Related papers: Concentration inequalities for leave-one-out cross…
In this article we develop a tractable procedure for testing strict stationarity in a double autoregressive model and formulate the problem as testing if the top Lyapunov exponent is negative. Without strict stationarity assumption, we…
Consider the following class of learning schemes: \begin{equation} \label{eq:main-problem1} \hat{\boldsymbol{\beta}} := \underset{\boldsymbol{\beta} \in \mathcal{C}}{\arg\min} \;\sum_{j=1}^n \ell(\boldsymbol{x}_j^\top\boldsymbol{\beta};…
The popular LSPE($\lambda$) algorithm for policy evaluation is revisited to derive a concentration bound that gives high probability performance guarantees from some time on.
When probabilistic classifiers are trained and calibrated, the so-called grouping loss component of the calibration loss can easily be overlooked. Grouping loss refers to the gap between observable information and information actually…
This paper provides the relevant literature with a complete toolkit for conducting robust estimation and inference about the parameters of interest involved in a high-dimensional panel data framework. Specifically, (1) we allow for…
We study in this paper stability estimates for the fault inverse problem. In this problem, faults are assumed to be planar open surfaces in a half space elastic medium with known Lam\'e coefficients. A traction free condition is imposed on…
Cross-validation is one of the most widely used methods for model selection and evaluation; its efficiency for large covariance matrix estimation appears robust in practice, but little is known about the theoretical behavior of its error.…
Cross validation is a central tool in evaluating the performance of machine learning and statistical models. However, despite its ubiquitous role, its theoretical properties are still not well understood. We study the asymptotic properties…
Concentration inequalities are fundamental tools in probabilistic combinatorics and theoretical computer science for proving that random functions are near their means. Of particular importance is the case where f(X) is a function of…
We present an extension to the robust phase estimation protocol, which can identify incorrect results that would otherwise lie outside the expected statistical range. Robust phase estimation is increasingly a method of choice for…
Lasso and other regularization procedures are attractive methods for variable selection, subject to a proper choice of shrinkage parameter. Given a set of potential subsets produced by a regularization algorithm, a consistent model…
We consider comparisons of statistical learning algorithms using multiple data sets, via leave-one-in cross-study validation: each of the algorithms is trained on one data set; the resulting model is then validated on each remaining data…
A crucial part of data analysis is the validation of the resulting estimators, in particular, if several competing estimators need to be compared. Whether an estimator can be objectively validated is not a trivial property. If there exists…
We make two contributions to the problem of estimating the $L_1$ calibration error of a binary classifier from a finite dataset. First, we provide an upper bound for any classifier where the calibration function has bounded variation.…
A major problem in solving multi-waves inverse problems is the presence of critical points where the collected data completely vanishes. The set of these critical points depend on the choice of the boundary conditions, and can be directly…
Algorithmic stability is a key characteristic to ensure the generalization ability of a learning algorithm. Among different notions of stability, \emph{uniform stability} is arguably the most popular one, which yields exponential…
We derive a reliable a posteriori error estimate for a cell-centered finite volume scheme approximating a cross-diffusion system modeling ion transport through nanopores. To this end, we derive a stability framework that is independent of…
Given a controlled diffusion and a connected, bounded, Lipschitz set, when is it possible to guarantee controlled set invariance with probability one? In this work, we answer this question by deriving the necessary and sufficient conditions…
In this paper, we introduce the notion of boundary delay equations, establishing a unified framework for analyzing linear time-invariant systems with pure time-delayed boundary conditions. We establish mild sufficient conditions for the…
In threshold-based anomaly detection, we want to tune the threshold of a detector to achieve an acceptable false alarm rate. However, tuning the threshold is often a non-trivial task due to unknown detector output distributions. A detector…