Semiparametric penalty function method in partially linear model selection

Model selection in nonparametric and semiparametric regression is of both theoretical and practical interest. Gao and Tong (2004) proposed a semiparametric leave–more–out cross–validation selection procedure for the choice of both the parametric and nonparametric regressors in a nonlinear time series regression model. As recognized by the authors, the implementation of the proposed procedure requires the availability of relatively large sample sizes. In order to address the model selection problem with small or medium sample sizes, we propose a model selection procedure for practical use. By extending the so–called penalty function method proposed in Zheng and Loh (1995, 1997) through the incorporation of features of the leave-one-out cross-validation approach, we develop a semiparametric, consistent selection procedure suitable for the choice of optimum subsets in a partially linear model. The newly proposed method is implemented using the full set of data, and simulations show that it works well for both small and medium sample sizes.Linear model; model selection; nonparametric method; partially linear model; semiparametric method

Machine Learning-Driven Surrogate Models for Electrolytes

We have developed a lattice Monte Carlo (MC) simulation based on the diffusion-limited aggregation model that accounts for the effect of the physical properties of ionic liquids (ILs) on lithium dendrite growth. Our simulations show that the size asymmetry between the cation and anion, the dielectric constant, and the volume fraction of ILs are critical factors to significantly suppress the dendrite growth, primarily due to substantial changes in electric-field screening. Specifically, the volume fraction of ILs has the optimal value for dendrite suppression. The present simulation method indicates potential challenges for the model extension to macroscopic systems. Therefore, we also develop ensemble neural networks (ENNs) in machine learning methods with training datasets derived from the MC simulations by considering the input descriptors with the dielectric constant, the model parameter for the fractal dimension of the dendrite, the volume fraction of ILs, and the applied voltage. Our ENNs can predict the highly nonmonotonic trend of the simulation results from only one-tenth of simulation runs, thus significantly reducing the required computation time. To further examine the efficacy of our new ENN methods in practical applications, we apply ENNs to the study of the dielectric constants of salt-free and salt-doped solvents. Seven common solvents and NaCl solutions with various salt concentrations are considered examples. Despite the significant 50-time reduction in the number of training data, the predictions of the ENNs with batch normalization or bootstrap aggregating are largely consistent with the ground truths, tracing the optimal values out of statistically noisy data. Furthermore, we investigate the phase behaviors of cellulose and ILs mixtures by combining ENNs with unsupervised learning. As a result, K-means clustering and hierarchical clustering can automatically classify solubility phases and determine the boundaries of phases. Our work proves that machine learning could be a promising tool for studying soft matter systems