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Using sparse coding to find independent components of conflict | Convex Quadratic Programming with Variable Bounds

Bryan Daniels | Hyemin Jeon , Post-doc in WID and graduate student in IE respectively

Date and Time: Feb 15, 2012 (12:30 PM)
Location: Orchard room (3280) at the Wisconsin Institute for Discovery Building


Both cognitive constraints and limited amounts of data restrict the
complexity of inferential models. Sparse coding is an elegant way to
address these restrictions, extracting correlated subparts from data
in a way that can be efficient, predictive, and adaptive. We present
a sparse coding method for use on binary data and use it to
study correlated groups in conflict in a macaque society. The
method reveals specific groups as predictable components of
conflict in our data, and a description of collective behavior in
terms of sparse groups can be shown to be cognitively efficient.

A mixed binary set constrained by convex, nonseparable quadratic functions appears as a substructure in many practical mixed integer nonlinear programs (MINLPs) including portfolio management or model selection. We aim to obtain a good approximation of its convex hull, and our approach starts by transforming the set using Cholesky factorization. A number of valid nonlinear inequalities for the transformed set are derived, most of which are represented as second-order cone constraints. Computational experiments were conducted to compare the relaxations to the convex hull.