The paper presents a self-adaptive feature selection algorithm we developed for solving high-dimensional uncertainty quantification problems. The development of the algorithm was motivated and supported by the benchmarking of the Transient Reactor Test (TREAT) transient test 2857. The generalized polynomial chaos expansion scheme was adopted to decompose the response functions. Our algorithm was applied to select the dominant basis from the candidate polynomial basis in a self-adaptive manner by assigning weights to the polynomial basis and adjusting the weights using the least absolute shrinkage and selection operator regularization–estimated coefficients through iterations. The developed algorithm can recognize the significant basis terms in the polynomial expansion of the response functions and therefore build a sparse polynomial expansion using a limited number of samples. The algorithm was implemented and verified through three different TREAT modeling cases. The testing results demonstrated the general stability and prediction performance of our algorithm and provided useful information about the uncertainty mechanism of the TREAT transient test 2857.