An Extended Result on the Optimal Estimation under Minimum Error Entropy Criterion

The minimum error entropy (MEE) criterion has been successfully used in fields such as parameter estimation, system identification and the supervised machine learning. There is in general no explicit expression for the optimal MEE estimate unless some constraints on the conditional distribution are imposed. A recent paper has proved that if the conditional density is conditionally symmetric and unimodal (CSUM), then the optimal MEE estimate (with Shannon entropy) equals the conditional median. In this study, we extend this result to the generalized MEE estimation where the optimality criterion is the Renyi entropy or equivalently, the \alpha-order information potential (IP).Comment: 15 pages, no figures, submitted to Entrop

Information theoretic novelty detection

We present a novel approach to online change detection problems when the training sample size is small. The proposed approach is based on estimating the expected information content of a new data point and allows an accurate control of the false positive rate even for small data sets. In the case of the Gaussian distribution, our approach is analytically tractable and closely related to classical statistical tests. We then propose an approximation scheme to extend our approach to the case of the mixture of Gaussians. We evaluate extensively our approach on synthetic data and on three real benchmark data sets. The experimental validation shows that our method maintains a good overall accuracy, but significantly improves the control over the false positive rate

The Global Joint Distribution of Income and Health

We investigate the evolution of global welfare in two dimensions: income per capita and life expectancy. First, we estimate the marginal distributions of income and life expectancy separately. More importantly, in contrast to previous univariate approaches, we consider income and life expectancy jointly and estimate their bivariate global distribution for 137 countries during 1970 - 2000. We reach several conclusions: the global joint distribution has evolved from a bimodal into a unimodal one, the evolution of the health distribution has preceded that of income, global inequality and poverty has decreased over time and the evolution of the global distribution has been welfare improving. Our decomposition of overall welfare indicates that global inequality would be underestimated if within-country inequality is not taken into account. Moreover, global inequality and poverty would be substantially underestimated if the dependence between the income and health distributions is ignored.Income; Health; Global Distribution; Inequality; Poverty

The Global Joint Distribution of Income and Health

We investigate the evolution of global welfare in two dimensions: income per capita and life expectancy. First, we estimate the marginal distributions of income and life expectancy separately. More importantly, in contrast to previous univariate approaches, we consider income and life expectancy jointly and estimate their bivariate global distribution for 137 countries during 1970 - 2000. We reach several conclusions: the global joint distribution has evolved from a bimodal into a unimodal one, the evolution of the health distribution has preceded that of income, global inequality and poverty has decreased over time and the evolution of the global distribution has been welfare improving. Our decomposition of overall welfare indicates that global inequality would be underestimated if within-country inequality is not taken into account. Moreover, global inequality and poverty would be substantially underestimated if the dependence between the income and health distributions is ignored.income, health, global distribution, inequality, poverty