The topics will be further introduced and the students can choose between them at an introductory seminar on Tuesday, October 6 at 14:15 in room 1019.
* - the number of supervised students is full
It turns out that main segmentation algorithms (Viterbi, PMAP) can be applied for PMM’s, because they solely relay on Markov property of (X,Y). Therefore, from a segmentation point of view, there is no restriction to use PMM’s instead of HMM’s.
• Gets familiar with HMM and PMM models
• Gives the classification of PMM models and the sufficient conditions fo Y being Markov chain.
• Studies Viterbi, PMAP and hybrid algorithms for HMM’s and generalizes them for PMM’s.
• Implements these algorithms for linear Markov switching models.
• Investigates the effect of PMM (correlated noise) in segmentation. Does the increase of dependence between the observations decrease the difference between PMAP and Viterbi paths.
1. A. Koloydenko, J. Lember, Bridging Viterbi and posterior decoding: A generalized risk approach to hidden path inference based on hidden Markov models, Journal of Machine Learning Research, 15, (2014), 1–58.
2. S. Derrode, W. Piecynski, Signal and image segmentation using pairwise Markov chains, IEEE Trans. Signal Process. 52 (9) (2004) 2477–2489.
3. W. Pieczynski, Pairwise Markov chains, IEEE Trans. Pattern Anal. Mach. Intell. 25 (5) (2003) 634–639.
4. I. Gorynin, H. Gangloff, E. Monfrini, W. Pieczynski, Assessing the segmentation performance of pairwise and triplet Markov models, Signal Process. 145 (2018) 183–192.
5. J. Hamilton, A new approach to the economic analysis of nonstationary time series and the business cycle, Econometrica (1989) 357–384.
6. J. Hamilton, Analysis of time series subject to changes in regime, J. Econometrics 45 (1–2) (1990) 39–70.
7. J. Hamilton, Regime switching models, in: Macroeconometrics and Time Series Analysis, Springer, (2010), 202–209.
8. J. Lember, J.Sova, Existence of infinite Viterbi path for pairwise Markov model, Stochastic Processes and their Applications (to appear)
9. J. Lember, Introduction to statistical learning theory (lecture notes), 2012
10. A. Koloydenko, K. Kuljus, J. Lember, Theory of segmentation, In: Hidden Markov Models, INTECH (2011)
11. L. Rabiner, A tutorial on Hidden Markov Models and selected applications in speech recognition, Proc. IEEE (1989), 1-58
 S. Haykin, Neural Networks and Learning Machines, Pearson College, 3rd ed. 2008
 B. de Vries, J.C. Principe, A theory for neural networks with time delays, in: Proceedings: Conference on Advances in Neural Information Processing Systems (NIPS-3), 1990, pp. 162–168.
 F. Colace, V. Loia, S. Tomasiello, Revising Recurrent Neural Networks from a Granular perspective, Applied Soft Computing, 2019, 82, 105535
 A. Nordbo, J. Wyller, G.T. Einevoll, Neural network firing-rate models on integral form: Effects of temporal coupling kernels on equilibrium-state stability, Biological Cybernetics, 2007, 97 (3), 195–209.
 M. Corazza et al. Design of adaptive Elman networks for credit risk assessment, Quantitative Finance, 2020, in press
Because of this more and more attention is brought on simulating transactional data. For example, in the UK a synthetic dataset is being built. It would be freely distributable, would try to model real life and would be flexible to simulate drastic changes within society (e.g. aftermath of COVID-19 pandemic).
The master thesis comprises a review on simulating transactional data and builds a framework to simulate a network of financial institutions (based on literature review). The topic requires knowledge of mathematical modelling, stochastic distributions and good programming skills.
Money laundering is a process that takes illegally obtained finances and puts it through a cycle of transactions in a bank (or network of banks) for it to appear to be from a legitimate source. Banks usually do not know if their client X wishes to commit a money laundering act (i.e. hidden information). But the bank will see the manifestation of this hidden information - transactions + their characteristics (sum, counterparty, time etc.). The bank will have to analyse transactional data and give an estimate - is the new transaction of illicit nature or not.
Current thesis aims to improve and elaborate results of the aforementioned master thesis - take a look at the theoretical background and elaborate the empirical study.
The topic requires basic knowledge in probability theory, knowledge of hidden Markov chains and the financial sector will come handy.
Longstaff, F.A., Schwartz, E.S., “Valuing American options by simulation: A simple least squares approach,” (2001)
Tilley, J. A,. 1993, "Valuing American Options in a Path Simulation model."
Yue-Kuen Kwok. Mathematical Models of Financial Derivatives, p.352-369. (2008)
Broadie, M., Glasserman, P., “Pricing American-style securities using simulation (1997)
Glasserman, P., Monte Carlo methods in financial engineering, Springer, New York (2004).
A consensus on a definition of interpretability has not been achieved yet, even though a position paper recently appeared . Broadly speaking, interpretability can be meant as human readability. For instance, in a certain model, it easily allows to detect the reasons why the predictions go wrong. Lately, interpretability has become a requirement to comply with government regulations for sensitive applications, such as in finance, public health, and transportation. In fact, this issue has received attention from the European Parliament whose General Data Protection Regulation recognizes the right to receive an explanation for algorithmic decisions . The aim of this thesis is to investigate and revise some existing approaches from the perspective of interpretability, with application to financial time series forecasting. This implies also a clear mathematical formulation of the methods.
 Bao W, Yue J, Rao Y (2017) A deep learning framework for financial time series using stacked autoencoders and long-short term memory. PLoS ONE 12(7): e0180944.
 A. Preeti et al. Financial Time Series Forecasting Using Deep Learning Network, in G. C. Deka et al. (Eds.): ICACCT 2018, CCIS 899, pp. 23–33, 2018.
 A. Vlasenko et al. A Novel Ensemble Neuro-Fuzzy Model for Financial Time Series Forecasting, Data, 2019, 4, 126
 Lipton, Z. C. (2018) The mythos of model interpretability. ACM Queue 16(3), 1–27.
 Regulation (EU) 2016/679 on the protection of natural persons with regard to the processing of personal data and on the free movement of such data, and repealing. Directive 95/46/EC (General Data Protection Regulation)  OJ L119/1.
The aim of this thesis is to investigate a neural network-like approach for the numerical solution of a class of fractional PDEs, and in particular the space fractional Black–Scholes equation for pricing European options, which has been recently considered in  by using a finite difference scheme.
 V. Dwivedi, B. Srinivasan, Physics Informed Extreme Learning Machine (PIELM)–A rapid method for the numerical solution of partial differential equations, Neurocomputing 391 (2020) 96–118
 Q. Wei, Y. Jiang, J. Z. Y. Chen, Machine-learning solver for modified diffusion equations, PHYSICAL REVIEW E 98 (2018) 053304
 H. Qu, Z. She, X. Liu, Neural network method for solving fractional diffusion equations, Applied Mathematics and Computation 391 (2021) 125635
 K. S. Patel , M. Mehra, Fourth order compact scheme for space fractional advection–diffusion reaction equations with variable coefficients, Journal of Computational and Applied Mathematics 380 (2020) 112963
 M. Raissi, G. E.Karniadakis, Hidden physics models: Machine learning of nonlinear partial differential equations, J. Comput. Phys. 357 (2018) 125–14
1. H. Schmidle , Risk Theory. Springer, 2017.
2. H. Schmidle, An extension to the renewal theorem and an application to risk theory. The Annales of Applied Probability, 1997,7, 121-133.
3. T. Polski, H. Schmidli, V. Schmidt, J. Teugels, Stochastic Processes for Insurance and Finance, Vol.505, Wiley,2009.
13. TAKEN: Tree-based methods in supervised learning with Estonian Health Insurance Fond data, supervisors Jüri Lember, Mark Gimbutas