arXiv subjects

Laura Lützow

Publications and source records attributed to Laura Lützow.

5 recordsLinked to original sources

arXiv2026

Multi-Variable Conformal Prediction: Optimizing Prediction Sets without Data Splitting

Conformal prediction constructs prediction sets with finite-sample coverage guarantees, but its calibration stage is structurally constrained to a scalar score function and a single threshold variable - forcing shapes of prediction sets to be fixed before calibration, typically through data splitting. We introduce multi-variable conformal prediction (MCP), a framework that extends conformal prediction to vector-valued score functions with multiple simultaneous calibration variables. Building on scenario theory as a principled framework for certifying data-driven decisions, MCP unifies prediction set design and calibration into a single optimization problem, eliminating data splitting without sacrificing coverage guarantees. We propose two computationally efficient variants: RemMCP, grounded in constrained optimization with constraint removal, which admits a clean generalization of split conformal prediction; and RelMCP, based on iterative optimization with constraint relaxation, which supports non-convex score functions at the cost of possibly greater conservatism. Through numerical experiments on ellipsoidal and multi-modal prediction sets, we demonstrate that RemMCP and RelMCP consistently meet the target coverage with prediction set sizes smaller than or comparable to those of baselines with data split, while considerably reducing variance across calibration runs - a direct consequence of using all available data for shape optimization and calibration simultaneously.

stat.ML↗

arXiv2026

Zono-Conformal Prediction: Zonotope-Based Uncertainty Quantification for Regression and Classification Tasks

Conformal prediction is a popular uncertainty quantification method that augments a base predictor to return sets of predictions with statistically valid coverage guarantees. However, current methods are often computationally expensive and data-intensive, as they require constructing an uncertainty model before calibration. Moreover, existing approaches typically represent the prediction sets with intervals, which limits their ability to capture dependencies in multi-dimensional outputs. We address these limitations by introducing zono-conformal prediction, a novel approach inspired by interval predictor models and reachset-conformant identification that constructs prediction zonotopes with assured coverage. By placing zonotopic uncertainty sets directly into the model of the base predictor, zono-conformal predictors can be identified via a single, data-efficient linear program. While we can apply zono-conformal prediction to arbitrary nonlinear base predictors, we focus on feed-forward neural networks in this work. Aside from regression tasks, we also construct optimal zono-conformal predictors in classification settings where the output of an uncertain predictor is a set of possible classes. We provide probabilistic coverage guarantees and present methods for detecting outliers in the identification data. In extensive numerical experiments, we show that zono-conformal predictors are less conservative than interval predictor models and standard conformal prediction methods, while achieving a similar coverage over the test data.

cs.LG↗

arXiv2025

Reachset-Conformant System Identification

Formal verification techniques play a pivotal role in ensuring the safety of complex cyber-physical systems. To transfer model-based verification results to the real world, we require that the measurements of the target system lie in the set of reachable outputs of the corresponding model, a property we refer to as reachset conformance. This paper is on automatically identifying those reachset-conformant models. While state-of-the-art reachset-conformant identification methods focus on linear state-space models, we generalize these methods to nonlinear state-space models and linear and nonlinear input-output models. Furthermore, our identification framework adapts to different levels of prior knowledge on the system dynamics. In particular, we identify the set of model uncertainties for white-box models, the parameters and the set of model uncertainties for gray-box models, and entire reachset-conformant black-box models from data. The robustness and efficacy of our framework are demonstrated in extensive numerical experiments using simulated and real-world data.

eess.SY↗

arXiv2023

Reachability Analysis of ARMAX Models

Reachability analysis is a powerful tool for computing the set of states or outputs reachable for a system. While previous work has focused on systems described by state-space models, we present the first methods to compute reachable sets of ARMAX models - one of the most common input-output models originating from data-driven system identification. The first approach we propose can only be used with dependency-preserving set representations such as symbolic zonotopes, while the second one is valid for arbitrary set representations but relies on a reformulation of the ARMAX model. By analyzing the computational complexities, we show that both approaches scale quadratically with respect to the time horizon of the reachability problem when using symbolic zonotopes. To reduce the computational complexity, we propose a third approach that scales linearly with respect to the time horizon when using set representations that are closed under Minkowski addition and linear transformation and that satisfy that the computational complexity of the Minkowski sum is independent of the representation size of the operands. Our numerical experiments demonstrate that the reachable sets of ARMAX models are tighter than the reachable sets of equivalent state space models in case of unknown initial states. Therefore, this methodology has the potential to significantly reduce the conservatism of various verification techniques.

eess.SY↗

arXiv2023

Density Planner: Minimizing Collision Risk in Motion Planning with Dynamic Obstacles using Density-based Reachability

Uncertainty is prevalent in robotics. Due to measurement noise and complex dynamics, we cannot estimate the exact system and environment state. Since conservative motion planners are not guaranteed to find a safe control strategy in a crowded, uncertain environment, we propose a density-based method. Our approach uses a neural network and the Liouville equation to learn the density evolution for a system with an uncertain initial state. We can plan for feasible and probably safe trajectories by applying a gradient-based optimization procedure to minimize the collision risk. We conduct motion planning experiments on simulated environments and environments generated from real-world data and outperform baseline methods such as model predictive control and nonlinear programming. While our method requires offline planning, the online run time is 100 times smaller compared to model predictive control.

cs.RO↗