High-dimensional analysis of double descent for linear regression with random projections
This work offers theoretical insights into overparameterized models for researchers in machine learning and statistics, though it is incremental as it builds on existing ridge regression results.
The paper tackles the double descent phenomenon in linear regression with random projections, providing a high-dimensional analysis using random matrix theory to derive asymptotic expressions for generalization performance in terms of squared bias and variance.
We consider linear regression problems with a varying number of random projections, where we provably exhibit a double descent curve for a fixed prediction problem, with a high-dimensional analysis based on random matrix theory. We first consider the ridge regression estimator and review earlier results using classical notions from non-parametric statistics, namely degrees of freedom, also known as effective dimensionality. We then compute asymptotic equivalents of the generalization performance (in terms of squared bias and variance) of the minimum norm least-squares fit with random projections, providing simple expressions for the double descent phenomenon.