## 4 Conclusions and Discussion  
An interpretable integrated diagnostic approach has been developed and demonstrated to be effective and accurate even with limited datasets. A number of transfer learning models are also investigated and compared. This study demonstrates the feasibility of developing a computer-aided diagnostic system that can assist doctors in reliably and quickly distinguishing thermograms with or without tumors. However, the model's performance is complicated by the sparse data. More breast thermal images from patients with cancerous cells and individuals without cancerous cells will help the model become more reliable and accurate. Overall, the usage of the transfer learning approach yields better results compared to the baseline approach. One of the best results, by most of the metrics results, is obtained by MobileNet, at 93.8% accuracy amongst the four transfer learning models. The application of transformer models for this study also shows competitive results even compared with the state-of-the-art transfer learning models. These approaches demonstrated high performance compared to the previously published works, such as in [11; 12].  
Finally, this work reports the successful construction of expert models with the help of BNs and a combination of BNs and CNNs. Two BN-based expert systems have been designed, one using image features and medical data and the second using the previous data plus a CNN prediction. The analysis showed that all these expert models have similarly high accuracy, with BN + CNN models at 90.85% and ResNet50 achieving 93.8%. Thus, it can be claimed and concluded that the crucial factors which drive the decision in the BN models comprise a trusted interpretable diagnosis model which is useful both for a patient and a physician. The developed integrated system can be easily implemented on low-cost portable devices for automatic mass screening and breast self-examination (BSE) as envisaged by the WHO to eradicate breast cancer.  
Conceptualization, N.A. and E.Y.K.N.; Methodology, Y.Z., V.Z. and E.Y.K.N.; Software, N.A. and V.Z.; Validation, Y.Z.; Formal analysis, N.A. and V.Z.; Resources, A.M. ([PERSON]), A.M. ([PERSON]) and O.M.; Data curation, A.M. ([PERSON]); Writing--original draft, N.A. and A.M. ([PERSON]); Writing--review & editing, Y.Z., E.Y.K.N. and V.Z.; Visualization, V.Z. and O.M.; Supervision, Y.Z.; Project administration, A.M. ([PERSON]), Y.Z. and O.M.; Funding acquisition, A.M. ([PERSON]); V.Z. for the Bayesian networks design and construction. All authors have read and agreed to the published version of the manuscript.  
This research has been funded by the Science Committee of the Ministry of Science and Higher Education of the Republic of Kazakhstan (Grant No. AP08857347 \"Integrating Physic-Informed Neural Network, Bayesian and Convolutional Neural Networks for early breast cancer detection using thermography\").  
The presented research was certified by the Institutional Research Ethics Committee (IREC) of Nazarbayev University (identification number: 592/21072022).  
Informed Consent Statement: Informed consent was obtained from all subjects involved in the study.  
The first set of data that support the findings of this study are openly available in Visual Lab at [[http://visual.ic.uff.br/dmi/](http://visual.ic.uff.br/dmi/)]([http://visual.ic.uff.br/dmi/](http://visual.ic.uff.br/dmi/)), reference number [11]. The second set of data were generated at Astana Multifunctional Hospital by mammologist, oncologist. Derived data supporting the findings of this study are available from the corresponding author [PERSON] on request.  
The authors declare no conflict of interest.