Some common techniques, listed from less complex to more complex, are: linear regression, linear lasso regression, linear ridge regression, k-nearest neighbors regression, (plain) kernel regression, ...

Sokbae Lee, Myung Hwan Seo, Youngki Shin, The lasso for high dimensional regression with a possible change point, Journal of the Royal Statistical Society. Series B (Statistical Methodology), Vol. 78, ...

Leo Breiman, Better Subset Regression Using the Nonnegative Garrote, Technometrics, Vol. 37, No. 4 (Nov., 1995), pp. 373-384 ...