arXiv subjects

Johan Hallberg Szabadváry

Publications and source records attributed to Johan Hallberg Szabadváry.

7 recordsLinked to original sources

arXiv2026

Betting on Moments: Legendre Jumper Martingales for Online Exchangeability Testing

A fundamental assumption in statistics and machine learning is that ``the future looks like the past,'' formalized as exchangeability: the joint data distribution is order-invariant. In practice, this assumption is often violated due to distribution shifts over time. Early detection of exchangeability violations is crucial to prevent performance degradation and enable timely interventions like model retraining. Conformal test martingales offer a flexible, distribution-free framework for sequential exchangeability testing with guaranteed false-alarm rate control by betting against the uniformity of conformal p-values. While alternatives such as plug-in martingales and mixture-based strategies exist, computationally efficient baselines like the Simple Jumper are limited to detecting mean location shifts. We propose a family of conformal test martingales based on shifted Legendre polynomials that extend the Simple Jumper to higher-order moments. The Simple Legendre Jumper replaces linear betting functions with polynomials of arbitrary degree, enabling rapid detection of variance, skewness, and other higher-order deviations. The Product Legendre Jumper combines multiple polynomial degrees into a single betting function but suffers from exponential state-space growth, termed the jumping tax. To resolve this, we introduce the Variational Legendre Jumper, which employs a mean-field approximation to reduce complexity to constant time per step with minimal power loss, providing an expressive, scalable framework for real-time distribution shift monitoring.

stat.ML↗

arXiv2026

A Fast, Closed-Form Bandwidth Selector for the Beta Kernel Density Estimator

The Beta kernel estimator offers a theoretically superior alternative to the Gaussian kernel for unit interval data, eliminating boundary bias without requiring reflection or transformation. However, its adoption remains limited by the lack of a reliable bandwidth selector; practitioners currently rely on iterative optimization methods that are computationally expensive and prone to instability. We derive the ``Beta Reference Rule,'' a fast, closed-form bandwidth selector based on the unweighted Asymptotic Mean Integrated Squared Error (AMISE) of a beta reference distribution. To address boundary integrability issues, we introduce a principled heuristic for U-shaped and J-shaped distributions. By employing a method-of-moments approximation, we reduce the bandwidth selection complexity from iterative optimization to $\mathcal{O}(1)$. Extensive Monte Carlo simulations demonstrate that our rule matches the accuracy of numerical optimization while delivering a speedup of over 35,000 times. Real-world validation on socioeconomic data shows that it avoids the ``vanishing boundary'' and ``shoulder'' artifacts common to Gaussian-based methods. We provide a comprehensive, open-source Python package to facilitate the immediate adoption of the Beta kernel as a drop-in replacement for standard density estimation tools.

stat.ME↗

arXiv2026

Conformal Blindness: A Note on $A$-Cryptic change-points

Conformal Test Martingales (CTMs) are a standard method within the Conformal Prediction framework for testing the crucial assumption of data exchangeability by monitoring deviations from uniformity in the p-value sequence. Although exchangeability implies uniform p-values, the converse does not hold. This raises the question of whether a significant break in exchangeability can occur, such that the p-values remain uniform, rendering CTMs blind. We answer this affirmatively, demonstrating the phenomenon of \emph{conformal blindness}. Through explicit construction, for the theoretically ideal ``predictive oracle'' conformity measure (given by the true conditional density), we demonstrate the possibility of an \emph{$A$-cryptic change-point} (where $A$ refers to the conformity measure). Using bivariate Gaussian distributions, we identify a line along which a change in the marginal means does not alter the distribution of the conformity scores, thereby producing perfectly uniform p-values. Simulations confirm that even a massive distribution shift can be perfectly cryptic to the CTM, highlighting a fundamental limitation and emphasising the critical role of the alignment of the conformity measure with potential shifts. By contrasting the predictive oracle with recent results on detection-optimal scores, we emphasise that validity monitoring in safety-critical systems requires careful separation of predictive and diagnostic goals.

stat.ML↗

arXiv2025

Classification with Reject Option: Distribution-free Error Guarantees via Conformal Prediction

Machine learning (ML) models always make a prediction, even when they are likely to be wrong. This causes problems in practical applications, as we do not know if we should trust a prediction. ML with reject option addresses this issue by abstaining from making a prediction if it is likely to be incorrect. In this work, we formalise the approach to ML with reject option in binary classification, deriving theoretical guarantees on the resulting error rate. This is achieved through conformal prediction (CP), which produce prediction sets with distribution-free validity guarantees. In binary classification, CP can output prediction sets containing exactly one, two or no labels. By accepting only the singleton predictions, we turn CP into a binary classifier with reject option. Here, CP is formally put in the framework of predicting with reject option. We state and prove the resulting error rate, and give finite sample estimates. Numerical examples provide illustrations of derived error rate through several different conformal prediction settings, ranging from full conformal prediction to offline batch inductive conformal prediction. The former has a direct link to sharp validity guarantees, whereas the latter is more fuzzy in terms of validity guarantees but can be used in practice. Error-reject curves illustrate the trade-off between error rate and reject rate, and can serve to aid a user to set an acceptable error rate or reject rate in practice.

stat.ML↗

arXiv2025

Beyond Conformal Predictors: Adaptive Conformal Inference with Confidence Predictors

Adaptive Conformal Inference (ACI) provides finite-sample coverage guarantees, enhancing the prediction reliability under non-exchangeability. This study demonstrates that these desirable properties of ACI do not require the use of Conformal Predictors (CP). We show that the guarantees hold for the broader class of confidence predictors, defined by the requirement of producing nested prediction sets, a property we argue is essential for meaningful confidence statements. We empirically investigate the performance of Non-Conformal Confidence Predictors (NCCP) against CP when used with ACI on non-exchangeable data. In online settings, the NCCP offers significant computational advantages while maintaining a comparable predictive efficiency. In batch settings, inductive NCCP (INCCP) can outperform inductive CP (ICP) by utilising the full training dataset without requiring a separate calibration set, leading to improved efficiency, particularly when the data are limited. Although these initial results highlight NCCP as a theoretically sound and practically effective alternative to CP for uncertainty quantification with ACI in non-exchangeable scenarios, further empirical studies are warranted across diverse datasets and predictors.

stat.ML↗

arXiv2024

Adaptive Conformal Inference for Multi-Step Ahead Time-Series Forecasting Online

The aim of this paper is to propose an adaptation of the well known adaptive conformal inference (ACI) algorithm to achieve finite-sample coverage guarantees in multi-step ahead time-series forecasting in the online setting. ACI dynamically adjusts significance levels, and comes with finite-sample guarantees on coverage, even for non-exchangeable data. Our multi-step ahead ACI procedure inherits these guarantees at each prediction step, as well as for the overall error rate. The multi-step ahead ACI algorithm can be used with different target error and learning rates at different prediction steps, which is illustrated in our numerical examples, where we employ a version of the confromalised ridge regression algorithm, adapted to multi-input multi-output forecasting. The examples serve to show how the method works in practice, illustrating the effect of variable target error and learning rates for different prediction steps, which suggests that a balance may be struck between efficiency (interval width) and coverage.t

stat.ML↗

arXiv2021

On qualitative analysis of a discrete time SIR epidemical model

The main purpose of this paper is to study the local dynamics and bifurcations of a discrete-time SIR epidemiological model. The existence and stability of disease-free and endemic fixed points are investigated along with a fairly complete classification of the systems bifurcations, in particular, a complete analysis on local stability and codimension 1 bifurcations in the parameter space. Sufficient conditions for positive trajectories are given. The existence of a 3-cycle is shown, which implies the existence of cycles of arbitrary length by the celebrated Sharkovskii's theorem. Generacity of some bifurcations is examined both analytically and through numerical computations. Bifurcation diagrams along with numerical simulations are presented. The system turns out to have both rich and interesting dynamics.

math.DS↗