Abstract: Probabilistic graphical models play a crucial role in machine learning and have wide applications in various fields. One pivotal subset is undirected graphical models, also known as Markov random fields. In this work, we investigate the structure learning methods of Markov random fields on quantum computers. We propose a quantum algorithm for structure learning of an r-wise Markov Random Field with a bounded degree underlying graph, based on a nearly optimal classical greedy algorithm. The quantum algorithm provides a polynomial speed-up over the classical counterpart in terms of the number of variables.

UNet [27] is widely used in semantic segmentation due to its simplicity and effectiveness. However, its manually-designed architecture is applied to a large number of problem settings, either with no architecture optimizations, or with manual tuning, which is time consuming and can be sub-optimal. In this work, firstly, we propose Markov Random Field Neural Architecture Search (MRF-NAS) that extends and improves the recent Adaptive and Optimal Network Width Search (AOWS) method [4] with (i) a more general MRF framework (ii) diverse M-best loopy inference (iii) differentiable parameter learning. This provides the necessary NAS framework to efficiently explore network architectures that induce loopy inference graphs, including loops that arise from skip connections. With UNet as the backbone, we find an architecture, MRF-UNet, that shows several interesting characteristics. Secondly, through the lens of these characteristics, we identify the sub-optimality of the original UNet architecture and further improve our results with MRF-UNetV2. Experiments show that our MRF-UNets significantly outperform several benchmarks on three aerial image datasets and two medical image datasets while maintaining low computational costs.