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.
Discovery Building, Orchard View Room
Bryan Daniels, Hyemin Jeon