Nonparametric Estimation of the Bayes Error

This thesis is concerned with the performance of nonparametric classifiers and their application to the estimation of the Rayes error. Although the behavior of these classifiers as the number of preclassified design samples becomes infinite is well understood, very little is known regarding their finite sample error performance. Here, we examine the performance of Parzen and k-nearest neighbor (k-NN) classifiers, relating the expected error rates to the size of the design set and the various, design parameters (kernel size and shape, value of k, distance metric for nearest neighbor calculation, etc.). These results lead to several significant improvements in the design procedures for nonparametric classifiers, as well as improved estimates of the Bayes error rate. , Our results show that increasing the sample size is in many cases not an effective practical means of improving the classifier performance. Rather, careful attention must be paid to the decision threshold, selection of the kernel size and shape (for Parzen classifiers), and selection of k and the distance metric (for k-NN classifiers). Guidelines are developed toward propper selection of each of these parameters. The use of nonparametric error rates for Bayes error estimation is also considered, and techniques are given which reduce or compensate for the biases of the nonparametric error rates. A bootstrap technique is also developed which allows the designer to estimate the standard deviation of a nonparametric estimate of the Bayes error

Kernel methods in machine learning

We review machine learning methods employing positive definite kernels. These methods formulate learning and estimation problems in a reproducing kernel Hilbert space (RKHS) of functions defined on the data domain, expanded in terms of a kernel. Working in linear spaces of function has the benefit of facilitating the construction and analysis of learning algorithms while at the same time allowing large classes of functions. The latter include nonlinear functions as well as functions defined on nonvectorial data. We cover a wide range of methods, ranging from binary classifiers to sophisticated methods for estimation with structured data.Comment: Published in at http://dx.doi.org/10.1214/009053607000000677 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Classification of non-heat generating outdoor objects in thermal scenes for autonomous robots

We have designed and implemented a physics-based adaptive Bayesian pattern classification model that uses a passive thermal infrared imaging system to automatically characterize non-heat generating objects in unstructured outdoor environments for mobile robots. In the context of this research, non-heat generating objects are defined as objects that are not a source for their own emission of thermal energy, and so exclude people, animals, vehicles, etc. The resulting classification model complements an autonomous bot\u27s situational awareness by providing the ability to classify smaller structures commonly found in the immediate operational environment. Since GPS depends on the availability of satellites and onboard terrain maps which are often unable to include enough detail for smaller structures found in an operational environment, bots will require the ability to make decisions such as go through the hedges or go around the brick wall. A thermal infrared imaging modality mounted on a small mobile bot is a favorable choice for receiving enough detailed information to automatically interpret objects at close ranges while unobtrusively traveling alongside pedestrians. The classification of indoor objects and heat generating objects in thermal scenes is a solved problem. A missing and essential piece in the literature has been research involving the automatic characterization of non-heat generating objects in outdoor environments using a thermal infrared imaging modality for mobile bots. Seeking to classify non-heat generating objects in outdoor environments using a thermal infrared imaging system is a complex problem due to the variation of radiance emitted from the objects as a result of the diurnal cycle of solar energy. The model that we present will allow bots to see beyond vision to autonomously assess the physical nature of the surrounding structures for making decisions without the need for an interpretation by humans.;Our approach is an application of Bayesian statistical pattern classification where learning involves labeled classes of data (supervised classification), assumes no formal structure regarding the density of the data in the classes (nonparametric density estimation), and makes direct use of prior knowledge regarding an object class\u27s existence in a bot\u27s immediate area of operation when making decisions regarding class assignments for unknown objects. We have used a mobile bot to systematically capture thermal infrared imagery for two categories of non-heat generating objects (extended and compact) in several different geographic locations. The extended objects consist of objects that extend beyond the thermal camera\u27s field of view, such as brick walls, hedges, picket fences, and wood walls. The compact objects consist of objects that are within the thermal camera\u27s field of view, such as steel poles and trees. We used these large representative data sets to explore the behavior of thermal-physical features generated from the signals emitted by the classes of objects and design our Adaptive Bayesian Classification Model. We demonstrate that our novel classification model not only displays exceptional performance in characterizing non-heat generating outdoor objects in thermal scenes but it also outperforms the traditional KNN and Parzen classifiers

Restricted Minimum Error Entropy Criterion for Robust Classification

The minimum error entropy (MEE) criterion has been verified as a powerful approach for non-Gaussian signal processing and robust machine learning. However, the implementation of MEE on robust classification is rather a vacancy in the literature. The original MEE only focuses on minimizing the Renyi's quadratic entropy of the error probability distribution function (PDF), which could cause failure in noisy classification tasks. To this end, we analyze the optimal error distribution in the presence of outliers for those classifiers with continuous errors, and introduce a simple codebook to restrict MEE so that it drives the error PDF towards the desired case. Half-quadratic based optimization and convergence analysis of the new learning criterion, called restricted MEE (RMEE), are provided. Experimental results with logistic regression and extreme learning machine are presented to verify the desirable robustness of RMEE

Physically inspired methods and development of data-driven predictive systems.

Traditionally building of predictive models is perceived as a combination of both science and art. Although the designer of a predictive system effectively follows a prescribed procedure, his domain knowledge as well as expertise and intuition in the field of machine learning are often irreplaceable. However, in many practical situations it is possible to build well–performing predictive systems by following a rigorous methodology and offsetting not only the lack of domain knowledge but also partial lack of expertise and intuition, by computational power. The generalised predictive model development cycle discussed in this thesis is an example of such methodology, which despite being computationally expensive, has been successfully applied to real–world problems. The proposed predictive system design cycle is a purely data–driven approach. The quality of data used to build the system is thus of crucial importance. In practice however, the data is rarely perfect. Common problems include missing values, high dimensionality or very limited amount of labelled exemplars. In order to address these issues, this work investigated and exploited inspirations coming from physics. The novel use of well–established physical models in the form of potential fields, has resulted in derivation of a comprehensive Electrostatic Field Classification Framework for supervised and semi–supervised learning from incomplete data. Although the computational power constantly becomes cheaper and more accessible, it is not infinite. Therefore efficient techniques able to exploit finite amount of predictive information content of the data and limit the computational requirements of the resource–hungry predictive system design procedure are very desirable. In designing such techniques this work once again investigated and exploited inspirations coming from physics. By using an analogy with a set of interacting particles and the resulting Information Theoretic Learning framework, the Density Preserving Sampling technique has been derived. This technique acts as a computationally efficient alternative for cross–validation, which fits well within the proposed methodology. All methods derived in this thesis have been thoroughly tested on a number of benchmark datasets. The proposed generalised predictive model design cycle has been successfully applied to two real–world environmental problems, in which a comparative study of Density Preserving Sampling and cross–validation has also been performed confirming great potential of the proposed methods