arXiv subjects

Florian Sobieczky

Publications and source records attributed to Florian Sobieczky.

10 recordsLinked to original sources

arXiv2026

Surrogate Modeling for Explainable Predictive Time Series Corrections

We introduce a local surrogate approach for explainable time-series forecasting. An initially non-interpretable predictive model to improve the forecast of a classical time-series 'base model' is used. 'Explainability' of the correction is provided by fitting the base model again to the data from which the error prediction is removed (subtracted), yielding a difference in the model parameters which can be interpreted. We provide illustrative examples to demonstrate the potential of the method to discover and explain underlying patterns in the data.

stat.ML↗

arXiv2026

Reinforcement Learning for Accelerated Aerodynamic Shape Optimisation

We introduce a reinforcement learning (RL) based adaptive optimization algorithm for aerodynamic shape optimization focused on dimensionality reduction. The form in which RL is applied here is that of a surrogate-based, actor-critic policy evaluation MCMC approach allowing for temporal 'freezing' of some of the parameters to be optimized. The goals are to minimize computational effort, and to use the observed optimization results for interpretation of the discovered extrema in terms of their role in achieving the desired flow-field. By a sequence of local optimized parameter changes around intermediate CFD simulations acting as ground truth, it is possible to speed up the global optimization if (a) the local neighbourhoods of the parameters in which the changed parameters must reside are sufficiently large to compete with the grid-sized steps and its large number of simulations, and (b) the estimates of the rewards and costs on these neighbourhoods necessary for a good step-wise parameter adaption are sufficiently accurate. We give an example of a simple fluid-dynamical problem on which the method allows interpretation in the sense of a feature importance scoring.

cs.LG↗

arXiv2024

Predictive change point detection for heterogeneous data

A change point detection (CPD) framework assisted by a predictive machine learning model called "Predict and Compare" is introduced and characterised in relation to other state-of-the-art online CPD routines which it outperforms in terms of false positive rate and out-of-control average run length. The method's focus is on improving standard methods from sequential analysis such as the CUSUM rule in terms of these quality measures. This is achieved by replacing typically used trend estimation functionals such as the running mean with more sophisticated predictive models (Predict step), and comparing their prognosis with actual data (Compare step). The two models used in the Predict step are the ARIMA model and the LSTM recursive neural network. However, the framework is formulated in general terms, so as to allow the use of other prediction or comparison methods than those tested here. The power of the method is demonstrated in a tribological case study in which change points separating the run-in, steady-state, and divergent wear phases are detected in the regime of very few false positives.

cs.LG↗

arXiv2023

Explainable AI by BAPC -- Before and After correction Parameter Comparison

A local surrogate for an AI-model correcting a simpler 'base' model is introduced representing an analytical method to yield explanations of AI-predictions. The approach is studied here in the context of the base model being linear regression. The AI-model approximates the residual error of the linear model and the explanations are formulated in terms of the change of the interpretable base model's parameters. Criteria are formulated for the precise relation between lost accuracy of the surrogate, the accuracy of the AI-model, and the surrogate fidelity. It is shown that, assuming a certain maximal amount of noise in the observed data, these criteria induce neighborhoods of the instances to be explained which have an ideal size in terms of maximal accuracy and fidelity.

stat.ML↗

arXiv2020

Graph-based calibration transfer

The problem of transferring calibrations from a primary to a secondary instrument, i.e. calibration transfer (CT), has been a matter of considerable research in chemometrics over the past decades. Current state-of-the-art (SoA) methods like (piecewise) direct standardization perform well when suitable transfer standards are available. However, stable calibration standards that share similar (spectral) features with the calibration samples are not always available. Towards enabling CT with arbitrary calibration standards, we propose a novel CT technique that employs manifold regularization of the partial least squares (PLS) objective. In particular, our method enforces that calibration standards, measured on primary and secondary instruments, have (nearly) invariant projections in the latent variable space of the primary calibration model. Thereby, our approach implicitly removes inter-device variation in the predictive directions of X which is in contrast to most state-of-the-art techniques that employ explicit pre-processing of the input data. We test our approach on the well-known corn benchmark data set employing the NBS glass standard spectra for instrument standardization and compare the results with current SoA methods.

stat.ML↗

arXiv2012

Bounds for the annealed return probability on large finite percolation clusters

Bounds for the expected return probability of the delayed random walk on finite clusters of an invariant percolation on transitive unimodular graphs are derived. They are particularly suited for the case of critical Bernoulli percolation and the associated heavy-tailed cluster size distributions. The upper bound relies on the fact that cartesian products of finite graphs with cycles of a certain minimal size are Hamiltonian. For critical Bernoulli bond percolation on the homogeneous tree this bound is sharp. The asymptotic type of the expected return probability for large times t in this case is of order of the 3/4'th power of 1/t.

math.PR↗

arXiv2012

Random walks on random horospheric products

By developing the entropy theory of random walks on equivalence relations and analyzing the asymptotic geometry of horospheric products we describe the Poisson boundary for random walks on random horospheric products of trees.

math.PR↗

arXiv2009

Stochastic homogenization of horospheric tree products

We construct measures invariant with respect to equivalence relations which are graphed by horospheric products of trees. The construction is based on using conformal systems of boundary measures on treed equivalence relations. The existence of such an invariant measure allows us to establish amenability of horospheric products of random trees.

math.PR↗

arXiv2009

Amenability of horocyclic products of percolation trees

For horocyclic products of percolation subtrees of regular trees, we show almost sure amenability. Under a symmetry condition concerning the growth of the two percolation trees, we show the existence of an increasing Foelner sequence (which we call strong amenability).

math.PR↗

arXiv2008

An interlacing technique for spectra of random walks and its application to finite percolation clusters

A comparison technique for finite random walks on finite graphs is introduced, using the well-known interlacing method. It yields improved return probability bounds. A key feature is the incorporation of parts of the spectrum of the transition matrix other than just the principal eigenvalue. As an application, an upper bound of the expected return probability of a random walk with symmetric transition probabilities is found. In this case, the state space is a random partial graph of a regular graph of bounded geometry and transitive automorphism group. The law of the random edge-set is assumed to be stationary with respect to some transitive subgroup of the automorphism group (`invariant percolation'). Given that this subgroup is unimodular, it is shown that stationarity strengthens the upper bound of the expected return probability, compared with standard bounds derived from the Cheeger inequality.

math.PR↗