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We consider linear regression problems with a varying number of randomprojections, where we provably exhibit a double descent curve for a fixedprediction problem, with a high-dimensional analysis based on random matrixtheory. We first consider the ridge regression estimator and review earlierresults using classical notions from non-parametric statistics, namely degreesof freedom, also known as effective dimensionality. We then compute asymptoticequivalents of the generalization performance (in terms of squared bias andvariance) of the minimum norm least-squares fit with random projections,providing simple expressions for the double descent phenomenon.

High-dimensional analysis of double descent for linear regression with random projections