Related papers: The Sets of Power
We consider the set M_n of all n-truncated power moment sequences of probability measures on [0,1]. We endow this set with the uniform probability. Picking randomly a point in M_n, we show that the upper canonical measure associated with…
This article reviews the empirical evidence on the use of patent citations as a proxy for invention importance. It distinguishes between technical merit, private economic value, and social value, and surveys validation studies using expert…
Probability measures by themselves, are known to be inappropriate for modeling the dynamics of plain belief and their excessively strong measurability constraints make them unsuitable for some representational tasks, e.g. in the context of…
Computing value of information (VOI) is a crucial task in various aspects of decision-making under uncertainty, such as in meta-reasoning for search; in selecting measurements to make, prior to choosing a course of action; and in managing…
A ranking is an ordered sequence of items, in which an item with higher ranking score is more preferred than the items with lower ranking scores. In many information systems, rankings are widely used to represent the preferences over a set…
Minibatching is a very well studied and highly popular technique in supervised learning, used by practitioners due to its ability to accelerate training through better utilization of parallel processing power and reduction of stochastic…
A sequence of recent papers has considered the role of measurement scales in information retrieval (IR) experimentation, and presented the argument that (only) uniform-step interval scales should be used, and hence that well-known metrics…
Research on summarization has mainly been driven by empirical approaches, crafting systems to perform well on standard datasets with the notion of information Importance remaining latent. We argue that establishing theoretical models of…
Recently, it was shown that most popular IR measures are not interval-scaled, implying that decades of experimental IR research used potentially improper methods, which may have produced questionable results. However, it was unclear if and…
This is an introduction to measure theory, integration and function spaces, with all the needed preliminaries included, and with some applications included as well. We first discuss some basic motivations, coming from discrete probability,…
We construct measure which determines a two-variable mean in a very natural way. Using that measure we can extend the mean to infinite sets as well. E.g. we can calculate the geometric mean of any set with positive Lebesgue measure. We also…
Probability metrics constitute an important tool in probability theory and statistics \cite{DKS91}, \cite{R91}, \cite{Z83} as they are specific metrics on spaces of random variables which, by satisfying an extra condition, concord well with…
The probabilistic investigation on record values and record times of a sequence of random variables defined on the same probability space has received much attention from 1952 to now. A great deal of such theory focused on \textit{iid} or…
While the methodological rigor of computing research has improved considerably in the past two decades, quantitative software engineering research is hampered by immature measures and inattention to theory. Measurement-the principled…
The performance of algorithms, methods, and models tends to depend heavily on the distribution of cases on which they are applied, this distribution being specific to the applicative domain. After performing an evaluation in several…
Much research in electoral control -- one of the most studied form of electoral attacks, in which an entity running an election alters the structure of that election to yield a preferred outcome -- has focused on giving decision complexity…
A general approach to the measurement of an observable with pre- and post-selection is presented. The limit of weak measurement is studied in detail, and it is shown that the phase of the probe, including a Hamiltonian contribution to it,…
The problem of the estimation of relevance to a set of histograms generated by samples of a discrete time process is discussed on the base of the variational principles proposed in the previous paper [1]. Some conditions for dimension…
We examine a new approach to modeling uncertainty based on plausibility measures, where a plausibility measure just associates with an event its plausibility, an element is some partially ordered set. This approach is easily seen to…
We consider the power to reject false values of the parameter in Frequentist methods for the calculation of confidence intervals. We connect the power with the physical significance (reliability) of confidence intervals for a parameter…