We present an algorithm for the statistical learning setting with a bounded exp-concave loss in d dimensions that obtains excess risk O(d/n) with high probability: the dependence on the confidence parameter δ is polylogarithmic in 1/δ. The core technique is to boost the confidence of recent O(d/n) bounds, without sacrificing the rate, by leveraging a Bernstein-type condition which holds due to ...

Hybrid poplars have demonstrated high productivity as short rotation woody crops (SRWCs) in the U.S. Midwest, and the hybrid aspen ‘Crandon’ (Populus alba L. × P. grandidenta Michx.) has exhibited particularly promising yields across topographic positions (including sloping marginal lands) in Iowa. However, a key obstacle for landowner acceptance of SRWCs is the lack of economic returns early i...

We study the robust proper learning of univariate log-concave distributions (over continuous and discrete domains). Given a set of samples drawn from an unknown target distribution, we want to compute a log-concave hypothesis distribution that is as close as possible to the target, in total variation distance. In this work, we give the first computationally efficient algorithm for this learning...

Let R = (r1, . . . , rm) and C = (c1, . . . , cn) be positive integer vectors such that r1 + . . .+ rm = c1 + . . .+ cn. We consider the set Σ(R, C) of non-negative m × n integer matrices (contingency tables) with row sums R and column sums C as a finite probability space with the uniform measure. We prove that a random table D ∈ Σ(R, C) is close with high probability to a particular matrix (“t...

Perception-based function (PBF) is a fuzzy function obtained as a result of reconstruction of human judgments given by a sequence of rules Rk: If T is Tk then S is Sk, where Tk are perception-based intervals defined on the domain of independent variable T, and Sk are perception-based shape patterns of variable S on interval Tk. Intervals Tk can be expressed by words like Between N and M, Approx...