Wire arc additive manufacturing (WAAM) is capable of rapidly depositing metal materials thus facilitating the fabrication of large-shape metal components. However, due to the multi-process-variability in the WAAM process, the deposited shape (bead width, height, depth of penetration) is difficult to predict and control within the desired level. Ultimately, the overall build will not achieve a near-net shape and will further hinder the part from performing its functionality without post-processing. Previous research primarily utilizes data analytical models (e.g., regression model, artificial neural network (ANN)) to forwardly predict the deposition width and height variation based on single or cross-linked process variables. However, these methods cannot effectively determine the optimal printable zone based on the desired deposition shape due to the inability to inversely deduce from these data analytical models. Additionally, the process variables are intercorrelated, and the bead width, height, and depth of penetration are highly codependent. Therefore, existing analysis cannot grant a reliable prediction model that allows the deposition (bead width, height, and penetration height) to remain within the desired level. This paper presents a novel machine learning framework for quantitatively analyzing the correlated relationship between the process parameters and deposition shape, thus providing an optimal process parameter selection to control the final deposition geometry. The proposed machine learning framework can systematically and quantitatively predict the deposition shape rather than just qualitatively as with other existing machine learning methods. The prediction model can also present the complex process-quality relations, and the determination of the deposition quality can guide the WAAM to be more prognostic and reliable. The correctness and effectiveness of the proposed quantitative process-quality analysis will be validated through experiments.