arXiv subjects

Anna Timonina-Farkas

Publications and source records attributed to Anna Timonina-Farkas.

3 recordsLinked to original sources

arXiv2025

Some Remarks on the $l_1$-Robust Solution of LexRank Problem

Graph-based ranking methods, such as LexRank, are fundamental in Natural Language Processing (NLP) applications like text summarization, as they measure the relative importance of textual units. Building on recent advances in ranking methods for growing and dynamic graphs, we develop a robust variant of LexRank that operates on stochastic similarity graphs with uncertain and expanding structure. Our approach introduces a novel $l_1$-based formulation that captures ambiguity in both transition probabilities and graph size, while maintaining sparsity. The resulting non-convex problem is upper-bounded by a linear program, providing a tractable and interpretable approximation.

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arXiv2025

A Quick Estimation of Fréchet Quantizers for a Dynamic Solution to Flood Risk Management Problems

Multi-stage stochastic optimization is a well-known quantitative tool for decision-making under uncertainty. It is broadly used in financial and investment planning, inventory control, and also natural disaster risk management. Theoretical solutions of multi-stage stochastic programs can be found explicitly only in very exceptional cases due to their variational form and interdependency of uncertainty in time. Nevertheless, numerical solutions are often inaccurate, as they rely on Monte-Carlo sampling, which requires the Law of Large Numbers to hold for the approximation quality. In this article, we introduce a new approximation scheme, which computes and groups together stage-wise optimal quantizers of conditional Fréchet distributions for optimal weighting of value functions in the dynamic programming. We consider optimality of scenario quantization methods in the sense of minimal Kantorovich-Wasserstein distance at each stage of the scenario tree. By this, we bound the approximation error with convergence guarantees. We also provide global solution guarantees under convexity and monotonicity conditions on the value function. We apply the developed methods to the governmental budget allocation problem for risk management of flood events in Austria. For this, we propose an extremely efficient way to approximate optimal quantizers for conditional Fréchet distributions. Our approach allows to enhance the overall efficiency of dynamic programming via the use of different parameter estimation methods for different groups of quantizers. The groups are distinguished by a particular risk threshold and are able to differentiate between higher- and lower-impact flood events.

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arXiv2025

Forward-Backward Quantization of Scenario Processes in Multi-Stage Stochastic Optimization

Multi-stage stochastic optimization lies at the core of decision-making under uncertainty. As the analytical solution is available only in exceptional cases, dynamic optimization aims to efficiently find approximations but often neglects non-Markovian time-interdependencies. Methods on scenario trees can represent such interdependencies but are subject to the curse of dimensionality. To ease this problem, researchers typically approximate the uncertainty by smaller but more accurate trees. In this article, we focus on multi-stage optimal tree quantization methods of time-interdependent stochastic processes, for which we develop novel bounds and demonstrate that the upper bound can be minimized via projected gradient descent incorporating the tree structure as linear constraints. Consequently, we propose an efficient quantization procedure, which improves forward-looking samples using a backward step on the tree. We apply the results to the multi-stage inventory control with time-interdependent demand. For the case with one product, we benchmark the approximation because the problem allows a solution in closed-form. For the multi-dimensional problem, our solution found by optimal discrete approximation demonstrates the importance of holding mitigation inventory in different phases of the product life cycle.

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