Research And Application Of Needle

Spike and Slab prior is used to encourage the sparsity of continuous random variables. Compared with the popular l1norm regularization method which gets sparse solution by minimizing a cost function with non-differentiable point at zero, Spike and Slab prior makes use of a special Two-Components Mixture of Gaussians and models the zero/non-zero property of the continuous variables directly. What is more, Spike and Slab prior can also be used to model the complex relationship between some variables’zero/non-zero property and other random variables. In this article we will study the Spike and Slab prior and explore its applications:First, we use Spike and Slab prior to encourage the sparsity of inverse co-variance matrix. Compared with the popular l1norm regularization method, the inverse covariance matrix obtained by our new model is sparser and of higher predictive quality. By taking the Bayesian treatment to the parameters of Spike and Slab prior, the difficulty for model selection is significantly reduced.Second, we use Spike and Slab Prior to select the dynamic users, i.e., the users requiring more variables to model their interests drift, in Collaborative Filtering system. The proposed dynamic/static mixture model is capable of providing the dynamic/static judgment along with its uncertainty. On Netflix dataset, the pro-posed method gets promising results for rating prediction.Third, we use Spike and Slab prior for subspace clustering. In the proposed hierarchical model, Spike and Slab prior is used as a bridge connecting sample labels and reconstruction matrix, to make the reconstruction weight to be small if two samples are from different subspaces. Such constraints reduce the dependency of the model on subspace independent assumption. On both synthetic and real dataset, the proposed model shows promising results.