PRR Project

Summary

Job descriptionCEMAT is interested in a new area of application of mathematics, related with statistical models for 3D point cloud data, having in mind applications in healthcare. For this position, the researcher will investigate solutions for prediction and classification of 3D medical data and develop efficient and automatic solutions that are not tailored to specific datasets/or settings. The applications in mind could contemplate any shape modelling task setting such as shape completion, shape prediction, anomaly detection, shape classification, etc. And consequently, be applied in several possible real/life applications: the prothesis case (shape completion), anthropological case (shape prediction or classification), or disease classification based on medical 3D scans. A popular and possible approach to develop automatic search methods for kernel selection and hyperparameter estimation is Compositional Kernel search, where a complex kernel is built from a set of base kernels through allowed operations. This compositional approach has the advantage of producing a more interpretable result, passible of human interpretation. Therefore, it can also be adjusted to include additional input from medical experts that would require no alterations of the model itself. And it could be independently used by healthcare professionals with no knowledge of the intricacies of the statistical model.  These models can be computationally expensive if implemented naively. To address this, several approximations or exact solutions have been proposed for large-scale GPR. However, the specific characteristics of the shape modeling setting have yet to be explored. Namely, structure on the input point cloud datasets and the iterative nature of the method on subsets of a constant template, allow for additional assumptions than those found in generic GPR applications. By exploring these two aspects, one can get more accurate approximations or even more efficient exact computations of the GP posterior and marginal-likelihood.The researcher will present a strong research plan, supervise, and mentor students, provide curricular contributions to PhD and Master programs at IST, develop and maintain a solid line of research and produce excellent scientific output, interact with CEMAT members, organize and host scientific meetings at local and international level, and attract competitive funding. Scientific ProfileThe position is intended for a young researcher, preferably with a PhD in industrial problems, and with collaborations with industry. The ideal candidate should have a PhD in Mathematics or related areas, with international experiences. The candidate for this position must be proficient with Machine Learning methods, stochastic optimization, and numerical analysis, with experience in Gaussian Processes for Shape Modelling. RationaleOne of the areas of research of CEMAT is Mathematical Modelling in Medicine. Currently, the areas of investigation include models for the human cardiovascular system such as blood flow under healthy and pathological conditions, infectious disease dynamics and epidemiology, antibiotic resistance, and cancer. The research uses sophisticated multi-scale mathematical models, highly integrated with efficient algorithms for their computing and simulation.But with the advent of machine learning (ML), there is a vast field of possible developments with an extraordinary impact and benefits in the health sector, in particular. Randomness is an important element in ML. It helps eliminate inherent biases and is conducive to building a generalized machine learning model. However, incorporating randomness without care can hamper the results. Hence the use of these possible solutions based in ML is still limited due to the high risk involved. These solutions should ideally consider medical experts’ knowledge, but in a way that this could be easily introduced in the models without considerable additional workload.There is also the need for automation in parameter estimation and model selection that still hinders the applicability of many models to new applications/datasets. This topic is related with the area of interest and expertise of CEMAT:  Statistics and Stochastic process, in particular, about robust estimation and hypothesis testing in common principal components, and detection of influential observations in principal components and common principal components.At CEMAT we have identified excellent potential candidates amongst those that are eligible for the FCT Tenure program, in particular former researchers from the H2020 MSCA- ITN -EID program, and whom we know will be interested in applying for a research position at CEMAT that fits the profile here described.