arXiv subjects

Georgios Gavrilopoulos

Publications and source records attributed to Georgios Gavrilopoulos.

5 recordsLinked to original sources

arXiv2026

Uncertainty quantification for expectation-calibrated predictions

The existing literature on model calibration focuses mainly on classification and probabilistic prediction. In this work, we address calibrated point predictions for the conditional mean. Although existing impossibility results preclude exact out-of-sample calibrated predictions, we develop calibrated confidence intervals that provide uncertainty quantification around such predictions. Our results come with distribution-free theoretical guarantees and are applicable in model-agnostic, finite-sample settings under exchangeability by leveraging conformal prediction. Calibrated confidence intervals rely on a general underlying binning scheme. We present two examples of such a binning scheme, one based on a data-independent partition and the other on isotonic regression. Under structural assumptions, we prove that calibrated confidence intervals based on isotonic regression come with strong asymptotic consistency properties and have an asymptotically vanishing width. We illustrate the empirical performance of our methods by applying them first in a simulated setting and then to a highly imbalanced insurance dataset.

stat.ME↗

arXiv2026

Matrix asymptotic calculus for plug-in maximum likelihood estimators in finite Markov chains

In this work, we develop a unified matrix-level asymptotic calculus for plug-in non-parametric maximum likelihood estimators in finite Markov models. Starting from the asymptotic distribution of the estimated transition matrix, the limiting object is kept in its natural matrix form as a Gaussian random matrix, while the corresponding row-wise vector representation remains immediately available. The main point is that the stochastic constraints of the transition matrix need not be removed by a minimal parametrization: they are carried by the tangent directions and by the covariance structure of the limiting Gaussian matrix, whereas the relevant differentials are computed directly in matrix spaces. A single stochastic calculus theorem gives first-order limit distributions, finite-order developments for sufficiently differentiable functionals, and analytic expansions when the functional is analytic. This provides a common source for asymptotic formulas for matrix powers, stationary characteristics, finite-dimensional curves of Markov characteristics, additive-functional variances, entropy-type quantities and reliability indicators. The resulting covariance operators lead directly to confidence intervals, confidence regions, simultaneous finite-dimensional bands and Wald-type tests. Since the derivations are expressed through matrix products and Kronecker representations rather than coordinate-wise calculations, the method also gives substantial simplifications and, in many cases, computational gains. The second-order terms identify curvature corrections of smooth functionals and provide refined approximations whenever higher-order information is useful.

math.ST↗

arXiv2025

In-sample calibration yields conformal calibration guarantees

Conformal prediction produces a set of predictions that has out-of-sample calibration guarantees by construction, under the assumption of exchangeability. In this work, we study the calibration properties of conformal predictive systems, which issue sets of predictive distributions for real-valued outcomes. We demonstrate that conformal predictive systems implicitly exploit prediction methods that are in-sample calibrated to construct sets that are guaranteed to contain a calibrated predictive distribution out-of-sample. This allows us to take any prediction method that is in-sample calibrated, and conformalize it to obtain a predictive system with out-of-sample calibration guarantees. While the satisfied notion of calibration is typically that prediction intervals derived from the predictive distribution have the correct marginal coverage, we show that this line of reasoning can be extended to stronger conditional notions of calibration that are common in statistical forecasting theory. Using this, we introduce two predictive systems that satisfy stronger out-of-sample calibration guarantees than existing conformal predictive systems. The first method corresponds to a binning of the data, while the second leverages isotonic distributional regression (IDR), a non-parametric distributional regression method under order constraints. We study the theoretical properties of these new predictive systems, and compare their performance in a simulation experiment. They are then applied to two case studies on European temperature forecasts and on predictions for the length of patient stay in Swiss intensive care units. Both approaches are found to outperform existing conformal predictive systems, while conformal IDR additionally provides a natural method for quantifying epistemic uncertainty of the predictions.

stat.ME↗

arXiv2024

Sequential model confidence sets

In most prediction and estimation situations, scientists consider various statistical models for the same problem, and naturally want to select amongst the best. Hansen et al. (2011) provide a powerful solution to this problem by the so-called model confidence set, a subset of the original set of available models that contains the best models with a given level of confidence. Importantly, model confidence sets respect the underlying selection uncertainty by being flexible in size. However, they presuppose a fixed sample size which stands in contrast to the fact that model selection and forecast evaluation are inherently sequential tasks where we successively collect new data and where the decision to continue or conclude a study may depend on the previous outcomes. In this article, we extend model confidence sets sequentially over time by relying on sequential testing methods. Recently, e-processes and confidence sequences have been introduced as new, safe methods for assessing statistical evidence. Sequential model confidence sets allow to continuously monitor the models' performances and come with time-uniform, nonasymptotic coverage guarantees.

stat.ME↗

arXiv2024

A Geometrical Analysis of Kernel Ridge Regression and its Applications

We obtain upper bounds for the estimation error of Kernel Ridge Regression (KRR) for all non-negative regularization parameters, offering a geometric perspective on various phenomena in KRR. As applications: 1. We address the multiple descent problem, unifying the proofs of arxiv:1908.10292 and arxiv:1904.12191 for polynomial kernels and we establish multiple descent for the upper bound of estimation error of KRR under sub-Gaussian design and non-asymptotic regimes. 2. For a sub-Gaussian design vector and for non-asymptotic scenario, we prove a one-sided isomorphic version of the Gaussian Equivalent Conjecture. 3. We offer a novel perspective on the linearization of kernel matrices of non-linear kernel, extending it to the power regime for polynomial kernels. 4. Our theory is applicable to data-dependent kernels, providing a convenient and accurate tool for the feature learning regime in deep learning theory. 5. Our theory extends the results in arxiv:2009.14286 under weak moment assumption. Our proof is based on three mathematical tools developed in this paper that can be of independent interest: 1. Dvoretzky-Milman theorem for ellipsoids under (very) weak moment assumptions. 2. Restricted Isomorphic Property in Reproducing Kernel Hilbert Spaces with embedding index conditions. 3. A concentration inequality for finite-degree polynomial kernel functions.

math.ST↗