Mgr. Jakub Mareček, Ph.D.

There has been much recent interest in the bias of artificial-intelligence (AI) systems and, consequently, the regulation thereof. Bias often arises out of mental short cuts taken in model building and underrepresentation of sections of population in the data, rather than as a result of a wilful, nefarious operation. Many vendors of AI systems may be willing to test for the presence of bias, should there be a widely accepted definition and a method for estimating the bias. One of the significant conceptual challenges in regards to the target of mitigating bias in AI is the lack of a consensus as to what would be the best definition of measuring bias or fairness. For almost any problem, one can have multiple measures of individual fairness and multiple measures of subgroup fairness. Often, there are multiple protected attributes (such as race, sex, or ethnicity) defining a number of subgroups within the population. Thus, one obtains a multitude of combinations of a subgroup and a fairness measure, all of which should be considered to some extent. There have been recently proposed a number of definitions of bias and numerical methods for quantifying of thus defined bias in AI systems. It is clearly desirable to inform users as comprehensively as possible as to the fairness implications of their AI pipeline, rather than to consider a single definition of bias to the exclusion of others. Another challenge is the lack of understanding of the definitions of bias and the sample complexity of its detection. As it seems, one may need to study hundreds of thousands of “comparable” interactions with the AI system, in many cases. A thorough and comprehensive characterization of the existing definitions and the number of samples required to detect bias of various kinds up to a certain error with a certain probability, is clearly desirable. This can take the form of guarantees of probabilistically approximately correct (PAC) learning, or confidence intervals for the estimates produced otherwise. Finally, a major challenge lies in the lack of libraries for the detection of bias. The most widely used library, AI Fairness 360, covers only a few types of bias and does not allow for the estimation of confidence intervals. We would like to develop an open-source toolbox for the detection and quantification of multiple types of bias.

It is well known that what we eat can affect our health – that people with lower quality diets are more likely to develop diseases like heart disease, diabetes, and obesity. However, there is remarkably little known about the crucial steps in between – the changes and processes that take place within our bodies as a result of what we eat that actually lead to us to developing these diseases. In this project, we develop causal models of metabolism. In terms of methods, this draws on a history of work on learning dynamical systems. In terms of inputs, this draws on the information we gather from existing research, the information we get from new ways to monitor diets, as well as other information that often isn’t considered, such as genetics, metabolism, and gut bacteria, to improve our understanding of this pathway and discover new indicators of disease risk. The project will also use AI to help us analyse this information and to connect the dots that humans usually wouldn’t be able to find.

Polynomial optimization is an exciting area of research in optimization, just at the boundary between what is undecidable (continuous optimization) and what is efficiently solvable (easier conic optimization problems, such as linear and semidefinite programming). Sustained progress in the field over the past two decades has enabled new applications within many areas of engineering. Multiple novel applications arises in quantum technologies. Notably, quantum optimal control is behind many recent advances in science and technology, where one shapes a laser or microwave pulse, so as to optimise a functional of the states produced. In biology, quantum optimal control allows nuclear magnetic resonance (NMR) spectroscopy to study large biomolecules in solution. In chemistry, quantum optimal control in laser spectroscopy brings fundamental insights into reaction dynamics; laser control directs chemical reactions to a desired target or even enables a design of new chemical species and materials. In neurology and neurosciences, quantum optimal control provides radio-frequency pulses yielding higher resolution in functional magnetic resonance imaging (fMRI), and hence better diagnoses with less time spent in the scanner. In photonics and metrology, interferometers utilise quantum optimal control as a means of designing semi-classical probes. In quantum computing, better quantum optimal control provides faster and more accurate two-qubit gates, and multi-level operations in general. We have recently shown that quantum optimal control can be formulated as a commutative (arXiv:2209.05790) or non-commutative (arXiv:2001.06464) polynomial optimization problem. To take full advantage of quantum systems, e.g., within quantum optimal control, we need to learn a model of the quantum system. Although the identification of the Hamiltonian of an open or closed quantum system is a very natural problem, progress has been hindered by the interdisciplinary nature of the problem. Indeed, it requires nontrivial Computer Science and Statistics (statistical learning theory, system identification), Mathematics (algebraic geometry andnonconvex optimization in the form of non-commutative polynomial optimization), and Physics (quantum information theory), in order to extend the well-established results of system identification from classical to quantum systems. We have recently made some progress in this direction (arXiv:2203.17164). There is funding available from the Czech Science Foundation (GACR) under award number GA23-07947S (Learning Models of Quantum Systems as a Non-Commutative Polynomial Optimization Problem) and from the European Commission under grant agreement number 101120296 (HORIZON-MSCA-2022-DN-01 Tensor modEliNg, geOmetRy and optimiSation). This topic is supervised by Jakub Marecek and Vyacheslav Kungurtsev (Dept. of Computer Science), in close collaboration with Milan Korda and Didier Henrion (Dept. of Control Engineering; both co-PIs on the project funded in HORIZON-MSCA-2022-DN-01) and their research team in Toulouse, France (LAAS CNRS is a beneficiary of the project funded in HORIZON-MSCA-2022-DN-01) and Georgios Korpas and his research team in London, UK (HSBC is an associate partner for the project funded in HORIZON-MSCA-2022-DN-01).

Polynomial optimization is an exciting area of research in optimization, just at the boundary between what is undecidable (continuous optimization) and what is efficiently solvable (easier conic optimization problems, such as linear and semidefinite programming). Sustained progress in the field over the past two decades has enabled new applications within many areas of engineering. One novel application arises in structural engineering. There, thin frame and shell theories have been successfully used in diverse applications encompassing, e.g., the construction of the Eiffel tower and wind-turbine towers. Designing such structures for optimal mechanical performance is notoriously challenging because of the inherent non-convexity of the resulting optimization problems. A certain static minimum-compliance problem can be cast as a polynomial optimization program, which in turn, can be solved to the guaranteed global optimality by a hierarchy of convexifications. This opens entirely new avenues in the optimal design of bending-resistant structures that we wish to explore in the current project in the context of structural dynamics. This topic is supervised by Didier Henrion (Dept. of Control Engineering) and Jakub Marecek and Vyacheslav Kungurtsev (Dept. of Computer Science), in close collaboration with the team of Jan Zeman (Department of Mechanics) and world-leading experts in structural optimization at the University of Birmingham (UK). There is funding available from the Czech Science Foundation (GACR) under award number 22-15524S.