Showing papers by "Pritam Ranjan published in 2013"

GPfit: An R package for Gaussian Process Model Fitting using a New Optimization Algorithm

Abstract: Gaussian process (GP) models are commonly used statistical metamodels for emulating expensive computer simulators. Fitting a GP model can be numerically unstable if any pair of design points in the input space are close together. Ranjan, Haynes, and Karsten (2011) proposed a computationally stable approach for fitting GP models to deterministic computer simulators. They used a genetic algorithm based approach that is robust but computationally intensive for maximizing the likelihood. This paper implements a slightly modified version of the model proposed by Ranjan et al. (2011), as the new R package GPfit. A novel parameterization of the spatial correlation function and a new multi-start gradient based optimization algorithm yield optimization that is robust and typically faster than the genetic algorithm based approach. We present two examples with R codes to illustrate the usage of the main functions in GPfit. Several test functions are used for performance comparison with a popular R package mlegp. GPfit is a free software and distributed under the general public license, as part of the R software project (R Development Core Team 2012).

Efficient Optimization of the Likelihood Function in Gaussian Process Modelling

Abstract: Gaussian Process (GP) models are popular statistical surrogates used for emulating computationally expensive computer simulators. The quality of a GP model fit can be assessed by a goodness of fit measure based on optimized likelihood. Finding the global maximum of the likelihood function for a GP model is typically very challenging as the likelihood surface often has multiple local optima, and an explicit expression for the gradient of the likelihood function is typically unavailable. Previous methods for optimizing the likelihood function (e.g. MacDonald et al. (2013)) have proven to be robust and accurate, though relatively inefficient. We propose several likelihood optimization techniques, including two modified multi-start local search techniques, based on the method implemented by MacDonald et al. (2013), that are equally as reliable, and significantly more efficient. A hybridization of the global search algorithm Dividing Rectangles (DIRECT) with the local optimization algorithm BFGS provides a comparable GP model quality for a fraction of the computational cost, and is the preferred optimization technique when computational resources are limited. We use several test functions and a real application from an oil reservoir simulation to test and compare the performance of the proposed methods with the one implemented by MacDonald et al. (2013) in the R library GPfit. The proposed method is implemented in a Matlab package, GPMfit.

Space-filling Latin Hypercube Designs based on Randomization Restrictions in Factorial Experiments

Abstract: Latin hypercube designs (LHDs) with space-filling properties are widely used for emulating computer simulators. Over the last three decades, a wide spectrum of LHDs have been proposed with space-filling criteria like minimum correlation among factors, maximin interpoint distance, and orthogonality among the factors via orthogonal arrays (OAs). Projective geometric structures like spreads, covers and stars of PG(p-1,q) can be used to characterize the randomization restriction of multistage factorial experiments. These geometric structures can also be used for constructing OAs and nearly OAs (NOAs). In this paper, we present a new class of space-filling LHDs based on NOAs derived from stars of PG(p-1, 2).

A new Bayesian ensemble of trees classifier for identifying multi-class labels in satellite images

Abstract: Classification of satellite images is a key component of many remote sensing applications. One of the most important products of a raw satellite image is the classified map which labels the image pixels into meaningful classes. Though several parametric and non-parametric classifiers have been developed thus far, accurate labeling of the pixels still remains a challenge. In this paper, we propose a new reliable multiclass-classifier for identifying class labels of a satellite image in remote sensing applications. The proposed multiclass-classifier is a generalization of a binary classifier based on the flexible ensemble of regression trees model called Bayesian Additive Regression Trees (BART). We used three small areas from the LANDSAT 5 TM image, acquired on August 15, 2009 (path/row: 08/29, L1T product, UTM map projection) over Kings County, Nova Scotia, Canada to classify the land-use. Several prediction accuracy and uncertainty measures have been used to compare the reliability of the proposed classifier with the state-of-the-art classifiers in remote sensing.

Comment: EI Criteria for Noisy Computer Simulators

Abstract: The author believes that the methodologies presented by Picheny et al. are innovative and should be useful for computer experiment practitioners.

A New Tree-based Classifier for Satellite Images

Abstract: Classification of satellite images is a key component of many remote sensing applications. One of the most important products of a raw satellite image is the classified map which labels the image pixels into meaningful classes. Though several parametric and non-parametric classifiers have been developed thus far, accurate labeling of the pixels still remains a challenge. In this paper, we propose a new reliable multiclass-classifier for identifying class labels of a satellite image in remote sensing applications. The proposed multiclass-classifier is a generalization of a binary classifier based on the flexible ensemble of regression trees model called Bayesian Additive Regression Trees (BART). We used three small areas from the LANDSAT 5 TM image, acquired on August 15, 2009 (path/row: 08/29, L1T product, UTM map projection) over Kings County, Nova Scotia, Canada to classify the land-use. Several prediction accuracy and uncertainty measures have been used to compare the reliability of the proposed classifier with the state-of-the-art classifiers in remote sensing.

Isomorphism Check for $2^n$ Factorial Designs with Randomization Restrictions

Abstract: Factorial designs with randomization restrictions are often used in industrial experiments when a complete randomization of trials is impractical. In the statistics literature, the analysis, construction and isomorphism of factorial designs has been extensively investigated. Much of the work has been on a case-by-case basis -- addressing completely randomized designs, randomized block designs, split-plot designs, etc. separately. In this paper we take a more unified approach, developing theoretical results and an efficient relabeling strategy to both construct and check the isomorphism of multi-stage factorial designs with randomization restrictions. The examples presented in this paper particularly focus on split-lot designs.

A New Tree-Based Classifier for Satellite Images

Abstract: Classification of satellite images is a key component of many remote sensing applications. One of the most important products of a raw satellite image is the classified map which labels the image pixels into meaningful classes. Though several parametric and non-parametric classifiers have been developed thus far, accurate labeling of the pixels still remains a challenge. In this paper, we propose a new reliable multiclass-classifier for identifying class labels of a satellite image in remote sensing applications. The proposed multiclass-classifier is a generalization of a binary classifier based on the flexible ensemble of regression trees model called Bayesian Additive Regression Trees (BART). We used three small areas from the LANDSAT 5 TM image, acquired on August 15, 2009 (path/row: 08/29, L1T product, UTM map projection) over Kings County, Nova Scotia, Canada to classify the land-use. Several prediction accuracy and uncertainty measures have been used to compare the reliability of the proposed classifier with the state-of-the-art classifiers in remote sensing.

A Unified Approach to Factorial Designs with Randomization Restrictions

Abstract: AbtsrcatFactorial designs are commonly used to assess the impact of factors and factor combinations in industrial and agricultural experiments. Though preferred, complete randomization of trials is often infeasible, and randomization restrictions are imposed. In this paper, we discuss a finite projective geometric (PG) approach to unify the existence, construction and analysis of multistage factorial designs with randomization restrictions using randomization defining contrast subspaces (or flats of a PG). Our main focus will be on the construction of such designs, and developing a word length pattern scheme that can be used for generalizing the traditional design rank- ing criteria for factorial designs. We also present a novel isomorphism check algorithm for these designs.

Ecient Optimization of the Likelihood Function in

Abstract: Gaussian Process (GP) models are popular statistical surrogates used for emulating computationally expensive computer simulators. The quality of a GP model t can be assessed by a goodness of t measure based on optimized likelihood. Finding the global maximum of the likelihood function for a GP model is typically very challenging as the likelihood surface often has multiple local optima, and an explicit expression for the gradient of the likelihood function is typically unavailable. Previous methods for optimizing the likelihood function (e.g., MacDonald et al. (2013)) have proven to be robust and accurate, though relatively inecient. We propose several likelihood optimization techniques, including two modied multi-start local search techniques, based on the method implemented by MacDonald et al. (2013), that are equally as reliable, and signicantly more ecient. A hybridization of the global search algorithm Dividing Rectangles (DIRECT) with the local optimization algorithm BFGS provides a comparable GP model quality for a fraction of the computational cost, and is the preferred optimization technique when computational resources are limited. We use several test functions and a real application from an oil reservoir simulation to test and compare the performance of the proposed methods with the one implemented by MacDonald et al. (2013) in the R library GPt . The proposed method is implemented in a Matlab package, GPMt .