Journal of Data Science

Inspired by the impressive successes of compress sensing-based machine learning algorithms, data augmentation-based efficient Gibbs samplers for Bayesian high-dimensional classification models are developed by compressing the design matrix to a much lower dimension. Ardent care is exercised in the choice of the projection mechanism, and an adaptive voting rule is employed to reduce sensitivity to the random projection matrix. Focusing on the high-dimensional Probit regression model, we note that the naive implementation of the data augmentation-based Gibbs sampler is not robust to the presence of co-linearity in the design matrix – a setup ubiquitous in $n\lt p$ problems. We demonstrate that a simple fix based on joint updates of parameters in the latent space circumnavigates this issue. With a computationally efficient MCMC scheme in place, we introduce an ensemble classifier by creating R ($\sim 25$–50) projected copies of the design matrix, and subsequently running R classification models with the R projected design matrix in parallel. We combine the output from the R replications via an adaptive voting scheme. Our scheme is inherently parallelizable and capable of taking advantage of modern computing environments often equipped with multiple cores. The empirical success of our methodology is illustrated in elaborate simulations and gene expression data applications. We also extend our methodology to a high-dimensional logistic regression model and carry out numerical studies to showcase its efficacy.

Abstract: Many nations’ defence departments use capabilitybased planning to guide their investment and divestment decisions. This planning process involves a variety of data that in its raw form is difficult for decisionmakers to use. In this paper we describe how dimensionality reduction and partition clustering are used in the Canadian Armed Forces to create visualizations that convey how important military capabilities are in planning scenarios and how much capacity the planned force structure has to provide the capabilities. Together, these visualizations give decisionmakers an overview of which capabilities may require investment or may be candidates for divestment.

Probabilistic topic models have become a standard in modern machine learning to deal with a wide range of applications. Representing data by dimensional reduction of mixture proportion extracted from topic models is not only richer in semantics interpretation, but could also be informative for classification tasks. In this paper, we describe the Topic Model Kernel (TMK), a topicbased kernel for Support Vector Machine classification on data being processed by probabilistic topic models. The applicability of our proposed kernel is demonstrated in several classification tasks with real world datasets. TMK outperforms existing kernels on the distributional features and give comparative results on nonprobabilistic data types.