Analytic solution and stationary phase approximation for the Bayesian lasso and elastic net

摘要: The lasso and elastic net linear regression models impose a double-exponential prior distribution on the model parameters to achieve shrinkage variable selection, allowing inference of robust from large data sets. However, there has been limited success in deriving estimates for full posterior coefficients these models, due need evaluate analytically intractable partition function integrals. Here, Fourier transform is used express integrals as complex-valued oscillatory over "regression frequencies". This results an analytic expansion stationary phase approximation functions Bayesian net, where non-differentiability so far eluded such approach. Use this leads highly accurate numerical expectation values marginal distributions coefficients, allows much higher dimensional than previously possible.