In machine learning, model selection is the process of choosing the best model for a given dataset. This can be a challenging task, especially when dealing with large datasets or complex models. A recent approach to model selection is penalized logistic regression, which uses penalties to shrink the parameters towards zero. However, this method assumes that the penalty term decays rapidly as the parameter increases, leading to inconsistent results in high-dimensional models.
Motivation
The authors aim to develop a non-asymptotic approach to model selection via penalization in high-dimensional mixture of experts models. They propose an efficient linear programming method for optimal penalization in this context, which is computationally effective and can handle large datasets.
Methodology
The proposed method uses a majorization-minimization (MM) algorithm to construct the reduction estimator. This algorithm is computationally effective and can handle large datasets. The authors study the statistical and numerical properties of the proposed reduction estimator on experiments that demonstrate its performance compared to the global estimator constructed in a centralized way from the full dataset.
Results
The authors demonstrate the effectiveness of their approach through extensive experiments conducted on both simulated and real-world datasets. They show that their method is computationally faster than the existing methods while maintaining comparable performance. Additionally, they provide publicly available codes on Github for reproducing their results.
Conclusion
In conclusion, the authors propose a non-asymptotic approach to model selection via penalization in high-dimensional mixture of experts models. Their method is computationally effective and can handle large datasets, making it a promising solution for practical applications. The authors provide extensive experiments to demonstrate the effectiveness of their approach and make their codes publicly available for reproducing their results. This article provides a valuable contribution to the field of machine learning and model selection, and its findings have important implications for real-world applications.
