  In high-dimensional generalized linear models, it is crucial to identify a
sparse model that adequately accounts for response variation. Although the best
subset section has been widely regarded as the Holy Grail of problems of this
type, achieving either computational efficiency or statistical guarantees is
challenging. In this article, we intend to surmount this obstacle by utilizing
a fast algorithm to select the best subset with high certainty. We proposed and
illustrated an algorithm for best subset recovery in regularity conditions.
Under mild conditions, the computational complexity of our algorithm scales
polynomially with sample size and dimension. In addition to demonstrating the
statistical properties of our method, extensive numerical experiments reveal
that it outperforms existing methods for variable selection and coefficient
estimation. The runtime analysis shows that our implementation achieves
approximately a fourfold speedup compared to popular variable selection
toolkits like glmnet and ncvreg.
