Founded in 1991, we are a global quantitative and systematic asset management firm applying a scientific approach to finance to develop alternative investment strategies that create value for our clients.
We value innovation, dedication, collaboration, and the ability to make an impact. Together, we create a stimulating environment for talented and passionate experts in research, technology, and business to explore new ideas and challenge existing assumptions.

Description

In spite of tremendous progresses in sampling in the last decades, multimodality remains an important challenge in many fields where statistics is applied. When mentally representing a probability distribution, one often thinks of a bump centered around a mean, with a certain spill accounting for variance. In many applications though, realistic distributions are made of several such bumps, centered around various points in phase space, and each with a certain spillover. Some examples are:
- Images: there is a centered distribution around dog images, one around cats, etc.
- Physics: physical systems have typically different stable distributions (a phenomenon called metastability) corresponding to states: alpha versus beta crystals, folded vs unfolded proteins, etc.
- Inverse problems: due to ill-posedness of inverse problems, several concurrent solutions generally appear in practice, forming different centers for the posterior distribution.
 

In all cases, standard sampling strategies are very long to converge, which triggered a very wide literature to get improvements in this direction.

Internship Objective:

The primary goal of this internship is to develop methods to detect a priori whether a given distribution is multimodal and to quantify its degree of multimodality. Rather than focusing on sampling strategies, we aim to understand the underlying dynamics of mappings between a simple distribution (such as a Gaussian distribution) and the target distribution. By utilizing tools from dynamical systems, such as Ordinary Differential Equations (ODEs) and Partial Differential Equations (PDEs), we seek to extract valuable insights into multimodality from these dynamics.

Start Date: Flexible

We are continuously striving to be an equal opportunity employer and we prohibit any discrimination based on sex, disability, origin, sexual orientation, gender identity, age, race, or religion. We believe that our diversity, breadth of experience, and multiple points of view are among the leading factors in our success.
CFM is a signatory of the Women Empowerment Principles.
 

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Profile description:

• Student in gap year or end of study ( engineering school, Master in mathematics, statistics or equivalent ) 
• Strong foundation in Machine Learning and Statistics.
• Keen interest in Dynamical Systems (ODEs, PDEs) and Numerical Analysis.
• Experience with programming in Python.
• Interest in research and the ability to work independently and creatively.