Occupational outcomes like entrepreneurship are generally considered personal information that individuals should have the autonomy to disclose. With the advancing capability of artificial intelligence (AI) to infer private details from widely available human-centric data (e.g., social media), it is crucial to investigate whether AI can accurately extract private occupational information from such data. In this study, we demonstrate that deep neural networks can classify individuals as entrepreneurs with high accuracy based on facial images sourced from Crunchbase, a premier source for entrepreneurship data. Utilizing a dataset comprising facial images of 40,728 individuals, including both entrepreneurs and non-entrepreneurs, we train a Convolutional Neural Network (CNN) using a contrastive learning approach based on pairs of facial images (one entrepreneur and one non-entrepreneur per pair). While human experts (n=650) and trained participants (n=133) were unable to classify entrepreneurs with accuracy above chance levels (>50%), our AI model achieved a classification accuracy of 79.51%. Several robustness tests indicate that this high level of accuracy is maintained under various conditions. These results indicate privacy risks for entrepreneurs.