A simple linear averaging of the outputs of several networks as e.g. in bagging 3], seems to follow naturally from a bias/variance decomposition of the sum-squared error. The sum-squared error of the average model is a quadratic function of the weighting factors assigned to the networks in the ensemble 7], suggesting a quadratic programmingalgorithm for nding the \optimal"weighting factors. If ...

In this paper we present an algorithm of quasi-linear complexity for exactly calculating the infimal convolution of convex quadratic functions. The algorithm exactly and simultaneously solves a separable uniparametric family of quadratic programming problems resulting from varying the equality constraint.

In this paper, we consider minimizing the ratio of two indefinite quadratic functions subject to two quadratic constraints. Using the extension of Charnes– Cooper transformation, we transform the problem to a homogenized quadratic problem. Then, we show that, under certain assumptions, it can be solved to global optimality using semidefinite optimization relaxation.

If A is a finite set of cardinality n ≥ 1, 2 is the set of all subsets of A, and S is a nonempty subset of 2, we say that S has the odd-intersection property if there exists a subset N of A such that the cardinality of N ∩S is odd for each S ∈ S. Let OIP (n) denote the set of all subsets of 2 with the odd-intersection property. A nonempty set S of nonempty subsets of A is an obstruction (to the...

We consider the nonconvex problem minimizing the ratio of two quadratic functions over finitely many nonconvex quadratic inequalities. Relying on the homogenization technique we establish a sufficient condition that warrants the attainment of an optimal solution. Our result allows to extend and recover known conditions for some interesting special instances of the problem and to derive further ...

In this paper we answer certain questions posed by V.I. Arnold, namely, we study periods of continued fractions for solutions of quadratic equations in the form x + px = q with integer p and q, p + q ≤ R. Our results concern the average sum of period elements and Gauss–Kuzmin statistics as R → ∞.