47,429 research outputs found
Identifying Risk Factors for Severe Childhood Malnutrition by Boosting Additive Quantile Regression
Ordinary linear and generalized linear regression models relate the mean of a response variable to a linear combination of covariate effects and, as a consequence, focus on average properties of the response. Analyzing childhood malnutrition in developing or transition countries based on such a regression model implies that the estimated effects describe the average nutritional status. However, it is of even larger interest to analyze quantiles of the response distribution such as the 5% or 10% quantile that relate to the risk of children for extreme malnutrition. In this paper, we analyze data on childhood malnutrition collected in the 2005/2006 India Demographic and Health Survey based on a semiparametric extension of quantile
regression models where nonlinear effects are included in the model equation, leading to additive quantile regression. The variable selection and model choice problems associated with estimating an additive quantile regression model are addressed by a novel boosting approach. Based on this rather general class of statistical learning procedures for empirical risk minimization, we develop, evaluate and apply a boosting algorithm for quantile regression. Our proposal allows for data-driven determination of the amount of smoothness required for the nonlinear effects and combines model selection with an automatic variable selection property. The results of our empirical evaluation suggest that boosting is an appropriate tool for estimation in linear and additive quantile regression models and helps to identify yet unknown risk factors for childhood malnutrition
Escaping Local Optima in a Class of Multi-Agent Distributed Optimization Problems: A Boosting Function Approach
We address the problem of multiple local optima commonly arising in
optimization problems for multi-agent systems, where objective functions are
nonlinear and nonconvex. For the class of coverage control problems, we propose
a systematic approach for escaping a local optimum, rather than randomly
perturbing controllable variables away from it. We show that the objective
function for these problems can be decomposed to facilitate the evaluation of
the local partial derivative of each node in the system and to provide insights
into its structure. This structure is exploited by defining "boosting
functions" applied to the aforementioned local partial derivative at an
equilibrium point where its value is zero so as to transform it in a way that
induces nodes to explore poorly covered areas of the mission space until a new
equilibrium point is reached. The proposed boosting process ensures that, at
its conclusion, the objective function is no worse than its pre-boosting value.
However, the global optima cannot be guaranteed. We define three families of
boosting functions with different properties and provide simulation results
illustrating how this approach improves the solutions obtained for this class
of distributed optimization problems
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