Related papers: Concentration inequalities for leave-one-out cross…
This study's first purpose is to provide quantitative evidence that would incentivize researchers to instead use the more robust method of nested cross-validation. The second purpose is to present methods and MATLAB codes for doing power…
This work performs a non-asymptotic analysis of the generalized Lasso under the assumption of sub-exponential data. Our main results continue recent research on the benchmark case of (sub-)Gaussian sample distributions and thereby explore…
This paper considers extensions of minimum-disparity estimators to the problem of estimating parameters in a regression model that is conditionally specified; that is where a parametric model describes the distribution of a response $y$…
We study the problem of estimating a distribution over a finite alphabet from an i.i.d. sample, with accuracy measured in relative entropy (Kullback-Leibler divergence). While optimal bounds on the expected risk are known, high-probability…
In this paper we consider the stability issue for the inverse problem of determining an unknown inclusion contained in an elastic body by all the pairs of measurements of displacement and traction taken at the boundary of the body. Both the…
We address the construction of stable random matrix ensembles as the generalization of the stable random variables (Levy distributions). With a simple method we derive the Cauchy case, which is known to have remarkable properties. These…
Linear systems governed by continuous-time difference equations cover a wide class of linear systems. From the Lyapunov-Krasovskii approach, we investigate stability for such a class of systems. Sufficient conditions, and in some particular…
The cross entropy loss is widely used due to its effectiveness and solid theoretical grounding. However, as training progresses, the loss tends to focus on hard to classify samples, which may prevent the network from obtaining gains in…
We consider stability analysis of constrained switching linear systems in which the dynamics is unknown and whose switching signal is constrained by an automaton. We propose a data-driven Lyapunov framework for providing probabilistic…
We establish a general upper bound for $K$-fold cross-validation ($K$-CV) errors that can be adapted to many $K$-CV-based estimators and learning algorithms. Based on Rademacher complexity of the model and the Orlicz-$\Psi_{\nu}$ norm of…
We treat the stability of determining the boundary impedance of an obstacle by scattering data, with a single incident field. A previous result by Sincich (SIAM J. Math. Anal. 38, (2006), 434-451) showed a log stability when the boundary of…
Reinforcement Learning (RL) has achieved remarkable success in safety-critical areas, but it can be weakened by adversarial attacks. Recent studies have introduced "smoothed policies" in order to enhance its robustness. Yet, it is still…
Recent advances in center-based clustering continue to improve upon the drawbacks of Lloyd's celebrated $k$-means algorithm over $60$ years after its introduction. Various methods seek to address poor local minima, sensitivity to outliers,…
This paper uses the notion of algorithmic stability to derive novel generalization bounds for several families of transductive regression algorithms, both by using convexity and closed-form solutions. Our analysis helps compare the…
We describe a fast computation method for leave-one-out cross-validation (LOOCV) for $k$-nearest neighbours ($k$-NN) regression. We show that, under a tie-breaking condition for nearest neighbours, the LOOCV estimate of the mean square…
Current PAC-Bayes generalisation bounds are restricted to scalar metrics of performance, such as the loss or error rate. However, one ideally wants more information-rich certificates that control the entire distribution of possible…
Calibration and uncertainty estimation are crucial topics in high-risk environments. We introduce a new diversity regularizer for classification tasks that uses out-of-distribution samples and increases the overall accuracy, calibration and…
A general framework is that the estimators of a distribution are obtained by minimizing a function (the estimating function) and they are assessed through another function (the assessment function). The estimating and assessment functions…
We test a crossing orbit stability criterion for eccentric planetary systems, based on Wisdom's criterion of first order mean motion resonance overlap (Wisdom, 1980). We show that this criterion fits the stability regions in real exoplanet…
Concentration inequalities quantify the deviation of a random variable from a fixed value. In spite of numerous applications, such as opinion surveys or ecological counting procedures, few concentration results are known for the setting of…