Chenguang Dai

Xin Xing, Yu Gui, Chenguang Dai et al.

Deep neural networks (DNNs) have become increasingly popular and achieved outstanding performance in predictive tasks. However, the DNN framework itself cannot inform the user which features are more or less relevant for making the prediction, which limits its applicability in many scientific fields. We introduce neural Gaussian mirrors (NGMs), in which mirrored features are created, via a structured perturbation based on a kernel-based conditional dependence measure, to help evaluate feature importance. We design two modifications of the DNN architecture for incorporating mirrored features and providing mirror statistics to measure feature importance. As shown in simulated and real data examples, the proposed method controls the feature selection error rate at a predefined level and maintains a high selection power even with the presence of highly correlated features.

Chenguang Dai, Jun S. Liu

We show that the Wang-Landau algorithm can be formulated as a stochastic gradient descent algorithm minimizing a smooth and convex objective function, of which the gradient is estimated using Markov chain Monte Carlo iterations. The optimization formulation provides us a new way to establish the convergence rate of the Wang-Landau algorithm, by exploiting the fact that almost surely, the density estimates (on the logarithmic scale) remain in a compact set, upon which the objective function is strongly convex. The optimization viewpoint motivates us to improve the efficiency of the Wang-Landau algorithm using popular tools including the momentum method and the adaptive learning rate method. We demonstrate the accelerated Wang-Landau algorithm on a two-dimensional Ising model and a two-dimensional ten-state Potts model.