Sigurd Holmsen | Search arXiv

arXiv2026

Non-Parametric Mutual Information Estimation with Vine Copulas

We introduce VINE: a non-parametric mutual information (MI) estimator based on simplified D-vine copulas. Approximating the joint density with a simplified D-vine allows the density ratio to simplify to a product of pair copulas, which we can estimate non-parametrically. This structural simplification yields VINE, a flexible and computationally efficient MI estimator. We compare VINE against SotA neural MI estimators on a range of datasets, both under settings where the simplified D-vine assumption holds and where it is violated, demonstrating competitive accuracy at a lower computational cost for low- to medium-dimensional datasets.

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arXiv2024

Pseudo-Hamiltonian system identification

Identifying the underlying dynamics of physical systems can be challenging when only provided with observational data. In this work, we consider systems that can be modelled as first-order ordinary differential equations. By assuming a certain pseudo-Hamiltonian formulation, we are able to learn the analytic terms of internal dynamics even if the model is trained on data where the system is affected by unknown damping and external disturbances. In cases where it is difficult to find analytic terms for the disturbances, a hybrid model that uses a neural network to learn these can still accurately identify the dynamics of the system as if under ideal conditions. This makes the models applicable in some situations where other system identification models fail. Furthermore, we propose to use a fourth-order symmetric integration scheme in the loss function and avoid actual integration in the training, and demonstrate on varied examples how this leads to increased performance on noisy data.

eess.SY↗