Browsing by Subject "Statistical decision"

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Adaptive hierarchical classification with limited training data
(2002) Morgan, Joseph Troy; Crawford, Melba M.
This research focused on the development of a hierarchical approach for classification that is robust with respect to training data that are limited both in quantity and spatial extent. Many difficult classification problems involve a high dimensional input and output space (candidate labels). Due to the "curse of dimensionality," it is necessary to reduce the size of the input space when there is only a limited quantity of training data available. While a significant amount of research has focused on transforming the input space into a reduced feature space that accurately discriminates between the classes in a fixed output space, traditional approaches fail to capitalize on the domain knowledge and flexibility gained by transforming the feature space and the output space simultaneously. A new approach is proposed that utilizes domain knowledge, which is automatically discovered from the data, to combat the "small sample size" problem. Spatially limited training data can result in poor inference concerning the true populations. The detrimental impact that can result if this issue is ignored is explored and demonstrated. Transferal of information that was previously acquired is used to update the signatures with the new clusters if the hypothesis that the new clusters are indeed just deformed versions of what already exists in the spectral library is accepted. Independent of limited training data, both in terms of the spatial implications and limited quantity, different sampling subsets of the same ground truth may result in slightly different classifiers. This issue has not been addressed rigorously. The advantages gained by using an ensemble of classifiers built from sub-samples of training data are widely acknowledged but have not previously been used in the context of a hierarchical classifier for remote sensing data or for hyperspectral data in general. The ensemble of classifiers is used to identify a suitable level of the tree for situations where the resolution of the output space cannot be supported. Further decisions of how the classification structure should be adapted and at what level need to be made are explored. Furthermore, pseudolabeled data are utilized to improve classification results at that level of resolution.
Inevitable disappointment and decision making based on forecasts
(2006) Chen, Min; Dyer, James
In decision problems where decisions on risky pro jects are made based on the forecasts of their performance, ignoring the prediction errors can cause the problem known as post-decision disappointment. We describe the disappointment in situations when pro jects are accepted by comparing their forecasts with a threshold value directly, and discuss the conditions when it occurs. Next we study a general decision problem where one single unbiased estimate is available for the pro ject under consideration. A decision-theoretic model is proposed to show that the optimal decision can be obtained through a Bayesian updating procedure. And special interest is paid to a judgment decision procedure, in which the unknown true outcome is substituted by a forecast. Further, by extending the model we demonstrate that the Bayesian approach can aid the DM in nding the optimal decision using multiple forecasts. We also consider aggregating several correlated forecasts into a single predictor, and show that a mixed two-stage approach, by rst combining the forecasts into a weighted average and then applying the Bayesian updating procedure, vi is possible if the weighted average is a su cient statistic. Finally we describe how to dynamically update the estimate of a pro ject with forecasts from other correlated projects.
Prioritization and optimization in stochastic network interdiction problems
(2008-12) Michalopoulos, Dennis Paul, 1979-; Barnes, J. Wesley; Morton, David P.
The goal of a network interdiction problem is to model competitive decision-making between two parties with opposing goals. The simplest interdiction problem is a bilevel model consisting of an 'adversary' and an interdictor. In this setting, the interdictor first expends resources to optimally disrupt the network operations of the adversary. The adversary subsequently optimizes in the residual interdicted network. In particular, this dissertation considers an interdiction problem in which the interdictor places radiation detectors on a transportation network in order to minimize the probability that a smuggler of nuclear material can avoid detection. A particular area of interest in stochastic network interdiction problems (SNIPs) is the application of so-called prioritized decision-making. The motivation for this framework is as follows: In many real-world settings, decisions must be made now under uncertain resource levels, e.g., interdiction budgets, available man-hours, or any other resource depending on the problem setting. Applying this idea to the stochastic network interdiction setting, the solution to the prioritized SNIP (PrSNIP) is a rank-ordered list of locations to interdict, ranked from highest to lowest importance. It is well known in the operations research literature that stochastic integer programs are among the most difficult optimization problems to solve. Even for modest levels of uncertainty, commercial integer programming solvers can have difficulty solving models such as PrSNIP. However, metaheuristic and large-scale mathematical programming algorithms are often effective in solving instances from this class of difficult optimization problems. The goal of this doctoral research is to investigate different methods for modeling and solving SNIPs (optimization) and PrSNIPs (prioritization via optimization). We develop a number of different prioritized and unprioritized models, as well as exact and heuristic algorithms for solving each problem type. The mathematical programming algorithms that we consider are based on row and column generation techniques, and our heuristic approach uses adaptive tabu search to quickly find near-optimal solutions. Finally, we develop a group of hybrid algorithms that combine various elements of both classes of algorithms.