Related papers: A Bennett Inequality for the Missing Mass

Imbalance learning is a subfield of machine learning that focuses on learning tasks in the presence of class imbalance. Nearly all existing studies refer to class imbalance as a proportion imbalance, where the proportion of training samples…

Let $T$ be a general sampling statistic that can be written as a linear statistic plus an error term. Uniform and non-uniform Berry--Esseen type bounds for $T$ are obtained. The bounds are the best possible for many known statistics.…

We introduce Minimal Achievable Sufficient Statistic (MASS) Learning, a training method for machine learning models that attempts to produce minimal sufficient statistics with respect to a class of functions (e.g. deep networks) being…

Learning unbiased models on imbalanced datasets is a significant challenge. Rare classes tend to get a concentrated representation in the classification space which hampers the generalization of learned boundaries to new test examples. In…

We derive simple concentration inequalities for bounded random vectors, which generalize Hoeffding's inequalities for bounded scalar random variables. As applications, we apply the general results to multinomial and Dirichlet distributions…

We prove a Bennett-type concentration bound for suprema of empirical processes based on sampling without replacement and a corresponding bound in the case of an arbitrary Hoeffding statistics. We improve on the previous results of such…

This article studies the achievable guarantees on the error rates of certain learning algorithms, with particular focus on refining logarithmic factors. Many of the results are based on a general technique for obtaining bounds on the error…

We investigate the asymptotic normality of the posterior distribution in the discrete setting, when model dimension increases with sample size. We consider a probability mass function $\theta_0$ on $\mathbbm{N}\setminus \{0\}$ and a…

We extend Fano's inequality, which controls the average probability of events in terms of the average of some $f$--divergences, to work with arbitrary events (not necessarily forming a partition) and even with arbitrary $[0,1]$--valued…

Missing data is a common issue in many biomedical studies. Under a paired design, some subjects may have missing values in either one or both of the conditions due to loss of follow-up, insufficient biological samples, etc. Such partially…

We extend a general Bernstein-type maximal inequality of Kevei and Mason (2011) for sums of random variables.

This paper is devoted to establishing exponential bounds for the probabilities of deviation of a sample sum from its expectation, when the variables involved in the summation are obtained by sampling in a finite population according to a…

An infinite urn scheme is defined by a probability mass function $(p_j)_{j\geq1}$ over positive integers. A random allocation consists of a sample of $N$ independent drawings according to this probability distribution where $N$ may be…

We show sharp bounds for probabilities of large deviations for sums of independent random variables satisfying Bernstein's condition. One such bound is very close to the tail of the standard Gaussian law in certain case; other bounds…

The article is devoted to the problem of small learning samples in machine learning. The flaws of maximum likelihood learning and minimax learning are looked into and the concept of minimax deviation learning is introduced that is free of…

While tasks could come with varying the number of instances and classes in realistic settings, the existing meta-learning approaches for few-shot classification assume that the number of instances per task and class is fixed. Due to such…

We give the proof of a tight lower bound on the probability that a binomial random variable exceeds its expected value. The inequality plays an important role in a variety of contexts, including the analysis of relative deviation bounds in…

We develop novel empirical Bernstein inequalities for the variance of bounded random variables. Our inequalities hold under constant conditional variance and mean, without further assumptions like independence or identical distribution of…

A learning algorithm referred to as Maximum Margin (MM) is proposed for considering the class-imbalance data learning issue: the trained model tends to predict the majority of classes rather than the minority ones. That is, underfitting for…

The sample compression theory provides generalization guarantees for predictors that can be fully defined using a subset of the training dataset and a (short) message string, generally defined as a binary sequence. Previous works provided…