Subhashis Ghosal

Rui Zhu, Shuvrarghya Ghosh, Subhashis Ghosal

Semi-supervised learning is a model training method that uses both labeled and unlabeled data. This paper proposes a fully Bayes semi-supervised learning algorithm that can be applied to any multi-category classification problem. We assume the labels are missing at random when using unlabeled data in a semi-supervised setting. Suppose we have $K$ classes in the data. We assume that the observations follow $K$ multivariate normal distributions depending on their true class labels after some common unknown transformation is applied to each component of the observation vector. The function is expanded in a B-splines series, and a prior is added to the coefficients. We consider a normal prior on the coefficients and constrain the values to meet the normality and identifiability constraints requirement. The precision matrices of the Gaussian distributions are given a conjugate Wishart prior, while the means are given the improper uniform prior. The resulting posterior is still conditionally conjugate, and the Gibbs sampler aided by a data-augmentation technique can thus be adopted. An extensive simulation study compares the proposed method with several other available methods. The proposed method is also applied to real datasets on diagnosing breast cancer and classification of signals. We conclude that the proposed method has a better prediction accuracy in various cases.

Xingqi Du, Subhashis Ghosal

We consider a graphical model where a multivariate normal vector is associated with each node of the underlying graph and estimate the graphical structure. We minimize a loss function obtained by regressing the vector at each node on those at the remaining ones under a group penalty. We show that the proposed estimator can be computed by a fast convex optimization algorithm. We show that as the sample size increases, the estimated regression coefficients and the correct graphical structure are correctly estimated with probability tending to one. By extensive simulations, we show the superiority of the proposed method over comparable procedures. We apply the technique on two real datasets. The first one is to identify gene and protein networks showing up in cancer cell lines, and the second one is to reveal the connections among different industries in the US.