The True Destination of EGO is Multi-local Optimization

Efficient global optimization is a popular algorithm for the optimization of expensive multimodal black-box functions. One important reason for its popularity is its theoretical foundation of global convergence. However, as the budgets in expensive optimization are very small, the asymptotic properties only play a minor role and the algorithm sometimes comes off badly in experimental comparisons. Many alternative variants have therefore been proposed over the years. In this work, we show experimentally that the algorithm instead has its strength in a setting where multiple optima are to be identified

Variable selection for model-based clustering using the integrated complete-data likelihood

Variable selection in cluster analysis is important yet challenging. It can be achieved by regularization methods, which realize a trade-off between the clustering accuracy and the number of selected variables by using a lasso-type penalty. However, the calibration of the penalty term can suffer from criticisms. Model selection methods are an efficient alternative, yet they require a difficult optimization of an information criterion which involves combinatorial problems. First, most of these optimization algorithms are based on a suboptimal procedure (e.g. stepwise method). Second, the algorithms are often greedy because they need multiple calls of EM algorithms. Here we propose to use a new information criterion based on the integrated complete-data likelihood. It does not require any estimate and its maximization is simple and computationally efficient. The original contribution of our approach is to perform the model selection without requiring any parameter estimation. Then, parameter inference is needed only for the unique selected model. This approach is used for the variable selection of a Gaussian mixture model with conditional independence assumption. The numerical experiments on simulated and benchmark datasets show that the proposed method often outperforms two classical approaches for variable selection.Comment: submitted to Statistics and Computin

Iterative Residual Rescaling: An Analysis and Generalization of LSI

We consider the problem of creating document representations in which inter-document similarity measurements correspond to semantic similarity. We first present a novel subspace-based framework for formalizing this task. Using this framework, we derive a new analysis of Latent Semantic Indexing (LSI), showing a precise relationship between its performance and the uniformity of the underlying distribution of documents over topics. This analysis helps explain the improvements gained by Ando's (2000) Iterative Residual Rescaling (IRR) algorithm: IRR can compensate for distributional non-uniformity. A further benefit of our framework is that it provides a well-motivated, effective method for automatically determining the rescaling factor IRR depends on, leading to further improvements. A series of experiments over various settings and with several evaluation metrics validates our claims.Comment: To appear in the proceedings of SIGIR 2001. 11 page