Steven Kay

Bo Tang, Jun Yan, Steven Kay et al.

In this paper, we consider the problems of state estimation and false data injection detection in smart grid when the measurements are corrupted by colored Gaussian noise. By modeling the noise with the autoregressive process, we estimate the state of the power transmission networks and develop a generalized likelihood ratio test (GLRT) detector for the detection of false data injection attacks. We show that the conventional approach with the assumption of Gaussian noise is a special case of the proposed method, and thus the new approach has more applicability. {The proposed detector is also tested on an independent component analysis (ICA) based unobservable false data attack scheme that utilizes similar assumptions of sample observation.} We evaluate the performance of the proposed state estimator and attack detector on the IEEE 30-bus power system with comparison to conventional Gaussian noise based detector. The superior performance of {both observable and unobservable false data attacks} demonstrates the effectiveness of the proposed approach and indicates a wide application on the power signal processing.

Zhenghan Zhu, Steven Kay

In this paper, we derive a Bayesian model order selection rule by using the exponentially embedded family method, termed Bayesian EEF. Unlike many other Bayesian model selection methods, the Bayesian EEF can use vague proper priors and improper noninformative priors to be objective in the elicitation of parameter priors. Moreover, the penalty term of the rule is shown to be the sum of half of the parameter dimension and the estimated mutual information between parameter and observed data. This helps to reveal the EEF mechanism in selecting model orders and may provide new insights into the open problems of choosing an optimal penalty term for model order selection and choosing a good prior from information theoretic viewpoints. The important example of linear model order selection is given to illustrate the algorithms and arguments. Lastly, the Bayesian EEF that uses Jeffreys prior coincides with the EEF rule derived by frequentist strategies. This shows another interesting relationship between the frequentist and Bayesian philosophies for model selection.

Bo Tang, Steven Kay, Haibo He et al.

In this letter, we present a novel exponentially embedded families (EEF) based classification method, in which the probability density function (PDF) on raw data is estimated from the PDF on features. With the PDF construction, we show that class-specific features can be used in the proposed classification method, instead of a common feature subset for all classes as used in conventional approaches. We apply the proposed EEF classifier for text categorization as a case study and derive an optimal Bayesian classification rule with class-specific feature selection based on the Information Gain (IG) score. The promising performance on real-life data sets demonstrates the effectiveness of the proposed approach and indicates its wide potential applications.

Bo Tang, Steven Kay, Haibo He

Automated feature selection is important for text categorization to reduce the feature size and to speed up the learning process of classifiers. In this paper, we present a novel and efficient feature selection framework based on the Information Theory, which aims to rank the features with their discriminative capacity for classification. We first revisit two information measures: Kullback-Leibler divergence and Jeffreys divergence for binary hypothesis testing, and analyze their asymptotic properties relating to type I and type II errors of a Bayesian classifier. We then introduce a new divergence measure, called Jeffreys-Multi-Hypothesis (JMH) divergence, to measure multi-distribution divergence for multi-class classification. Based on the JMH-divergence, we develop two efficient feature selection methods, termed maximum discrimination ($MD$) and $MD-χ^2$ methods, for text categorization. The promising results of extensive experiments demonstrate the effectiveness of the proposed approaches.