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Researchers increasingly have access to two types of data: (i) large observational datasets where treatment (e.g., class size) is not randomized but several primary outcomes (e.g., graduation rates) and secondary outcomes (e.g., test…
Probabilities of causation play a crucial role in modern decision-making. Pearl defined three binary probabilities of causation, the probability of necessity and sufficiency (PNS), the probability of sufficiency (PS), and the probability of…
We find the value of constants related to constraints in characterization of some known statistical distributions and then we proceed to use the idea behind maximum entropy principle to derive generalized version of this distributions using…
We prove large deviation principles for the distribution of the empirical measure of the eigenvalues of Lax matrices following the Generalized Gibbs ensembles of the classical Toda chain introduced in [10]. We deduce the almost sure…
We discuss the possibilities and limitations of estimating the mean of a real-valued random variable from independent and identically distributed observations from a non-asymptotic point of view. In particular, we define estimators with a…
While statistics focusses on hypothesis testing and on estimating (properties of) the true sampling distribution, in machine learning the performance of learning algorithms on future data is the primary issue. In this paper we bridge the…
This paper is motivated by an astonishing result of H. Alzer and S. Ruscheweyh published in 2001 in the Proc. Amer. Math. Soc., which states that the intersection of the classes two-variable Gini means and Stolarsky means is equal to the…
Estimation of mutual information between (multidimensional) real-valued variables is used in analysis of complex systems, biological systems, and recently also quantum systems. This estimation is a hard problem, and universally good…
This paper introduces a novel concept of interval probability measures that enables the representation of imprecise probabilities, or uncertainty, in a natural and coherent manner. Within an algebra of sets, we introduce a notion of weak…
The present work provides a systematic approach for the design of sampled-data observers to a wide class of 1-D, parabolic PDEs with non-local outputs. The studied class of parabolic PDEs allows the presence of globally Lipschitz nonlinear…
We use bias-reduced estimators of high quantiles, of heavy-tailed distributions, to introduce a new estimator of the mean in the case of infinite second moment. The asymptotic normality of the proposed estimator is established and checked,…
We propose a framework to analyze and quantify the bias in adaptive data analysis. It generalizes that proposed by Russo and Zou'15, applying to measurements whose moment generating function exists, measurements with a finite $p$-norm, and…
Motivated by real-world machine learning applications, we consider a statistical classification task in a sequential setting where test samples arrive sequentially. In addition, the generating distributions are unknown and only a set of…
Several new estimation methods have been recently proposed for the linear regression model with observation error in the design. Different assumptions on the data generating process have motivated different estimators and analysis. In…
The complete group classification problem for the class of (1+1)-dimensional $r$th order general variable-coefficient Burgers-Korteweg-de Vries equations is solved for arbitrary values of $r$ greater than or equal to two. We find the…
The aim of this article is to introduce the Kantorovich form of generalized Szasz-type operators involving Charlier polynomials with certain parameters. In this paper we discussed the rate of convergence better error estimates and…
We characterize conditions under which collections of distributions on $\{0,1\}^\mathbb{N}$ admit uniform estimation of their mean. Prior work from Vapnik and Chervonenkis (1971) has focused on uniform convergence using the empirical mean…
The present manuscript is concerned with component-wise estimation of the positive power of ordered restricted standard deviation of two normal populations with certain restrictions on the means. We propose several improved estimators under…
In the face of uncertainty, the need for probabilistic assessments has long been recognized in the literature on forecasting. In classification, however, comparative evaluation of classifiers often focuses on predictions specifying a single…
Experimental studies are a cornerstone of Machine Learning (ML) research. A common and often implicit assumption is that the study's results will generalize beyond the study itself, e.g., to new data. That is, repeating the same study under…