This paper aims to present a novel pipeline for automated surgical skill assessment using video data and to showcase the effectiveness of the proposed approach in evaluating surgeon proficiency, its potential for targeted training interventions, and quality assurance in surgical departments. The pipeline incorporates a representation flow convolutional neural network and a novel tree-based Gaussian process classifier, which is robust to noise, while being computationally efficient. Additionally, new kernels are introduced to enhance accuracy. The performance of the pipeline is evaluated using the JIGSAWS dataset. Comparative analysis with existing literature reveals significant improvement in accuracy and betterment in computation cost. The proposed pipeline contributes to computational efficiency and accuracy improvement in surgical skill assessment using video data. Results of our study based on comments of our colleague surgeons show that the proposed method has the potential to facilitate skill improvement among surgery fellows and enhance patient safety through targeted training interventions and quality assurance in surgical departments.