Related papers: On the Significance of Digits in Interval Notation
In this paper, we present a comprehensive system for the treatment of the topic of limits--conceptually, computationally, and formally. The system addresses fundamental linguistic flaws in the standard presentation of limits, which attempts…
High-dimensional dense embeddings have become central to modern Information Retrieval, but many dimensions are noisy or redundant. Recently proposed DIME (Dimension IMportance Estimation), provides query-dependent scores to identify…
We consider the prospect of a processor that can perform interval arithmetic at the same speed as conventional floating-point arithmetic. This makes it possible for all arithmetic to be performed with the superior security of interval…
We introduce a new framework term coding for extremal problems in discrete mathematics and information flow, where one chooses interpretations of function symbols so as to maximise the number of satisfying assignments of a finite system of…
Information theory is a practical and theoretical framework developed for the study of communication over noisy channels. Its probabilistic basis and capacity to relate statistical structure to function make it ideally suited for studying…
In our recent work on iterative computation in hardware, we showed that arbitrary-precision solvers can perform more favorably than their traditional arithmetic equivalents when the latter's precisions are either under- or over-budgeted for…
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…
We consider the problem of estimating confidence intervals for the mean of a random variable, where the goal is to produce the smallest possible interval for a given number of samples. While minimax optimal algorithms are known for this…
This paper offers a commentary on the use of notions of statistical significance in choice modelling. We review the reasons for uncertainty in parameter estimates, provide a precise discussion on the computation of measures of uncertainty…
Numerical integration over the implicitly defined domains is challenging due to topological variances of implicit functions. In this paper, we use interval arithmetic to identify the boundary of the integration domain exactly, thus getting…
In this work we investigate the information loss in (nonlinear) dynamical input-output systems and provide some general results. In particular, we present an upper bound on the information loss rate, defined as the (non-negative) difference…
The signal to noise ratio, which plays such an important r\^ole in information theory, is shown to become pointless for digital communications where the demodulation is achieved via new fast estimation techniques. Operational calculus,…
We elucidate why an interval algorithm that computes the exact bounds on the amplitude and phase of the discrete Fourier transform can run in polynomial time. We address this question from a formal perspective to provide the mathematical…
Scientific discovery can be framed as a thermodynamic process in which an agent invests physical work to acquire information about an environment under a finite work budget. Using established results about the thermodynamics of computing,…
This essay looks at decision-making with interval-valued probability measures. Existing decision methods have either supplemented expected utility methods with additional criteria of optimality, or have attempted to supplement the…
In previous work (Fertig and Breese, 1989; Fertig and Breese, 1990) we defined a mechanism for performing probabilistic reasoning in influence diagrams using interval rather than point-valued probabilities. In this paper we extend these…
In this paper, a novel approach for coding nominal data is proposed. For the given nominal data, a rank in a form of complex number is assigned. The proposed method does not lose any information about the attribute and brings other…
Any system that is used for naming or representing numbers is a number system, also known as numeral system. The modern civilization is familiar with decimal number system using ten digits. However digital devices and computers use binary…
The aim of ordinal classification is to predict the ordered labels of the output from a set of observed inputs. Interval-valued data refers to data in the form of intervals. For the first time, interval-valued data and interval-valued…
There are numerous scenarios in source coding where not only the code length but the importance of each value should also be taken into account. Different from the traditional coding theorems, by adding the importance weights for the length…