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As counterfactual examples become increasingly popular for explaining decisions of deep learning models, it is essential to understand what properties quantitative evaluation metrics do capture and equally important what they do not…
Positive predictive value and negative predictive value are two widely used parameters to assess the clinical usefulness of a medical diagnostic test. When there are two diagnostic tests, it is recommendable to make a comparative assessment…
A distance measure is presented between two unitary propagators of quantum systems of differing dimensions along with a corresponding method of computation. A typical application is to compare the propagator of the actual (real) process…
The relation between tempered distributions and measures is analysed and clarified. While this is straightforward for positive measures, it is surprisingly subtle for signed or complex measures.
Quantum measurements of physical quantities are usually described as ideal measurements. However, only a few measurements fulfil the conditions of ideal measurements. The aim of the present work is to describe real position measurements…
Statistical samples, in order to be representative, have to be drawn from a population in a random and unbiased way. Nevertheless, it is common practice in the field of model-based diagnosis to make estimations from (biased) best-first…
Images are at the core of most modern biological experiments and are used as a major source of quantitative information. Numerous algorithms are available to process images and make them more amenable to be measured. Yet the nature of the…
The distinction between proper and improper mixtures is a staple of the discussion of foundational questions in quantum mechanics. Here we note an analogous distinction in the context of the theory of entanglement. The terminology of…
We discuss the paper "Citation Statistics" by the Joint Committee on Quantitative Assessment of Research [arXiv:0910.3529]. In particular, we focus on a necessary feature of "good" measures for ranking scientific authors: that good measures…
During many years since the birth of quantum mechanics, instrumentalist interpretations prevailed: the meaning of the theory was expressed in terms of measurements results. But in the last decades, several attempts to interpret it from a…
We take the view that physical quantities are values generated by processes in measurement, not pre-existent objective quantities, and that a measurement result is strictly a product of the apparatus and the subject of the measurement. We…
Determining and measuring cause-effect relationships is fundamental to most scientific studies of natural phenomena. The notion of causation is distinctly different from correlation which only looks at association of trends or patterns in…
Commonly used evaluation measures including Recall, Precision, F-Measure and Rand Accuracy are biased and should not be used without clear understanding of the biases, and corresponding identification of chance or base case levels of the…
Although a system is described by a well-known set of equations leading to a deterministic behavior, in the real world the value of a measurand obtained by an experiment will mostly scatter. Accordingly, an uncertainty is associated with…
Comparison and contrast are the basic means to unveil causation and learn which treatments work. To build good comparison groups, randomized experimentation is key, yet often infeasible. In such non-experimental settings, we illustrate and…
In this paper, the defining properties of a valid measure of the dependence between two random variables are reviewed and complemented with two original ones, shown to be more fundamental than other usual postulates. While other popular…
As is well known, quantum mechanical behavior cannot, in general, be simulated by a local hidden variables model. Most -if not all- the proofs of this incompatibility refer to the correlations which arise when each of two (or more) systems…
Efficient methods for characterizing the performance of quantum measurements are important in the experimental quantum sciences. Ideally, one requires both a physically relevant distinguishability measure between measurement operations and…
Measuring dependence between two events, or equivalently between two binary random variables, amounts to expressing the dependence structure inherent in a $2\times 2$ contingency table in a real number between $-1$ and $1$. Countless such…
Extracting noisy or incorrectly labeled samples from a labeled dataset with hard/difficult samples is an important yet under-explored topic. Two general and often independent lines of work exist, one focuses on addressing noisy labels, and…