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levocardia ◴[] No.41890447[source]
Good to see more research exploring the connection between trees, ensembles, and smoothing. Way back in Trevor Hastie's ESL book there's a section on how gradient boosting using "stumps" (trees with only one split) is equivalent to an additive spline model (GAM, technically) with a step function as a spline basis and adaptive knot placement.

I've always thought there should be a deep connection between ReLU neural nets and regularized adaptive smoothers as well, since the ReLU function is itself a spline basis (a so-called truncated linear spline) and happens to span the same functional basis as B-splines of the same degree.

replies(2): >>41892797 #>>41893418 #
1. almostgotcaught ◴[] No.41892797[source]
One of my biggest pet peeves is flagrant overuse of "deep". Everything is so deep around around here these days...

> since the ReLU function is itself a spline basis (a so-called truncated linear spline) and happens to span the same functional basis as B-splines of the same degree.

... you literally just spelled out the entire "depth" of it.