MATERIALS FOR : CONSISTENCY OF RANDOM FORESTS By Erwan Scornet
نویسندگان
چکیده
Technical Lemma 1. Assume that (H1) is satisfied and that L ≡ 0 for all cuts in some given cell A. Then the regression function m is constant on A. Proof of Technical Lemma 1. We start by proving the result in dimension p = 1. Letting A = [a, b] (0 ≤ a < b ≤ 1), and recalling that = − 1 (b − a) 2 b a m(t)dt 2 + 1 (b − a)(z − a) z a m(t)dt 2 + 1 (b − a)(b − z) b z m(t)dt 2. Let C = b a m(t)dt and M (z) = z a m(t)dt. Simple calculations show that L (1, z) = 1 (z − a)(b − z) M (z) − C z − a b − a 2 .
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