L1-Regularized Functional Support Vector Machine

In functional data analysis, binary classification with one functional covariate has been extensively studied. We aim to fill in the gap of considering multivariate functional covariates in classification. In particular, we propose an $L_1$-regularized functional support vector machine for binary classification. An accompanying algorithm is developed to fit the classifier. By imposing an $L_1$ penalty, the algorithm enables us to identify relevant functional covariates of the binary response. Numerical results from simulations and one real-world application demonstrate that the proposed classifier enjoys good performance in both prediction and feature selection.

Restricted Tweedie Stochastic Block Models

The stochastic block model (SBM) is a widely used framework for community detection in networks, where the network structure is typically represented by an adjacency matrix. However, conventional SBMs are not directly applicable to an adjacency matrix that consists of non-negative zero-inflated continuous edge weights. To model the international trading network, where edge weights represent trading values between countries, we propose an innovative SBM based on a restricted Tweedie distribution. Additionally, we incorporate nodal information, such as the geographical distance between countries, and account for its dynamic effect on edge weights. Notably, we show that given a sufficiently large number of nodes, estimating this covariate effect becomes independent of community labels of each node when computing the maximum likelihood estimator of parameters in our model. This result enables the development of an efficient two-step algorithm that separates the estimation of covariate effects from other parameters. We demonstrate the effectiveness of our proposed method through extensive simulation studies and an application to real-world international trading data.