Related papers: Validation design I: construction of validation de…
While many statistical models and methods are now available for network analysis, resampling network data remains a challenging problem. Cross-validation is a useful general tool for model selection and parameter tuning, but is not directly…
Model checking plays an important role in linear regression as model misspecification seriously affects the validity and efficiency of regression analysis. In practice, model checking is often performed by subjectively evaluating the plot…
The construction of computer models (mathematical models implemented in computer codes), with respect to observed phenomena, is usually undertaken by building different variants depending on modeller sensibility, and choosing the one…
The paper addresses the problem of defining families of ordered sequences $\{x_i\}_{i\in N}$ of elements of a compact subset $X$ of $R^d$ whose prefixes $X_n=\{x_i\}_{i=1}^{n}$, for all orders $n$, have good space-filling properties as…
We propose novel kernel-based tests for assessing the equivalence between distributions. Traditional goodness-of-fit testing is inappropriate for concluding the absence of distributional differences, because failure to reject the null…
When validated neural networks (NNs) are pruned (and retrained) before deployment, it is desirable to prove that the new NN behaves equivalently to the (original) reference NN. To this end, our paper revisits the idea of differential…
For large classes of group testing problems, we derive lower bounds for the probability that all significant items are uniquely identified using specially constructed random designs. These bounds allow us to optimize parameters of the…
A new goodness-of-fit test for normality in high-dimension (and Reproducing Kernel Hilbert Space) is proposed. It shares common ideas with the Maximum Mean Discrepancy (MMD) it outperforms both in terms of computation time and applicability…
We discuss, and give examples of, methods for randomly implementing some minimax robust designs from the literature. These have the advantage, over their deterministic counterparts, of having bounded maximum loss in large and very rich…
Quantum program generation demands a level of precision that may not be compatible with the statistical reasoning carried out in the inference of large language models (LLMs). Hallucinations are mathematically inevitable and not addressable…
The objective of this research is the development of a practical system to manipulate and validate software package specifications. The validation process developed is based on consistency checks. Furthermore, by means of scenarios, the…
A key issue of current quantum advantage experiments is that their verification requires a full classical simulation of the ideal computation. This limits the regime in which the experiments can be verified to precisely the regime in which…
Selective inference aims at providing valid inference after a data-driven selection of models or hypotheses. It is essential to avoid overconfident results and replicability issues. While significant advances have been made in this area for…
Cross-validation is a useful and generally applicable technique often employed in machine learning, including decision tree induction. An important disadvantage of straightforward implementation of the technique is its computational…
Support vector machines (SVMs) are special kernel based methods and belong to the most successful learning methods since more than a decade. SVMs can informally be described as a kind of regularized M-estimators for functions and have…
This paper introduces the Quantum Covariance Embedding, which embeds Positive Operator-Valued Measures into a tensor product of a Reproducing Kernel Hilbert Space and the quantum state space via a tensorized Bochner integral. This…
Support vector machine (SVM) is a well-known statistical technique for classification problems in machine learning and other fields. An important question for SVM is the selection of covariates (or features) for the model. Many studies have…
A new method of bandwidth selection for kernel density estimators is proposed. The method, termed indirect cross-validation, or ICV, makes use of so-called selection kernels. Least squares cross-validation (LSCV) is used to select the…
This paper is concerned with the approximation of a function $u$ in a given approximation space $V_m$ of dimension $m$ from evaluations of the function at $n$ suitably chosen points. The aim is to construct an approximation of $u$ in $V_m$…
Kernel density estimation (KDE) is integral to a range of generative and discriminative tasks in machine learning. Drawing upon tools from the multidimensional calculus of variations, we derive an optimal weight function that reduces bias…