January 26, 4:00pm - 5:00pm pm in Math Rm. 501
When
Where
Title: Estimation and Inference in Proportional High Dimensions
The first part will focus on ridge regression in linear models. We derive a distributional approximation for the ridge estimator via an associated Gaussian sequence model with “effective” noise and regularization parameters. This reduction provides a convenient way to analyze prediction and estimation risks and to support practical tuning rules, such as cross-validation and generalized cross-validation. It also yields a simple inference procedure based on a debiased ridge construction.
The second part will take an algorithmic perspective. Instead of analyzing only the final empirical risk minimizer, we view gradient descent iterates as estimators along an optimization path. We characterize the distribution of the iterates and use this characterization to construct data-driven estimates of generalization error and debiased iterates for statistical inference, including in settings beyond linear regression. I will conclude with simulations that illustrate the practical implications for tuning and inference.