Related papers: Asymptotic Supervised Predictive Classifiers under…

In this article, we derive the joint asymptotic distribution of empirical best linear unbiased predictors (EBLUPs) for individual and cell-level random effects in a crossed mixed effect model. Under mild conditions (which include moment…

We introduce the class of synchronous subsequential relations, a subclass of the synchronous relations which embodies some properties of subsequential relations. If we take relations of this class as forming the possible transitions of an…

We give two asymptotic results for the empirical distance covariance on separable metric spaces without any iid assumption on the samples. In particular, we show the almost sure convergence of the empirical distance covariance for any…

Conformal prediction has been a very popular method of distribution-free predictive inference in recent years in machine learning and statistics. Its popularity stems from the fact that it works as a wrapper around any prediction algorithm…

For a class of random partitions of an infinite set a de Finetti-type representation is derived, and in one special case a central limit theorem for the number of blocks is shown.

We present and empirically evaluate an efficient algorithm that learns to aggregate the predictions of an ensemble of binary classifiers. The algorithm uses the structure of the ensemble predictions on unlabeled data to yield significant…

Penalized $M-$estimators for logistic regression models have been previously study for fixed dimension in order to obtain sparse statistical models and automatic variable selection. In this paper, we derive asymptotic results for penalized…

It has been consistently reported that many machine learning models are susceptible to adversarial attacks i.e., small additive adversarial perturbations applied to data points can cause misclassification. Adversarial training using…

We consider the predictive problem of supervised ranking, where the task is to rank sets of candidate items returned in response to queries. Although there exist statistical procedures that come with guarantees of consistency in this…

We present large sample results for partitioning-based least squares nonparametric regression, a popular method for approximating conditional expectation functions in statistics, econometrics, and machine learning. First, we obtain a…

This work presents a new classifier that is specifically designed to be fully interpretable. This technique determines the probability of a class outcome, based directly on probability assignments measured from the training data. The…

Models based on recursive adaptive partitioning such as decision trees and their ensembles are popular for high-dimensional regression as they can potentially avoid the curse of dimensionality. Because empirical risk minimization (ERM) is…

We prove specific biases in the number of occurrences of parts belonging to two different residue classes $a$ and $b$, modulo a fixed non-negative integer $m$, for the sets of unrestricted partitions, partitions into distinct parts, and…

A new equivalence notion between non-stationary subdivision schemes, termed asymptotical similarity, which is weaker than asymptotical equivalence, is introduced and studied. It is known that asymptotical equivalence between a…

In a recent paper, Melbourne and Terhesiu [Operator renewal theory and mixing rates for dynamical systems with infinite measure, Invent. Math. 189 (2012), 61-110] obtained results on mixing and mixing rates for a large class of…

In this article, we construct semiparametrically efficient estimators of linear functionals of a probability measure in the presence of side information using an easy empirical likelihood approach. We use estimated constraint functions and…

We study high-dimensional asymptotic performance limits of binary supervised classification problems where the class conditional densities are Gaussian with unknown means and covariances and the number of signal dimensions scales faster…

State-of-the-art techniques of artificial intelligence, in particular deep learning, are mostly data-driven. However, collecting and manually labeling a large scale dataset is both difficult and expensive. A promising alternative is to…

Providing technologies to communities or domains where training data is scarce or protected e.g., for privacy reasons, is becoming increasingly important. To that end, we generalise methods for unsupervised transfer from multiple input…

Optimal values and solutions of empirical approximations of stochastic optimization problems can be viewed as statistical estimators of their true values. From this perspective, it is important to understand the asymptotic behavior of these…