Related papers: Generalizing the Mean and Variance to Categorical …

Word class flexibility refers to the phenomenon whereby a single word form is used across different grammatical categories. Extensive work in linguistic typology has sought to characterize word class flexibility across languages, but…

Uncertainty quantification is a critical aspect of machine learning models, providing important insights into the reliability of predictions and aiding the decision-making process in real-world applications. This paper proposes a novel way…

This text is devoted to the theory of varieties, which provides an important tool, based in universal algebra, for the classification of regular languages. In the introductory section, we present a number of examples that illustrate and…

The mean absolute deviation about the mean is an alternative to the standard deviation for measuring dispersion in a sample or in a population. For stationary, ergodic time series with a finite first moment, an asymptotic expansion for the…

The concept of a variance on a category is introduced as a two-sided strict factorization system. By employing variances, we define functors of variance in a more general setting than is usually considered, thereby eliminating the need for…

Various forms of Mean Value Theorems are available in the literature. If we use Flett's Mean Value Theorem in Extended Generalized Mean Value Theorem then what would the new theorem look like. A sincere effort is done to develop this…

In many applications of machine learning, a large number of variables are considered. Motivated by machine learning of interacting particle systems, we consider the situation when the number of input variables goes to infinity. First, we…

We prove large and moderate deviation principles for the distribution of an empirical mean conditioned by the value of the sum of discrete i.i.d. random variables. Some applications for combinatoric problems are discussed.

As machine learning becomes more and more available to the general public, theoretical questions are turning into pressing practical issues. Possibly, one of the most relevant concerns is the assessment of our confidence in trusting machine…

In the problem of domain generalization (DG), there are labeled training data sets from several related prediction problems, and the goal is to make accurate predictions on future unlabeled data sets that are not known to the learner. This…

Skewness measures can be used to measure the level of asymmetry of a distribution. Given the prevalence of statistical methods that assume underlying symmetry, and also the desire for symmetry in order to make meaningful judgements for…

Meaning can be generated when information is related at a systemic level. Such a system can be an observer, but also a discourse, for example, operationalized as a set of documents. The measurement of semantics as similarity in patterns…

Meta-analysis involves combining summary information for related but independent studies. It uses different relationship to combine position measure as well as dispersion measures. The objective of this study is to discuss a relationship…

Nowadays, the confidentiality of data and information is of great importance for many companies and organizations. For this reason, they may prefer not to release exact data, but instead to grant researchers access to approximate data. For…

Estimation of density functions supported on general domains arises when the data is naturally restricted to a proper subset of the real space. This problem is complicated by typically intractable normalizing constants. Score matching…

There has been an increased interest in data generation approaches to grammatical error correction (GEC) using pseudo data. However, these approaches suffer from several issues that make them inconvenient for real-world deployment including…

Empirical evidence shows that ensembles, such as bagging, boosting, random and rotation forests, generally perform better in terms of their generalization error than individual classifiers. To explain this performance, Schapire et al.…

Confidence intervals are a popular way to visualize and analyze data distributions. Unlike p-values, they can convey information both about statistical significance as well as effect size. However, very little work exists on applying…

As a part of the construction of an information theory based on general probabilistic theories, we propose and investigate the several distinguishability measures and "entropies" in general probabilistic theories. As their applications,…

This paper addresses the problem of segmenting a time-series with respect to changes in the mean value or in the variance. The first case is when the time data is modeled as a sequence of independent and normal distributed random variables…