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We prove semi-empirical concentration inequalities for random variables which are given as possibly nonlinear functions of independent random variables. These inequalities describe concentration of random variable in terms of the…
A sharp, distribution free, non-asymptotic result is proved for the concentration of a random function around the mean function, when the randomization is generated by a finite sequence of independent data and the random functions satisfy…
We present two alternative ways to apply PAC-Bayesian analysis to sequences of dependent random variables. The first is based on a new lemma that enables to bound expectations of convex functions of certain dependent random variables by…
In the PAC-Bayesian literature, the C-Bound refers to an insightful relation between the risk of a majority vote classifier (under the zero-one loss) and the first two moments of its margin (i.e., the expected margin and the voters'…
PAC-Bayes bounds have been proposed to get risk estimates based on a training sample. In this paper the PAC-Bayes approach is combined with stability of the hypothesis learned by a Hilbert space valued algorithm. The PAC-Bayes setting is…
We build a valid p-value based on a concentration inequality for bounded random variables introduced by Pelekis, Ramon and Wang. The motivation behind this work is the calibration of predictive algorithms in a distribution-free setting. The…
Aggregated predictors are obtained by making a set of basic predictors vote according to some weights, that is, to some probability distribution. Randomized predictors are obtained by sampling in a set of basic predictors, according to some…
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…
PAC generalization bounds on the risk, when expressed in terms of the expected loss, are often insufficient to capture imbalances between subgroups in the data. To overcome this limitation, we introduce a new family of risk measures, called…
Rating systems are ubiquitous, with applications ranging from product recommendation to teaching evaluations. Confidence intervals for functionals of rating data such as empirical means or quantiles are critical to decision-making in…
We focus on a stochastic learning model where the learner observes a finite set of training examples and the output of the learning process is a data-dependent distribution over a space of hypotheses. The learned data-dependent distribution…
Covariate balancing is a popular technique for controlling confounding in observational studies. It finds weights for the treatment group which are close to uniform, but make the group's covariate means (approximately) equal to those of the…
We consider the problem of estimating the mean of a sequence of random elements $f(X_1, \theta)$ $, \ldots, $ $f(X_n, \theta)$ where $f$ is a fixed scalar function, $S=(X_1, \ldots, X_n)$ are independent random variables, and $\theta$ is a…
Estimation of the complete distribution of a random variable is a useful primitive for both manual and automated decision making. This problem has received extensive attention in the i.i.d. setting, but the arbitrary data dependent setting…
Accurate estimates of causal effects play a key role in decision-making across applications such as healthcare, economics, and operations. In the absence of randomized experiments, a common approach to estimating causal effects uses…
We introduce a modified version of the excess risk, which can be used to obtain tighter, fast-rate PAC-Bayesian generalisation bounds. This modified excess risk leverages information about the relative hardness of data examples to reduce…
The topics dicussed in this paper take their origin inthe estimation of the Gram matrix of a random vector from a sample made of n independent copies. They comprise the estimation of the covariance matrix and the study of least squares…
The developments of Rademacher complexity and PAC-Bayesian theory have been largely independent. One exception is the PAC-Bayes theorem of Kakade, Sridharan, and Tewari (2008), which is established via Rademacher complexity theory by…
Almost 10 years ago, Impagliazzo and Kabanets (2010) gave a new combinatorial proof of Chernoff's bound for sums of bounded independent random variables. Unlike previous methods, their proof is constructive. This means that it provides an…
Current performance bounds for randomized iterative methods are often considered tight under per-iteration analyses, yet they are notoriously loose in practice. We derive asymptotic performance bounds that narrow this theory-practice gap,…