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Digitalization across all spheres of life has given rise to issues like data ownership and privacy. Privacy-Preserving Machine Learning (PPML), an active area of research, aims to preserve privacy for machine learning (ML) stakeholders like data owners, ML model owners, and inference users. The Paper, CoTraIn-VPD, proposes private ML inference and training of models for vertically partitioned datasets with Secure Multi-Party Computation (SPMC) and Differential Privacy (DP) techniques. The proposed approach addresses complications linked with the privacy of various ML stakeholders dealing with vertically portioned datasets. This technique is implemented in Python using open-source libraries such as SyMPC (SMPC functions), PyDP (DP aggregations), and CrypTen (secure and private training). The paper uses information privacy measures, including mutual information and KL-Divergence, across different privacy budgets to empirically demonstrate privacy preservation with high ML accuracy and minimal performance cost.