Post-Doctoral Research Visit F/M Interpretability of persistent homology

The post-holder will be a member of the DataShape team, and work under the supervision of Nina Otter. 

DataShape is a research team in Topological Data Analysis (TDA), constituted of researchers from Inria-Saclay, Inria Sophia Antipolis, and from the Laboratoire de Mathématiques d’Orsay. TDA is a recent field whose aim is to uncover, understand and exploit the topological and geometric structure underlying complex and possibly high-dimensional data. The DataShape team gathers a unique variety of expertise that allows it to embrace the mathematical, statistical, algorithmic and applied aspects of the field in a common framework ranging from fundamental theoretical studies to experimental research and software development.

More information on the proposed research subject :

Persistent homology (PH) is one of the most successful methods in the field of topological data analysis (TDA). In recent years, PH has seen important theoretical advancements on the one hand, and hundreds of successful applications on the other. There is, however, a lack of understanding on why PH is successful in these applications, as it is still elusive what type of topological and geometric features are captured with the long and short persistence intervals, which provide information about the connected components, holes and cycles in higher dimensions. The main overall objective of this project is to make first steps in bridging this gap, by gaining an understanding on why and when PH works. In particular, we will develop methods to study regions of data that are most relevant for a particular PH-based classification or regression pipeline, and subsequently use this framework to gain a better understanding on both new as well as existing successful applications of PH. New applications that will be investigated will stem from the fields of operations research (i.e., optimisation of humanitarian-aid relief networks) and medical imaging (i.e., breast-cancer prediction). 

Collaboration: 

The post-holder will closely work with Nina Otter. 

Responsibilities:
The person recruited is responsible for conducting research, preparing articles for peer-reviewed publications, disseminating research at local, national and international seminars and conferences.

Main activities:

• Propose a framework to study relevance of regions in data for PH-based pipelines
• Develop Python code to test such framework on a variety of synthetic and real-world data sets
• Test, change up until validation
• Write documentation and reports
• Prepare manuscript for submission in peer-reviewed journals of conference proceedings
• Present the work's progress to other DataShape group members during the DataShape seminar

Additional activities:

• Participation in local, national and international seminars and conferences

Technical skills and level required: PhD in mathematics, computer science, or other relevant domain; strong background in Topological Data Analysis, and research experience in the field.

Languages: English.

Relational skills: Experience in working in scientific collaborations.

• Subsidized meals
• Partial reimbursement of public transport costs
• Leave: 7 weeks of annual leave + 10 extra days off due to RTT (statutory reduction in working hours) + possibility of exceptional leave (sick children, moving home, etc.)
• Possibility of teleworking (after 6 months of employment) and flexible organization of working hours
• Professional equipment available (videoconferencing, loan of computer equipment, etc.)
• Social, cultural and sports events and activities
• Access to vocational training
• Social security coverage