KMLs are simplified representations of selected geographic areas from the U.S. Census Bureau's Master Address File / Topologically Integrated Geographic Encoding and Referencing (MAF/TIGER) Database (MTDB). These boundary files are specifically designed for small-scale thematic mapping. When possible, generalization is performed with the intent to maintain the hierarchical relationships among geographies and to maintain the alignment of geographies within a file set for a given year. Geographic areas may not align with the same areas from another year. Some geographies are available as nation-based files while others are available only as state-based files. Block Groups (BGs) are clusters of blocks within the same census tract. Each census tract contains at least one BG, and BGs are uniquely numbered within census tracts. BGs have a valid code range of 0 through 9. BGs have the same first digit of their 4-digit census block number from the same decennial census. For example, tabulation blocks numbered 3001, 3002, 3003,.., 3999 within census tract 1210.02 are also within BG 3 within that census tract. BGs coded 0 are intended to only include water area, no land area, and they are generally in territorial seas, coastal water, and Great Lakes water areas. Block groups generally contain between 600 and 3,000 people. A BG usually covers a contiguous area but never crosses county or census tract boundaries. They may, however, cross the boundaries of other geographic entities like county subdivisions, places, urban areas, voting districts, congressional districts, and American Indian / Alaska Native / Native Hawaiian areas. The generalized BG boundaries in this release are based on those that were delineated as part of the Census Bureau's Participant Statistical Areas Program (PSAP) for the 2020 Census.

기상전문이란 기상관측자료의 국제적 교환을 위해 세계기상기구(WMO)에 의해 명시된 규정에 따라 송수신에 적합하게 만든 자료를 말하며, 세계기상통신망인 GTS(Global Telecommunication System)을 통해 자료를 유통합니다.

The 2023 cartographic boundary KMLs are simplified representations of selected geographic areas from the U.S. Census Bureau's Master Address File / Topologically Integrated Geographic Encoding and Referencing (MAF/TIGER) Database (MTDB). These boundary files are specifically designed for small-scale thematic mapping. When possible, generalization is performed with the intent to maintain the hierarchical relationships among geographies and to maintain the alignment of geographies within a file set for a given year. Geographic areas may not align with the same areas from another year. Some geographies are available as nation-based files while others are available only as state-based files. Block Groups (BGs) are clusters of blocks within the same census tract. Each census tract contains at least one BG, and BGs are uniquely numbered within census tracts. BGs have a valid code range of 0 through 9. BGs have the same first digit of their 4-digit census block number from the same decennial census. For example, tabulation blocks numbered 3001, 3002, 3003,.., 3999 within census tract 1210.02 are also within BG 3 within that census tract. BGs coded 0 are intended to only include water area, no land area, and they are generally in territorial seas, coastal water, and Great Lakes water areas. Block groups generally contain between 600 and 3,000 people. A BG usually covers a contiguous area but never crosses county or census tract boundaries. They may, however, cross the boundaries of other geographic entities like county subdivisions, places, urban areas, voting districts, congressional districts, and American Indian / Alaska Native / Native Hawaiian areas. The generalized BG boundaries in this release are based on those that were delineated as part of the Census Bureau's Participant Statistical Areas Program (PSAP) for the 2020 Census.

We present a novel and general methodology for modeling time-varying vector autoregressive processes which are widely used in many areas such as modeling of chemical processes, mobile communication channels and biomedical signals. In the literature, most work utilize multivariate Gaussian models for the mentioned applications, mainly due to the lack of efficient analytical tools for modeling with non-Gaussian distributions. In this paper, we propose a particle filtering approach which can model non-Gaussian autoregressive processes having cross-correlations among them. Moreover, time-varying parameters of the process can be modeled as the most general case by using this sequential Bayesian estimation method. Simulation results justify the performance of the proposed technique, which potentially can model also Gaussian processes as a sub-case.