On the Statistical Efficiency of Compositional Nonparametric Prediction

Each component of u is a production of finite basis functions from Φ. Thus ||u||∞ ≤ 1. Then we show ||v||1 ≤ ||w||1 if ||w||1 ≤ 1 by induction: k = 0, ||v||1 = ||w||1; Assume that for any k < K and any weighted labeled binary tree h ∈ W2k+1, ||vh||1 ≤ ||wh||1. For k = K, decompose the tree h(x; f,w) ∈ W2K+1 by the left subtree hl(x; fl,wl) = 〈vl,ul〉 and the… CONTINUE READING