José Brito

Abstract
Data-based approach for diagnosis of thyroid disorders is still at its early stage. Most of the research outcomes deal with binary classification of the disorders, i.e. presence or not of some pathology (cancer, hyperthyroidism, hypothyroidism, etc.). In this paper we explore deep learning (DL) models to improve the multi-class diagnosis of thyroid disorders, namely hypothyroid, hyperthyroid and no pathology thyroid. The proposed DL models, including DNN, CNN, LSTM, and a hybrid CNN-LSTM architecture, are inspired by state-of-the-art work and demonstrate superior performance, largely due to careful feature selection and the application of SMOTE for class balancing prior to model training. Our experiments show that the CNN-LSTM model achieved the highest overall accuracy of 99%, with precision, recall, and F1-scores all exceeding 92% across the three classes. The use of SMOTE for class balancing improved most of the model’s performance. These results indicate that the proposed DL models not only effectively distinguish between different thyroid conditions but also hold promise for practical implementation in clinical settings, potentially supporting healthcare professionals in more accurate and efficient diagnosis. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2025.

Abstract
In this paper we explain how to compute gradients of functions of the form G = 1/2 Sigma(m)(i=1) (Ey(i) - C-i )(2), which often appear in the calibration of stochastic models, using automatic adjoint differentiation and parallelization. We expand on the work of Goloubentsev and Lakshtanov and give approaches that are faster and easier to implement. We also provide an implementation of our methods and apply the technique to calibrate European options.