Learning freely-described convex sets from data

This is the MATLAB implementation of the algorithm from the paper Free Descriptions of Convex Sets for learning convex sets instantiable in any dimension from data.

Prerequisites

Please install these packages and add them to MATLAB's path.

1. YALMIP with an SDP solver like MOSEK
2. Package to find null space of a sparse matrix

Main functions

1. Script to learn an SDP approximation of $\ell_p$ norms: LpNorm_learn.
2. Script to learn an SDP approximation of (variant of) quantum entropy: quantEntropy_learn.
3. Script to verify the graphon generation degree in Prop. 3.1: check_graphon_gen_deg
4. Scripts to compute dimensions for spaces of invariants / morphisms for the examples in Sec. 4.1: compute_dims_a, compute_dims_b, and compute_dims_c.

In case of issues or questions, please email Eitan (eitanl@caltech.edu)