Towards Machine Wald

The past century has seen a steady increase in the need of estimating and predicting complex systems and making (possibly critical) decisions with limited information. Although computers have made possible the numerical evaluation of sophisticated statistical models, these models are still designed \emph{by humans} because there is currently no known recipe or algorithm for dividing the design of a statistical model into a sequence of arithmetic operations. Indeed enabling computers to \emph{think} as \emph{humans} have the ability to do when faced with uncertainty is challenging in several major ways: (1) Finding optimal statistical models remains to be formulated as a well posed problem when information on the system of interest is incomplete and comes in the form of a complex combination of sample data, partial knowledge of constitutive relations and a limited description of the distribution of input random variables. (2) The space of admissible scenarios along with the space of relevant information, assumptions, and/or beliefs, tend to be infinite dimensional, whereas calculus on a computer is necessarily discrete and finite. With this purpose, this paper explores the foundations of a rigorous framework for the scientific computation of optimal statistical estimators/models and reviews their connections with Decision Theory, Machine Learning, Bayesian Inference, Stochastic Optimization, Robust Optimization, Optimal Uncertainty Quantification and Information Based Complexity.Comment: 37 page

RESULTS OF SHOULDER STABILIZATION BY A MODIFIED BRISTOW - LATARJET PROCEDURE WITH ARTHROSCOPY

The authors describe the minimally invasive technique for Bristow-Latarjet bone unfree autoplasty with arthroscopy in patients with bone loss more than 25% of anterior-posterior diameter of the glenoid, the poor quality of the capsule or deep defects of Hill-Sachs. The analysis of the early results of treatment in 19 patients and midterm results - in 13 soldiers operated in 2011-2014. Features of the proposed technique are the shortening of surgical approach and the reduction of subscapularis muscle damage. In addition, arthroscopic support allows to attain the precision location of the graft relative to the articular surface of scapula, at the same time restoring the damaged anatomy SLAP, rotator cuff tendons and posterior labrum and restore shoulder ligaments tension and isolate bone graft from the joint cavity, contributing to a better articulation of the humeral head and reducing the risk of nonunion and resorption

Global Optimization of Mixed-Integer Quadratically Constrained Quadratic Programs (MIQCQP) through Piecewise-Linear and Edge-Concave Relaxations

We propose a deterministic global optimization approach, whose novel contributions are rooted in the edge-concave and piecewise-linear underestimators, to address nonconvex mixed-integer quadratically-constrained quadratic programs (MIQCQP) to ε-global optimality. The facets of low-dimensional (n ≤ 3) edge-concave aggregations dominating the termwise relaxation of MIQCQP are introduced at every node of a branch-and-bound tree. Concave multivariable terms and sparsely distributed bilinear terms that do not participate in connected edge-concave aggregations are addressed through piecewise-linear relaxations. Extensive computational studies are presented for point packing problems, standard and generalized pooling problems, and examples from GLOBALLib (Meeraus, Globallib. http://www.gamsworld.org/global/globallib. htm). © 2012 Springer and Mathematical Optimization Society