Related papers: Generalizations of Maximal Inequalities to Arbitra…
In this paper we propose an optimal predictor of a random variable that has either an infinite mean or an infinite variance. The method consists of transforming the random variable such that the transformed variable has a finite mean and…
We establish empirical risk minimization principles for active learning by deriving a family of upper bounds on the generalization error. Aligning with empirical observations, the bounds suggest that superior query algorithms can be…
We generalize the optimal coupling theorem to multiple random variables: Given a collection of random variables, it is possible to couple all of them so that any two differ with probability comparable to the total-variation distance between…
We employ optimal control theory to study the problem of estimating the probability density function from a data set originating from an unknown probability distribution. The original variational problem is reformulated as a multi-stage…
For a random variable we can define a variational relationship with practical physical meaning as dI=dbar(x)-bar(dx), where I is called as uncertainty measurement. With the help of a generalized definition of expectation,…
The ranking and selection problem is a popular framework in the simulation literature for studying optimal information collection. We study a version of this problem in which the simulation output for each design is normally distributed…
We study a novel problem of fairness in ranking aimed at minimizing the amount of individual unfairness introduced when enforcing group-fairness constraints. Our proposal is rooted in the distributional maxmin fairness theory, which uses…
Maximum likelihood estimation in statistics leads to the problem of maximizing a product of powers of polynomials. We study the algebraic degree of the critical equations of this optimization problem. This degree is related to the number of…
We describe a method to computationally estimate the probability density function of a univariate random variable by applying the maximum entropy principle with some local conditions given by Gaussian functions. The estimation errors and…
Consider an urn filled with balls, each labeled with one of several possible collective decisions. Now, let a random voter draw two balls from the urn and pick her more preferred as the collective decision. Relabel the losing ball with the…
With the emergence of precision medicine, estimating optimal individualized decision rules (IDRs) has attracted tremendous attention in many scientific areas. Most existing literature has focused on finding optimal IDRs that can maximize…
We extend a recently established asymptotic normality theorem for generalized linear mixed models to include the dispersion parameter. The new results show that the maximum likelihood estimators of all model parameters have asymptotically…
This paper shows that the normalized maximum likelihood~(NML) code-length calculated in [1] is an upper bound on the NML code-length strictly calculated for the Gaussian Mixture Model. When we use this upper bound on the NML code-length, we…
The asymptotic normality of the Maximum Likelihood Estimator (MLE) is a long established result. Explicit bounds for the distributional distance between the distribution of the MLE and the normal distribution have recently been obtained for…
We define the min-min expectation selection problem (resp. max-min expectation selection problem) to be that of selecting k out of n given discrete probability distributions, to minimize (resp. maximize) the expectation of the minimum value…
We study two-sample variable selection: identifying variables that discriminate between the distributions of two sets of data vectors. Such variables help scientists understand the mechanisms behind dataset discrepancies. Although…
The goal of regression and classification methods in supervised learning is to minimize the empirical risk, that is, the expectation of some loss function quantifying the prediction error under the empirical distribution. When facing scarce…
The problem of simple $M-$ary hypothesis testing under a generic performance criterion that depends on arbitrary functions of error probabilities is considered. Using results from convex analysis, it is proved that an optimal decision rule…
In this article, we study rates of convergence of the generalization error of multi-class margin classifiers. In particular, we develop an upper bound theory quantifying the generalization error of various large margin classifiers. The…
We introduce a general class of algorithms and supply a number of general results useful for analysing these algorithms when applied to regular graphs of large girth. As a result, we can transfer a number of results proved for random…