Robust algorithmics: a foundation for science?!

Joachim Buhmann
ETH Zürich

The ALGORITHM is the idiom of modern science, as Bernard Chazelle phrazed it. In this talk, I like to forward the bold claim that algorithmics lays the foundation of modern science. The scientific method of "systematic observation, measurements, and experiments, as well as the formulation, testing, and modification of hypotheses" requires sophisticated and efficient algorithms for knowledge discovery in complex experimental situations. Algorithms in data science map data spaces to hypothesis classes. Beside running time and memory consumption, such algorithms should be characterized by their sensitivity to the signal in the input and their robustness to input
fluctuations. The achievable precision of an algorithm, i.e., the attainable resolution in output space, is determined by its capability to extract predictive information. I will advocate an information theoretic framework for algorithm analysis where an algorithm is characterized as a computational evolution of a posterior distribution on the output space.

The method allows us to investigate complex data analysis pipelines as they occur in computational neuroscience and neurology as well as in molecular biology. I will demonstrate this design concept for algorithm validation with a statistical analysis of diffusion tensor imaging data. A theoretical result for sparse minimum bisection yields
statistical hints why random combinatorial optimization problems are hard to solve.

Bio sketch:

Joachim M. Buhmann (1959) is full professor for Computer Science at ETH Zurich since 2003 representing the research area “Information Science and Engineering”. He studied physics at the Technical University of Munich and received a doctoral degree for his
research work on artificial neural networks. After research appointments at the University of Southern California (1988-1991) and at the Lawrence Livermore National Laboratory (1991-1992) he served as a professor for applied computer science at the University of Bonn (1992-2003) . His research interests range from statistical learning theory to applications of machine learning and artificial intelligence. Research projects are focused on topics in neuroscience, biology and medical sciences, as well as signal processing and
computer vision. He has presided the German Society for Pattern Recognition (DAGM e.V.) from 2009-2015. Since 2014 he serves as Vice-Rector for Study Programmes at ETH Zurich. In 2017, he was elected as a member of the Swiss Academy of Technical Sciences SATW, as an honorary member of the German Pattern Recognition Society DAGM and as a research council member of the Swiss National Science Foundation.

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