Newton

From Newton

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The Newton

Newton Trees

This paper presents Newton trees, a redefinition of probability estimation trees (PET) based on a stochastic understanding of decision trees that follows the principle of attraction (relating mass and distance through the Inverse Square Law). The structure, application and the graphical representation of Newton trees provide a way to make their stochastically driven predictions compatible with ...

Quasi-Newton Methods for Nonconvex Constrained Multiobjective Optimization

Here, a quasi-Newton algorithm for constrained multiobjective optimization is proposed. Under suitable assumptions, global convergence of the algorithm is established.

Graphical Newton

Computing the Newton step for a generic function f : R → R takes O(N) flops. In this paper, we explore avenues for reducing this bound, when the computational structure of f is known beforehand. It is shown that the Newton step can be computed in time, linear in the size of the computational-graph, and cubic in its tree-width.