05/10/2026
Tuesday, October 6, 3.15 pm, 2026. Seminar in Mathematical Statistics.
Recent Advances in High-Dimensional Data Modeling: From Variable Selection and Machine Learning to Post-Selection Shrinkage and Statistical Inference
Reza Arabi Belaghi, Department of Energy and Technology, Swedish University of Agricultural Sciences
Abstract: The rapid growth of high-dimensional data in genomics, biomedical research, environmental sciences, and other scientific disciplines has created statistical problems in which the number of potential predictors can be comparable to, or substantially larger than, the sample size. Although regularization methods such as LASSO and Elastic Net have transformed the analysis of such data, important challenges remain. In particular, variable selection can become unstable in the presence of highly correlated predictors, and procedures designed to produce sparse models may overlook predictors with weak but non-negligible signals. Consequently, selecting a sparse model is not necessarily the end of the statistical problem: how we estimate and make use of the information remaining after selection is equally important.
In this talk, I will discuss recent developments in high-dimensional statistical modeling from the complementary perspectives of variable selection, machine learning, and post-selection estimation. I will first examine the behaviour of classical penalized approaches such as LASSO and Elastic Net and contrast them with machine-learning-based screening methods such as Boruta. Particular attention will be given to the effects of dimensionality, predictor correlation, sample size, and signal strength on the ability of these methods to identify relevant variables.
I will then move from the question of which variables should be selected? to the equally important question of what should be done after selection? A central theme will be the distinction between strong, weak-to-moderate, and null signals. Rather than automatically discarding variables that fail to survive an initial sparse selection procedure, post-selection shrinkage methods can retain and appropriately down-weight information carried by weaker predictors. I will discuss recent extensions of this idea to high-dimensional generalized linear models and Cox proportional hazards models, including weighted-ridge and Stein-type shrinkage strategies designed to improve estimation and prediction in the presence of weak signals and multicollinearity.
Finally, I will discuss a broader "screen-then-shrink" perspective that combines machine-learning screening with statistical shrinkage. Using high-dimensional beta regression as an example, I will illustrate how Boruta-based screening can first reduce an ultra-high-dimensional feature space, after which ridge and Stein-type shrinkage can be used to stabilize estimation among correlated and potentially weak predictors. This provides a bridge between modern machine-learning feature discovery and classical statistical estimation and inference.
Throughout the talk, theoretical ideas will be connected with simulation studies and applications to biomedical and genomic data. The overall message is that high-dimensional modeling should not be viewed simply as a search for the smallest predictive model. Effective analysis requires careful consideration of correlation, weak signals, selection uncertainty, prediction, and post-selection estimation. I will conclude by discussing open methodological questions and potential directions for integrating machine-learning screening, regularization, shrinkage, and interpretable statistical inference in modern high-dimensional data analysis.
Location: BL34
The list of seminars in the series is available at http://www.ida.liu.se/divisions/stima/seminarier/StatSeminars.shtml .
Welcome! Krzysztof Bartoszek, Martin Singull
