Algorithms for the Communication of Samples

We consider the problem of reverse channel coding, that is, how to simulate a noisy channel over a digital channel efficiently. We propose two new coding schemes with practical advantages over previous approaches. First, we introduce ordered random coding (ORC) which uses a simple trick to reduce the coding cost of previous approaches based on importance sampling. Our derivation also illuminates a connection between these schemes and the so-called Poisson functional representation. Second, we describe a hybrid coding scheme which uses dithered quantization to efficiently communicate samples from distributions with bounded support.

Graph Minors Meet Machine Learning: the Power of Obstructions

Computational intractability has for decades motivated the development of a plethora of methodologies that mainly aimed at a quality-time trade-off. The use of Machine Learning techniques has finally emerged as one of the possible tools to obtain approximate solutions to ${\cal NP}$-hard combinatorial optimization problems. In a recent article, Dai et al. introduced a method for computing such approximate solutions for instances of the Vertex Cover problem. In this paper we consider the effectiveness of selecting a proper training strategy by considering special problem instances called "obstructions" that we believe carry some intrinsic properties of the problem itself. Capitalizing on the recent work of Dai et al. on the Vertex Cover problem, and using the same case study as well as 19 other problem instances, we show the utility of using obstructions for training neural networks. Experiments show that training with obstructions results in a huge reduction in number of iterations needed for convergence, thus gaining a substantial reduction in the time needed for training the model.