Mark A. Wolters

Simulated Annealing Model Search for Subset Selection in Screening Experiments

The analysis of screening experiments based on nonregular designs can lead to a model selection problem in which the number of variables is large, the number of trials is small, and there are constraints on model structure. Common subset selection methods do not perform well in this setting. We propose a new approach particularly well suited to screening. The method uses an intentionally nonconvergent stochastic search to generate a large set of well-fitting models, each with the same number of variables. Model selection is then viewed as a feature extraction problem from this set. An easy-to-use graphical method and an automatic approach are proposed to determine the best models. Computer code and additional supplementary materials are available online.

A particle swarm algorithm with broad applicability in shape-constrained estimation

In nonparametric function estimation, the inclusion of shape constraints can confer several advantages, including improved estimation accuracy, reduced sensitivity to smoothing parameters, and control over the qualitative appearance of the estimate. Finding shape-restricted estimates may require solving a difficult optimization problem, however, making these advantages hard to realize. A particle swarm algorithm is proposed to overcome this barrier and expand the possibilities for shape-constrained estimation. The algorithm uses a cooperative search strategy with two swarms, one focused on global exploration and one focused on local exploitation. The new heuristic has the added advantage of being a general tool, applicable without modification to a variety of estimators, constraints, and objective functions. The algorithm is demonstrated on a number of density estimation and regression problems, and the potential for further improvement is discussed. Supplementary materials, including source code, are available online.

Classification of Large-Scale Remote Sensing Images for Automatic Identification of Health Hazards

Remote sensing images from Earth-orbiting satellites are a potentially rich data source for monitoring and cataloguing atmospheric health hazards that cover large geographic regions. A method is proposed for classifying such images into hazard and nonhazard regions using the autologistic regression model, which may be viewed as a spatial extension of logistic regression. The method includes a novel and simple approach to parameter estimation that makes it well suited to handling the large and high-dimensional datasets arising from satellite-borne instruments. The methodology is demonstrated on both simulated images and a real application to the identification of forest fire smoke.

Issues in the Identification of Smoke in Hyperspectral Satellite Imagery — A Machine Learning Approach

Observations from earth-orbiting satellites play an important role in the study of various largescale surface and atmospheric phenomena. In many cases the data collected by such satellites are used and communicated in the form of raster images—three-dimensional data arrays where the first two dimensions define pixels corresponding to spatial coordinates. The third dimension contains one or more image planes. A greyscale image, for example, has one image plane, while a color (RGB) image has three planes, one each for the brightness in the red, green, and blue parts of the visible spectrum.

Better Autologistic Regression

Autologistic regression is an important probability model for dichotomous random variables observed along with covariate information. It has been used in various fields for analyzing binary data possessing spatial or network structure. The model can be viewed as an extension of the autologistic model (also known as the Ising model, quadratic exponential binary distribution, or Boltzmann machine) to include covariates. It can also be viewed as an extension of logistic regression to handle responses that are not independent. Not all authors use exactly the same form of the autologistic regression model. Variations of the model differ in two respects. First, the variable coding---the two numbers used to represent the two possible states of the variables---might differ. Common coding choices are (zero, one) and (minus one, plus one). Second, the model might appear in either of two algebraic forms: a standard form, or a recently proposed centered form. Little attention has been paid to the effect of these differences, and the literature shows ambiguity about their importance. It is shown here that changes to either coding or centering in fact produce distinct, non-nested probability models. Theoretical results, numerical studies, and analysis of an ecological data set all show that the differences among the models can be large and practically significant. Understanding the nature of the differences and making appropriate modelling choices can lead to significantly improved autologistic regression analyses. The results strongly suggest that the standard model with plus/minus coding, which we call the symmetric autologistic model, is the most natural choice among the autologistic variants.