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Jakub Marecek

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8 papers

2 author rows

TMLR Journal 2026 Journal Article

Online Learning with Multiple Fairness Regularizers via Graph-Structured Feedback

Quan Zhou
Jakub Marecek
Robert Noel Shorten

There is an increasing need to enforce multiple, often competing, measures of fairness within automated decision systems. The appropriate weighting of these fairness objectives is typically unknown a priori, may change over time and, in our setting, must be learned adaptively through sequential interactions. In this work, we address this challenge in a bandit setting, where decisions are made with graph-structured feedback.

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TMLR Journal 2025 Journal Article

ExDBN: Learning Dynamic Bayesian Networks using Extended Mixed-Integer Programming Formulations

Pavel Rytíř
Aleš Wodecki
Georgios Korpas
Jakub Marecek

Causal learning from data has received much attention recently. Bayesian networks can be used to capture causal relationships. There, one recovers a weighted directed acyclic graph in which random variables are represented by vertices, and the weights associated with each edge represent the strengths of the causal relationships between them. This concept is extended to capture dynamic effects by introducing a dependency on past data, which may be captured by the structural equation model. This formalism is utilized in the present contribution to propose a score-based learning algorithm. A mixed-integer quadratic program is formulated and an algorithmic solution proposed, in which the pre-generation of exponentially many acyclicity constraints is avoided by utilizing the so-called branch-and-cut (``lazy constraint'') method. Comparing the novel approach to the state-of-the-art, we show that the proposed approach turns out to produce more accurate results when applied to small and medium-sized synthetic instances containing up to 80 time series. Lastly, two interesting applications in bioscience and finance, to which the method is directly applied, further stress the importance of developing highly accurate, globally convergent solvers that can handle instances of modest size.

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ICLR Conference 2025 Conference Paper

Generating Likely Counterfactuals Using Sum-Product Networks

Jiri Nemecek 0002
Tomás Pevný
Jakub Marecek

The need to explain decisions made by AI systems is driven by both recent regulation and user demand. The decisions are often explainable only post hoc. In counterfactual explanations, one may ask what constitutes the best counterfactual explanation. Clearly, multiple criteria must be taken into account, although "distance from the sample" is a key criterion. Recent methods that consider the plausibility of a counterfactual seem to sacrifice this original objective. Here, we present a system that provides high-likelihood explanations that are, at the same time, close and sparse. We show that the search for the most likely explanations satisfying many common desiderata for counterfactual explanations can be modeled using Mixed-Integer Optimization (MIO). We use a Sum-Product Network (SPN) to estimate the likelihood of a counterfactual. To achieve that, we propose an MIO formulation of an SPN, which can be of independent interest. The source code with examples is available at https://github.com/Epanemu/LiCE.

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AAAI Conference 2024 Conference Paper

Taming Binarized Neural Networks and Mixed-Integer Programs

Johannes Aspman
Georgios Korpas
Jakub Marecek

There has been a great deal of recent interest in binarized neural networks, especially because of their explainability. At the same time, automatic differentiation algorithms such as backpropagation fail for binarized neural networks, which limits their applicability. We show that binarized neural networks admit a tame representation by reformulating the problem of training binarized neural networks as a subadditive dual of a mixed-integer program, which we show to have nice properties. This makes it possible to use the framework of Bolte et al. for implicit differentiation, which offers the possibility for practical implementation of backpropagation in the context of binarized neural networks. This approach could also be used for a broader class of mixed-integer programs, beyond the training of binarized neural networks, as encountered in symbolic approaches to AI and beyond.

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AAAI Conference 2021 Conference Paper

Fairness in Forecasting and Learning Linear Dynamical Systems

Quan Zhou
Jakub Marecek
Robert N. Shorten

In machine learning, training data often capture the behaviour of multiple subgroups of some underlying human population. When the amounts of training data for the subgroups are not controlled carefully, under-representation bias arises. We introduce two natural notions of subgroup fairness and instantaneous fairness to address such under-representation bias in time-series forecasting problems. In particular, we consider the subgroup-fair and instant-fair learning of a linear dynamical system (LDS) from multiple trajectories of varying lengths and the associated forecasting problems. We provide globally convergent methods for the learning problems using hierarchies of convexifications of non-commutative polynomial optimisation problems. Our empirical results on a biased data set motivated by insurance applications and the well-known COMPAS data set demonstrate both the beneficial impact of fairness considerations on statistical performance and the encouraging effects of exploiting sparsity on run time.

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AAAI Conference 2020 Conference Paper

Pursuit of Low-Rank Models of Time-Varying Matrices Robust to Sparse and Measurement Noise

Albert Akhriev
Jakub Marecek
Andrea Simonetto

In tracking of time-varying low-rank models of time-varying matrices, we present a method robust to both uniformlydistributed measurement noise and arbitrarily-distributed “sparse” noise. In theory, we bound the tracking error. In practice, our use of randomised coordinate descent is scalable and allows for encouraging results on changedetection. net, a benchmark.

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IJCAI Conference 2019 Conference Paper

Entropy-Penalized Semidefinite Programming

Mikhail Krechetov
Jakub Marecek
Yury Maximov
Martin Takac

Low-rank methods for semi-definite programming (SDP) have gained a lot of interest recently, especially in machine learning applications. Their analysis often involves determinant-based or Schatten-norm penalties, which are difficult to implement in practice due to high computational efforts. In this paper, we propose Entropy-Penalized Semi-Definite Programming (EP-SDP), which provides a unified framework for a broad class of penalty functions used in practice to promote a low-rank solution. We show that EP-SDP problems admit an efficient numerical algorithm, having (almost) linear time complexity of the gradient computation; this makes it useful for many machine learning and optimization problems. We illustrate the practical efficiency of our approach on several combinatorial optimization and machine learning problems.

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AAAI Conference 2019 Conference Paper

On-Line Learning of Linear Dynamical Systems: Exponential Forgetting in Kalman Filters

Mark Kozdoba
Jakub Marecek
Tigran Tchrakian
Shie Mannor

The Kalman filter is a key tool for time-series forecasting and analysis. We show that the dependence of a prediction of Kalman filter on the past is decaying exponentially, whenever the process noise is non-degenerate. Therefore, Kalman filter may be approximated by regression on a few recent observations. Surprisingly, we also show that having some process noise is essential for the exponential decay. With no process noise, it may happen that the forecast depends on all of the past uniformly, which makes forecasting more difficult. Based on this insight, we devise an on-line algorithm for improper learning of a linear dynamical system (LDS), which considers only a few most recent observations. We use our decay results to provide the first regret bounds w. r. t. to Kalman filters within learning an LDS. That is, we compare the results of our algorithm to the best, in hindsight, Kalman filter for a given signal. Also, the algorithm is practical: its per-update run-time is linear in the regression depth.

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