PhD position available in the project "Convergence rates of Markov processes with applications to computational statistics and machine learning"
The project will involve investigating convergence of various types of Markov processes, including solutions of stochastic differential equations (with and without jumps) and Markov chains (see papers [3] and [1]). Results of such type, besides their theoretical significance, have found numerous applications in computational statistics and machine learning. For instance, by employing the probabilistic coupling technique, one can analyse convergence of numerous Monte Carlo algorithms that are obtained via discretizations of stochastic differential equations and are used in computational statistics for sampling from high dimensional probability distributions [2]. For further examples of connections between some topics in stochastic analysis and machine learning, see [4] and [5].
The PhD student working on this project will be involved in a local collaboration with the research group of Dr Lukasz Szpruch (https://www.maths.ed.ac.uk/~lszpruch/) from the University of Edinburgh. There is also a possibility to be involved in international collaborations with research partners in China, Germany and France.
Instructions on how to apply can be found here. Note that the deadline for applications has been extended to the 1st of February. For further information, please contact me at m.majka (at) hw.ac.uk
References:
5. M. B. Majka, M. Sabate-Vidales and L. Szpruch, Multi-index Antithetic Stochastic Gradient Algorithm, submitted, 2020, [arXiv].
4. L.-J. Huang, M. B. Majka and J. Wang, Approximation of heavy-tailed distributions via stable-driven SDEs, Bernoulli (2020), in press, [arXiv].
3. M. Liang, M. B. Majka and J. Wang, Exponential ergodicity for SDEs and McKean-Vlasov processes with Lévy noise, Ann. Inst. Henri Poincaré Probab. Stat. (2020), in press, [arXiv].
2. M. B. Majka, A. Mijatović and L. Szpruch, Non-asymptotic bounds for sampling algorithms without log-concavity, Ann. Appl. Probab. 30 (2020), no. 4, 1534-1581, [link], [arXiv].
1. A. Eberle and M. B. Majka, Quantitative contraction rates for Markov chains on general state spaces, Electron. J. Probab. 24 (2019), paper no. 26, 36 pp., [link], [arXiv].