PaweÅ PrzybyÅowicz, Martyna WiÄ cek
We analyze the behavior of the Euler method for delay differential equations under nonstandard assumptions on the right-hand-side function f, when evaluations of f are corrupted by informational noise. We provide theoretical upper bounds on the Euler discretization error and present results from the numerical experiments.
Agnieszka Kopeć, Paweł Przybyłowicz, Martyna Wiącek
We investigate a forecasting framework based on a simple discrete-time dynamic model with coefficients varying in time. The parameters of the model are recovered within a deep learning framework, which makes it possible to retain a transparent parametric structure while simultaneously accounting for complex and nonstationary patterns in the observed phenomenon. Our analysis covers two specifications of the noise process. Besides the standard Gaussian setting, we also consider Laplace-distributed noise, which can offer a more adequate description in the presence of heavier tails and sharper local fluctuations. For both cases, we formulate the predictive scheme of the model and analyze the associated uncertainty quantification, including the construction of prediction intervals. The results illustrate that a relatively simple model, when combined with time-dependent parameter estimation, can serve as a mathematically tractable and practically flexible tool for forecasting complex dynamics under different noise assumptions. The general model is stated for TVAR($p$), while the prediction-interval formulas and the numerical experiments are developed for the TVAR(1) case.
Martyna Wiącek, Piotr Rybak, Łukasz Pszenny et al.
With the advancements of transformer-based architectures, we observe the rise of natural language preprocessing (NLPre) tools capable of solving preliminary NLP tasks (e.g. tokenisation, part-of-speech tagging, dependency parsing, or morphological analysis) without any external linguistic guidance. It is arduous to compare novel solutions to well-entrenched preprocessing toolkits, relying on rule-based morphological analysers or dictionaries. Aware of the shortcomings of existing NLPre evaluation approaches, we investigate a novel method of reliable and fair evaluation and performance reporting. Inspired by the GLUE benchmark, the proposed language-centric benchmarking system enables comprehensive ongoing evaluation of multiple NLPre tools, while credibly tracking their performance. The prototype application is configured for Polish and integrated with the thoroughly assembled NLPre-PL benchmark. Based on this benchmark, we conduct an extensive evaluation of a variety of Polish NLPre systems. To facilitate the construction of benchmarking environments for other languages, e.g. NLPre-GA for Irish or NLPre-ZH for Chinese, we ensure full customization of the publicly released source code of the benchmarking system. The links to all the resources (deployed platforms, source code, trained models, datasets etc.) can be found on the project website: https://sites.google.com/view/nlpre-benchmark.
Andrzej Kałuża, Paweł M. Morkisz, Bartłomiej Mulewicz et al.
We present a novel deep learning method for estimating time-dependent parameters in Markov processes through discrete sampling. Departing from conventional machine learning, our approach reframes parameter approximation as an optimization problem using the maximum likelihood approach. Experimental validation focuses on parameter estimation in multivariate regression and stochastic differential equations (SDEs). Theoretical results show that the real solution is close to SDE with parameters approximated using our neural network-derived under specific conditions. Our work contributes to SDE-based model parameter estimation, offering a versatile tool for diverse fields.