Related papers: An uncertainty principle for arithmetic sequences

When we work with information from multiple sources, the formalism each employs to handle uncertainty may not be uniform. In order to be able to combine these knowledge bases of different formats, we need to first establish a common basis…

Many learning machines such as normal mixtures and layered neural networks are not regular but singular statistical models, because the map from a parameter to a probability distribution is not one-to-one. The conventional statistical…

We study the empirical likelihood approach to construct confidence intervals for the optimal value and the optimality gap of a given solution, henceforth quantify the statistical uncertainty of sample average approximation, for optimization…

Existing approaches of prescriptive analytics -- where inputs of an optimization model can be predicted by leveraging covariates in a machine learning model -- often attempt to optimize the mean value of an uncertain objective. However,…

Using frequency distributions of daily closing price time series of several financial market indexes, we investigate whether the bias away from an equiprobable sequence distribution found in the data, predicted by algorithmic information…

Sufficiency, Conditionality and Invariance are basic principles of statistical inference. Current mathematical statistics courses do not devote much teaching time to these classical principles, and even ignore the latter two, in order to…

We present a theory of particles, obeying intermediate statistics ("anyons"), interpolating between Bosons and Fermions, based on the principle of Detailed Balance. It is demonstrated that the scattering probabilities of identical particles…

A new deterministic floating-point arithmetic called precision arithmetic is developed to track precision for arithmetic calculations. It uses a novel rounding scheme to avoid excessive rounding error propagation of conventional…

We introduce a novel uncertainty principle for generalized graph signals that extends classical time-frequency and graph uncertainty principles into a unified framework. By defining joint vertex-time and spectral-frequency spreads, we…

A person is given a numbered sequence of positions on a sheet of paper. The person is asked, "Which will be the next (or the next after that) position?" Everyone has an opinion as to how he or she would proceed. There are regular sequences…

In the present article, a new method for the evaluation of fractional derivatives of arbitrary real order is proposed. Numerous but inequivalent formulations have been given in the past. Some of them exhibit unsatisfactory properties such…

Across machine learning (ML) sub-disciplines, researchers make explicit mathematical assumptions in order to facilitate proof-writing. We note that, specifically in the area of fairness-accuracy trade-off optimization scholarship, similar…

Nonparametric estimation of a mixing distribution based on data coming from a mixture model is a challenging problem. Beyond estimation, there is interest in uncertainty quantification, e.g., confidence intervals for features of the mixing…

Dispersion is a fundamental concept in statistics, yet standard approaches - especially via stochastic orders - face limitations in the discrete setting. In particular, the classical dispersive order, well-established for continuous…

Uncertainty-quantification methods are applied to estimate the confidence of deep-neural-networks classifiers over their predictions. However, most widely used methods are known to be overconfident. We address this problem by developing an…

Functional data analysis is proved to be useful in many scientific applications. The physical process is observed as curves and often there are several curves observed due to multiple subjects, providing the replicates in statistical sense.…

Predictive algorithms are now used to help distribute a large share of our society's resources and sanctions, such as healthcare, loans, criminal detentions, and tax audits. Under the right circumstances, these algorithms can improve the…

An approach to reasoning with default rules where the proportion of exceptions, or more generally the probability of encountering an exception, can be at least roughly assessed is presented. It is based on local uncertainty propagation…

The issue of asymmetric uncertainties resulting from fits, nonlinear propagation and systematic effects is reviewed. It is shown that, in all cases, whenever a published result is given with asymmetric uncertainties, the value of the…

Uncertainty can be classified as either aleatoric (intrinsic randomness) or epistemic (imperfect knowledge of parameters). The majority of frameworks assessing infectious disease risk consider only epistemic uncertainty. We only ever…