Smooth mixtures, i.e. mixture models with covariate-dependent mixing weights, are very useful flexible models for conditional densities. Previous work shows that using too simple mixture components for modeling heteroscedastic and/or heavy tailed data can give a poor fit, even with a large number of components. This paper explores how well a smooth mixture of symmetric components can capture skewed data. Simulations and applications on real data show that including covariate-dependent skewness in the components can lead to substantially improved performance on skewed data, often using a much smaller number of components. Furthermore, variable selection is effective in removing unnecessary covariates in the skewness, which means that there is little loss in allowing for skewness in the components when the data are actually symmetric. We also introduce smooth mixtures of gamma and log-normal components to model positively-valued response variables.
Visual saliency plays an important role in various video applications such as video retargeting and intelligent video advertising. However, existing visual saliency estimation approaches often construct a unified model for all scenes, thus leading to poor performance for the scenes with diversified contents. To solve this problem, we propose a multi-task rank learning approach which can be used to infer multiple saliency models that apply to different scene clusters. In our approach, the problem of visual saliency estimation is formulated in a pair-wise rank learning framework, in which the visual features can be effectively integrated to distinguish salient targets from distractors. A multi-task learning algorithm is then presented to infer multiple visual saliency models simultaneously. By an appropriate sharing of information across models, the generalization ability of each model can be greatly improved. Extensive experiments on a public eye-fixation dataset show that our multi-task rank learning approach outperforms 12 state-of-the-art methods remarkably in visual saliency estimation.