Model Invariants and Functional Regularization

Explore the concept of model invariants and functional regularization in this 50-minute virtual talk presented by the SIAM Activity Group on Financial Mathematics and Engineering. Delve into the importance of creating models that extract facts about data itself rather than arbitrary factors. Examine different modeling approaches like regression, MLE, and Bayesian estimation, comparing their invariance properties to those of regularized regressions. Discover a proposed alternative called functional regularization, which aims to correct limitations in traditional regularization methods. Learn how this framework can make models invariant to linear transformations while offering greater flexibility and ease of understanding. Gain insights into applications in quantitative finance and machine learning, exploring topics such as ridge regression, lasso, forests, and gradient boosting with functional regularization.

Intro
Important legal Information
Introduction
Quantitative finance
Observations
Machine learning
Critical difference
Intrinsic
Theorems
Ridge regression
Maximum likelihood estimation
Bayesian estimation
Model invariance summary
Partial solution
New solution
Function norms
Ridge with linear invariance
Lasso with linear invariance
Forests
Gradient boost with functional regularization
Gradient boost with pixie dust
Conclusions
Questions