Uncertainty Quantification in High-Dimensional Structured Regression Problems

Publications produced as a result of this research

Adaptive confidence sets in shape restricted regression. Pierre C. Bellec. Bernoulli, 27 (1) 66 - 92, February 2021.

The cost-free nature of optimally tuning Tikhonov regularizers and other ordered smoothers. Pierre C Bellec and Dana Yang. Proceedings of the 37th International Conference on Machine Learning (ICML), pages 1621–1630, 2020.

First order expansion of convex regularized estimators. Pierre Bellec and Arun Kuchibhotla. In Advances in Neural Information Processing Systems (NeurIPS), pages 3457–3468, 2019.

Derivatives and residual distribution of regularized M-estimators with application to adaptive tuning. Pierre C Bellec and Yiwei Shen. Proceedings of Thirty Fifth Conference on Learning Theory (COLT), PMLR 178:1912-1947, 2022.

Second order Stein: SURE for SURE and other applications in high-dimensional inference. Pierre C Bellec and Cun-Hui Zhang. Ann. Statist., 49 (4) 1864 - 1903, August 2021.

Software and other code produced as a result of this research

The supplementary material at https://proceedings.mlr.press/v178/bellec22a.html provides the python code to reproduce figures and experiments of the paper "Derivatives and residual distribution of regularized M-estimators with application to adaptive tuning".

The supplementary material at https://proceedings.neurips.cc//paper/2020/hash/d87ca511e2a8593c8039ef732f5bffed-Abstract.html provides the python code to reproduce figures and experiments of the paper "Asymptotic normality and confidence intervals for derivatives of 2-layers neural network in the random features model", Advances in Neural Information Processing Systems 33 (NeurIPS 2020) "