Related papers: Learning discrete distributions with infinite supp…

The aim of this paper is to provide several novel upper bounds on the excess risk with a primal focus on classification problems. We suggest two approaches and the obtained bounds are represented via the distribution dependent local…

We consider a distributionally robust formulation of stochastic optimization problems arising in statistical learning, where robustness is with respect to uncertainty in the underlying data distribution. Our formulation builds on…

We consider the problem of hypothesis testing for discrete distributions. In the standard model, where we have sample access to an underlying distribution $p$, extensive research has established optimal bounds for uniformity testing,…

We consider the following basic learning task: given independent draws from an unknown distribution over a discrete support, output an approximation of the distribution that is as accurate as possible in $\ell_1$ distance (i.e. total…

We consider a linear model where the coefficients - intercept and slopes - are random with a law in a nonparametric class and independent from the regressors. Identification often requires the regressors to have a support which is the whole…

We introduce methods to bound the mean of a discrete distribution (or finite population) based on sample data, for random variables with a known set of possible values. In particular, the methods can be applied to categorical data with…

We introduce the concept of an extremely negatively dependent (END) sequence of random variables with a given common marginal distribution. The END structure, as a new benchmark for negative dependence, is comparable to comonotonicity and…

We address the problem of producing a lower bound for the mean of a discrete probability distribution, with known support over a finite set of real numbers, from an iid sample of that distribution. Up to a constant, this is equivalent to…

In this paper we develop a very general class of bivariate discrete distributions. The basic idea is very simple. The marginals are obtained by taking the random geometric sum of a baseline distribution function. The proposed class of…

We consider the problem of the estimation of the invariant distribution function of an ergodic diffusion process when the drift coefficient is unknown. The empirical distribution function is a natural estimator which is unbiased, uniformly…

Data-driven risk analysis involves the inference of probability distributions from measured or simulated data. In the case of a highly reliable system, such as the electricity grid, the amount of relevant data is often exceedingly limited,…

We develop a general technique for bounding the tail of the total variation distance between the empirical and the true distributions over countable sets. Our methods sharpen a deviation bound of Devroye (1983) for distributions over finite…

It is shown that at least 50% of the probability mass of a sum of independent Rademacher random variables is within one standard deviation from its mean. This lower bound is sharp, it is much better than for instance the bound that can be…

This paper establishes bounds on the performance of empirical risk minimization for large-dimensional linear regression. We generalize existing results by allowing the data to be dependent and heavy-tailed. The analysis covers both the…

Uniform deviation bounds limit the difference between a model's expected loss and its loss on an empirical sample uniformly for all models in a learning problem. As such, they are a critical component to empirical risk minimization. In this…

This paper proposes a statistically optimal approach for learning a function value using a confidence interval in a wide range of models, including general non-parametric estimation of an expected loss described as a stochastic programming…

We consider a general statistical learning problem where an unknown fraction of the training data is corrupted. We develop a robust learning method that only requires specifying an upper bound on the corrupted data fraction. The method…

We derive distributional limits for empirical transport distances between probability measures supported on countable sets. Our approach is based on sensitivity analysis of optimal values of infinite dimensional mathematical programs and a…

We consider noisy observations of a distribution with unknown support. In the deconvolution model, it has been proved recently [19] that, under very mild assumptions, it is possible to solve the deconvolution problem without knowing the…

Model risk measures consequences of choosing a model in a class of possible alternatives. We find analytical and simulated bounds for payoff functions on classes of plausible alternatives of a given discrete model. We measure the impact of…