Detecting malign cases from thyroid nodule examinations is crucial in healthcare particularly to improve the early detection of such cases. However, malign thyroid nodules can be extremely rare and is hard to find using the traditional rule based or expert-based methods. For this reason, the solutions backed by Machine Learning (ML) algorithms are key to improve the detection rates of such rare cases. In this paper, we investigate the application of ML in the healthcare domain for the detection of rare thyroid nodules. The utilized dataset is collected from 636 distinct patients in 99 unique days in Turkey. In addition to the texture feature data of the Ultrasound (US), we have also included the scores of different assessment methods created by different health institutions (e.g., Korean, American and European thyroid societies) as additional features. For detection of extremely rare malign cases, we use auto-encoder based neural network model. Through numerical results, it is shown that the auto-encoder based model can result in an average Recall score of 0.98 and a Sensitivity score of 1.00 for detecting malign and non-malign cases from the healthcare dataset outperforming the traditional classification algorithms that are trained after Synthetic Minority Oversampling Technique (SMOTE) oversampling.