One-Shot Neural Architecture Search (NAS) is a promising method to significantly reduce search time without any separate training. It can be treated as a Network Compression problem on the architecture parameters from an overparameterized network. However, there are two issues associated with most one-shot NAS methods. First, dependencies between a node and its predecessors and successors are often disregarded which result in improper treatment over zero operations. Second, architecture parameters pruning based on their magnitude is questionable. In this thesis, classic Bayesian learning approach is applied to alleviate these two issues. Unlike other NAS methods, we train the over-parameterized network for only one epoch before update network architecture. Impressively, this enabled us to find the optimal architecture in both proxy and proxyless tasks on CIFAR-10 within only 0.2 GPU days using a single GPU. As a byproduct, our approach can be transferred directly to convolutional neural networks compression by enforcing structural sparsity that is able to achieve extremely sparse networks without accuracy deterioration.