arXiv subjects

Pavel Rytir

Publications and source records attributed to Pavel Rytir.

6 recordsLinked to original sources

arXiv2025

ExDAG: an MIQP Algorithm for Learning DAGs

There has been a growing interest in causal learning in recent years. Commonly used representations of causal structures, including Bayesian networks and structural equation models (SEM), take the form of directed acyclic graphs (DAGs). We provide a novel mixed-integer quadratic programming formulation and an associated algorithm that identifies DAGs with a low structural Hamming distance between the identified DAG and the ground truth, under identifiability assumptions. The eventual exact learning is guaranteed by the global convergence of the branch-and-bound-and-cut algorithm, which is utilized. In addition to this, integer programming techniques give us access to the dual bound, which allows for a real time assessment of the quality of solution. Previously, integer programming techniques have been shown to lead to limited scaling in the case of DAG identification due to the super exponential number of constraints, which prevent the formation of cycles. The algorithm proposed circumvents this by selectively generating only the violated constraints using the so-called "lazy" constraints methodology. Our empirical results show that ExDAG outperforms state-of-the-art solvers in terms of structural Hamming distance and $F_1$ score when considering Gaussian noise on medium-sized graphs.

cs.LG↗

arXiv2025

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

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.

cs.LG↗

arXiv2025

Topological Quantum Compilation Using Mixed-Integer Programming

We introduce the Mixed-Integer Quadratically Constrained Quadratic Programming framework for the quantum compilation problem and apply it in the context of topological quantum computing. In this setting, quantum gates are realized by sequences of elementary braids of quasiparticles with exotic fractional statistics in certain two-dimensional topological condensed matter systems, described by effective topological quantum field theories. We specifically focus on a non-semisimple version of topological field theory, which provides a foundation for an extended theory of Ising anyons and which has recently been shown by Iulianelli et al., Nature Communications {\bf 16}, 6408 (2025), to permit universal quantum computation. While the proofs of this pioneering result are existential in nature, the mixed integer programming provides an approach to explicitly construct quantum gates in topological systems. We demonstrate this by focusing specifically on the entangling controlled-NOT operation, and its local equivalence class, using braiding operations in the non-semisimple Ising system. This illustrates the utility of the Mixed-Integer Quadratically Constrained Quadratic Programming for topological quantum compilation.

quant-ph↗

arXiv2025

Power System Steady-State Estimation Revisited

In power system steady-state estimation (PSSE), one needs to consider (1) the need for robust statistics, (2) the nonconvex transmission constraints, (3) the fast-varying nature of the inputs, and the corresponding need to track optimal trajectories as closely as possible. In combination, these challenges have not been considered, yet. In this paper, we address all three challenges. The need for robustness (1) is addressed by using an approach based on the so-called Huber model. The non-convexity (2) of the problem, which results in first order methods failing to find global minima, is dealt with by applying global methods. One of these methods is based on a mixed integer quadratic formulation, which provides results of several orders of magnitude better than conventional gradient descent. Lastly, the trajectory tracking (3) is discussed by showing under which conditions the trajectory tracking of the SDP relaxations has meaning.

math.OC↗

arXiv2024

Learning Dynamic Bayesian Networks from Data: Foundations, First Principles and Numerical Comparisons

In this paper, we present a guide to the foundations of learning Dynamic Bayesian Networks (DBNs) from data in the form of multiple samples of trajectories for some length of time. We present the formalism for a generic as well as a set of common types of DBNs for particular variable distributions. We present the analytical form of the models, with a comprehensive discussion on the interdependence between structure and weights in a DBN model and their implications for learning. Next, we give a broad overview of learning methods and describe and categorize them based on the most important statistical features, and how they treat the interplay between learning structure and weights. We give the analytical form of the likelihood and Bayesian score functions, emphasizing the distinction from the static case. We discuss functions used in optimization to enforce structural requirements. We briefly discuss more complex extensions and representations. Finally we present a set of comparisons in different settings for various distinct but representative algorithms across the variants.

cs.LG↗

arXiv2023

Scheduling a Multi-Product Pipeline: A Discretized MILP Formulation

Multi-product pipelines are a highly efficient means of transporting liquids. Traditionally used to transport petroleum, its products and derivatives, they are now being repurposed to transport liquified natural gas admixed with hydrogen of various colors. We propose a novel mixed-integer linear programming (MILP) formulation, which optimizes efficiency while satisfying a wide range of real-world constraints developed to meet the needs of the Czech national pipeline operator CEPRO. We provide tests on well-known synthetic (path-graph) networks and demonstrate the formulation's scaling properties using open-source and commercial MILP solvers.

math.OC↗