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High‐dimensional multinomial regression models are very useful in practice but have received less research attention than logistic regression models, especially from the perspective of statistical inference. In this work, we analyze the estimation and prediction error of the contrast‐based ‐penalized multinomial regression model and extend the debiasing method to the multinomial case, providing a valid confidence interval for each coefficient and value of the individual hypothesis test. We also examine cases of model misspecification and non‐identically distributed data to demonstrate the robustness of our method when some assumptions are violated. We apply the debiasing method to identify important predictors in the progression into dementia of different subtypes. Results from extensive simulations show the superiority of the debiasing method compared to other inference methods. 

The study of di-Higgs events, both resonant and non-resonant, plays a crucial role in understanding the fundamental interactions of the Higgs boson. In this work we consider di-Higgs events decaying into four b-quarks and propose to improve the experimental sensitivity by utilizing a novel machine learning algorithm known as Symmetry Preserving Attention Network (Spa-Net) — a neural network structure whose architecture is designed to incorporate the inherent symmetries in particle reconstruction tasks. We demonstrate that the Spa-Net can enhance the experimental reach over baseline methods such as the cut-based and the Dense Neural Network-based analyses. At the Large Hadron Collider, with a 14-TeV center-of-mass energy and an integrated luminosity of 300 fb−1, the Spa-Net allows us to establish 95% C.L. upper limits in resonant production cross-sections that are 10% to 45% stronger than baseline methods. For non-resonant di-Higgs production, Spa-Net enables us to constrain the self-coupling that is 9% more stringent than the baseline method.