Incomplete Generalized U-Statistics for Food Risk Assessment

Incomplete generalized U-statistics for food risk assessment.

This article proposes statistical tools for quantitative evaluation of the risk due to the presence of some particular contaminants in food. We focus on the estimation of the probability of the exposure to exceed the so-called provisional tolerable weekly intake (PTWI), when both consumption data and contamination data are independently available. A Monte Carlo approximation of the plug-in esti...

Scaling-up Empirical Risk Minimization: Optimization of Incomplete $U$-statistics

In a wide range of statistical learning problems such as ranking, clustering or metric learning among others, the risk is accurately estimated by U-statistics of degree d ≥ 1, i.e. functionals of the training data with low variance that take the form of averages over k-tuples. From a computational perspective, the calculation of such statistics is highly expensive even for a moderate sample siz...

Weak Convergence of Generalized U - Statistics

SGD Algorithms based on Incomplete U-statistics: Large-Scale Minimization of Empirical Risk

In many learning problems, ranging from clustering to ranking through metric learning, empirical estimates of the risk functional consist of an average over tuples (e.g., pairs or triplets) of observations, rather than over individual observations. In this paper, we focus on how to best implement a stochastic approximation approach to solve such risk minimization problems. We argue that in the ...

Maximal Deviations of Incomplete U-statistics with Applications to Empirical Risk Sampling

It is the goal of this paper to extend the Empirical Risk Minimization (ERM) paradigm, from a practical perspective, to the situation where a natural estimate of the risk is of the form of a K-sample U -statistics, as it is the case in the K-partite ranking problem for instance. Indeed, the numerical computation of the empirical risk is hardly feasible if not infeasible, even for moderate sampl...