SparseDeepLearning: ANewFrameworkImmune toLocalTrapsandMiscalibration

Dn) 1 as n, which means the most posterior mass falls in the neighbourhood of true parameter. Remarkonthenotation: ν() is similar toν() defined in Section 2.1 of the main text. Thenotationsweusedinthis proof are the same as in the proof of Theorem 2.1. Theorem 2.2 implies that a faithful prediction interval can be constructed for the sparse neural network learned by the proposed algorithms. In practice, for a normal regression problem with noise N(0,σ2), to construct the prediction interval for a test pointx0, the terms σ2 and Σ = γ µ(β,x0)TH 1 γ µ(β,x0) in Theorem 2.2 need to be estimated from data.