Related papers: What is an inductive mean?

The geometric mean of two matrices is considered and analyzed from a computational viewpoint. Some useful theoretical properties are derived and an analysis of the conditioning is performed. Several numerical algorithms based on different…

Sequence classification is the supervised learning task of building models that predict class labels of unseen sequences of symbols. Although accuracy is paramount, in certain scenarios interpretability is a must. Unfortunately, such…

Given a real valued functional T on the space of bounded random variables, we investigate the problem of the existence of a conditional version of nonlinear means. We follow a seminal idea by Chisini (1929), defining a mean as the solution…

In this paper we shall consider some famous means such as arithmetic, harmonic, geometric, root-square means, etc. Some new means recently studied are also presented. Different kinds of refinement of inequalities among these means are…

The predictability of a sequence is defined as the asymptotic performance of the best performing predictor in a given class. The value of the predictability of a sequence will in general depend on the choice of this predictor class. The…

We prove majorization inequalities for different means of positive definite matrices. These include the Cartan mean (the Karcher mean), the log Euclidean mean, the Wasserstein mean and the power mean.

Metric mean dimension is a metric-depedent quantity to characterize the topological complexity of systems with infinite topological entropy. In this paper, we investigate metric mean dimension of factor maps. (1) We introduce three types of…

The sample mean is often used to aggregate different unbiased estimates of a parameter, producing a final estimate that is unbiased but possibly high-variance. This paper introduces the Bayesian median of means, an aggregation rule that…

Metric mean dimension is a metric invariant of dynamical systems. It is a dynamical analogue of Minkowski dimension of metric spaces. We explain that old ideas of Bowen (1972) can be used for clarifying the local nature of metric mean…

Linear algebra's main concerns are sets of vectors, linear functions, subspaces, linear systems, matrices and concepts about those, such as whether the solution of linear system exists or is unique; a set of vectors is linearly independent…

We give an upper bound for the weighted geometric mean using the weighted arithmetic mean and the weighted harmonic mean. We also give a lower bound for the weighted geometric mean. These inequalities are proven for two invertible positive…

This paper attempts to answer a central question in unsupervised learning: what does it mean to "make sense" of a sensory sequence? In our formalization, making sense involves constructing a symbolic causal theory that both explains the…

Lagrangian averaging theories, most notably the Generalised Lagrangian Mean (GLM) theory of Andrews & McIntyre (1978), have been primarily developed in Euclidean space and Cartesian coordinates. We re-interpret these theories using a…

Starting with the most general four-dimensional spacetime possessing two commuting Killing vectors and a nontrivial Killing tensor, we analytically integrate Einstein-Yang-Mills equations for a completely arbitrary gauge group. It is…

This paper establishes that every positive-definite matrix can be written as a positive linear combination of outer products of integer-valued vectors whose entries are bounded by the geometric mean of the condition number and the dimension…

We give tight bounds for logarithmic mean. We also give new Frobenius norm inequalities for two positive semidefinite matrices. In addition, we give some matrix inequalities on matrix power mean.

Intercausal reasoning is a common inference pattern involving probabilistic dependence of causes of an observed common effect. The sign of this dependence is captured by a qualitative property called product synergy. The current definition…

The main goal of this article is to find the exact difference between a convex function and its secant, as a limit of positive quantities. This idea will be expressed as a convex inequality that leads to refinements and reversals of well…

A generalized definition of the determinant of matrices is given, which is compatible with the usual determinant for square matrices and keeps many important properties, such as being an alternating multilinear function, keeping…

In a previous paper, we have given an algebraic model to the set of intervals. Here, we apply this model in a linear frame. We define a notion of diagonalization of square matrices whose coefficients are intervals. But in this case, with…