PhD Fellowship in Rigorous uncertainty estimation

The Pioneer Centre for AI and the Department of Computer Science at the University of Copenhagen invite applications for a fully-funded PhD position.

The project

For many critical applications of machine learning (ML), accurate uncertainty estimates are required. We need methods that give us uncertainty estimates for state-of-the-art ML models (e.g., deep neural networks), are well calibrated, and come with theoretical guarantees.

This project is about developing such methods. Possible theoretical approaches include PAC-Bayesian analysis (in particular for unbounded loss functions) and conformal prediction. Interesting directions are the analysis of quantile regression, Bayesian modeling and ensemble predictions.

Goals include deriving prediction intervals for non-linear regression models under heteroskedastic noise and the application of novel uncertainty estimation techniques to ecosystem/climate modeling.

The main focus can be tailored to the applicant's profile and interests and discussed at a later stage of the interview process.

The project will be jointly supervised by Christian Igel (Professor, University of Copenhagen, Department of Computer Science), email: igel@di.ku.dk and another researcher in the Pioneer Centre for AI’s Learning and Optimization Collaboratory, depending on the final PhD project description.


The research environment

The candidate will be a member of the Pioneer Centre for Artificial Intelligence, a 5-university Danish research endeavor, and the Department of Computer Science at the University of Copenhagen. Both the centre and department are highly international and well-funded, working on a broad range of fundamental research topics. PhD students have access to funding for travel, guests, conferences and courses. The Pioneer Centre for AI and the Department of Computer Science maintain computing clusters and support for access to international facilities as needed.

We offer creative and stimulating working conditions and significant freedom in a dynamic and international research environment. Copenhagen is a vibrant city, with many cultural offerings and easy access to the rest of Europe.

For more information about working in Denmark, consult International Staff Mobility or write to Michelle Løkkegaard, Chief Operating Officer at the Pioneer Centre for AI, mcl@di.ku.dk.


Who are we looking for?

We are looking for candidates with knowledge and interest in the field(s) Machine Learning, Mathematical Modelling, Statistics. The project combines ideas from statistical causal modelling, graphical models, and analysis and implementation of efficient graphical algorithms. The main focus can be tailored to the applicant's profile and interests and discussed at a later stage of the interview process.


General qualifications

  • Master’s degree in Computer Science, Mathematical Sciences, or a related field.
  • A curious mind-set with a strong interest in machine learning models and theory.
  • Strong team working and critical thinking skills
  • Strong English language skills
  • Relevant publications, if any


The PhD programme

To be eligible for the PhD programme, you must have completed a degree programme, equivalent to a Danish master’s degree (180 ECTS/3 FTE BSc + 120 ECTS/2 FTE MSc) related to the subject area of the project, e.g. Computer Science or a related field.


For information of eligibility of completed programmes, see General assessments for specific countries and Assessment database.


Terms of employment in the regular programme

Employment as PhD fellow is full time and for maximum 3 years.

Employment is conditional upon your successful enrolment as a PhD student at the PhD School at the Faculty of SCIENCE, University of Copenhagen. This requires submission and acceptance of an application for the specific project formulated by the applicant.

The terms of employment and salary are in accordance with the agreement between the Ministry of Taxation and The Danish Confederation of Professional Associations on Academics in the State (AC). The position is covered by the Protocol on Job Structure.


Responsibilities and tasks in the PhD programme

  • Carry through an independent research project under supervision
  • Complete PhD courses corresponding to approx. 30 ECTS / ½ FTE
  • Participate in active research environments, including a stay at another research institution, preferably abroad
  • Teaching and knowledge dissemination activities
  • Write scientific papers aimed at high-impact journals
  • Write and defend a PhD thesis on the basis of your project



Application and Assessment Procedure

 Your application including all attachments must be in English and submitted electronically by clicking APPLY NOW below. Please include:

  • Motivated letter of application (max. one page)
  • Your motivation for applying for the specific PhD project
  • Curriculum vitae including information about your education, experience, language skills and other skills relevant for the position
  • Original diplomas for Bachelor of Science or Master of Science and transcript of records in the original language, including an authorized English translation if issued in another language than English or Danish. If not completed, a certified/signed copy of a recent transcript of records or a written statement from the institution or supervisor is accepted.
  • Publication list (if possible)
  • Reference letters (if available)

Application deadline

The deadline for applications is 22 March 2024, 23:59 GMT +1.


We reserve the right not to consider material received after the deadline, and not to consider applications that do not live up to the abovementioned requirements.


The further process

After deadline, a number of applicants will be selected for academic assessment by an unbiased expert assessor. You are notified, whether you will be passed for assessment.


The assessor will assess the qualifications and experience of the shortlisted applicants with respect to the above mentioned research area, techniques, skills and other requirements. The assessor will conclude whether each applicant is qualified and, if so, for which of the two models. The assessed applicants will have the opportunity to comment on their assessment. You can read about the recruitment process at https://employment.ku.dk/faculty/recruitment-process/.


Interviews with selected candidates are expected to be held toward the end of April/early May.



For specific information about the PhD fellowship, please contact the principal supervisor.


General information about PhD study at the Faculty of SCIENCE is available at the PhD School’s website: https://www.science.ku.dk/phd/.


The University of Copenhagen wishes to reflect the surrounding community and invites all regardless of personal background to apply for the position.




Part of the International Alliance of Research Universities (IARU), and among Europe’s top-ranking universities, the University of Copenhagen promotes research and teaching of the highest international standard. Rich in tradition and modern in outlook, the University gives students and staff the opportunity to cultivate their talent in an ambitious and informal environment. An effective organisation – with good working conditions and a collaborative work culture – creates the ideal framework for a successful academic career.
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Ph.D. positions

Department of Computer Science

Christian Igel 
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