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This paper deals with the comparison of two common types of equivalence groups of differential equations, and this gives rise to a number of results presented in the form of theorems. It is shown in particular that one type can be…

We collect in this note some observations on the role of symmetries in Bayesian inference problems, that can be useful or detrimental depending on the way they act on the signal and on the observations. We emphasize in particular the need…

Adversarial examples resulting from instability of current computer vision models are an extremely important topic due to their potential to compromise any application. In this paper we demonstrate that instability is inevitable due to a)…

Quantifying the similarity between two mathematical structures or datasets constitutes a particularly interesting and useful operation in several theoretical and applied problems. Aimed at this specific objective, the Jaccard index has been…

Bell inequalities bound the strength of classical correlations between observers measuring on a shared physical system. However, studies of physical correlations can be considered beyond the standard Bell scenario by networks of observers…

Matching is a widely used causal inference design that aims to approximate a randomized experiment using observational data by forming matched sets of treated and control units based on similarities in their covariates. Ideally, treated…

Data-driven methods that detect anomalies in times series data are ubiquitous in practice, but they are in general unable to provide helpful explanations for the predictions they make. In this work we propose a model-agnostic algorithm that…

This paper re-examines the first normalized incomplete moment, a well-established measure of inequality with wide applications in economic and social sciences. Despite the popularity of the measure itself, existing statistical inference…

In this paper we provide a comprehensive study of statistical inference in linear and allied models which exhibit some analytic perturbations in their design and covariance matrices. We also indicate a few potential applications. In the…

We study ratio metrics in A/B testing at the presence of correlation among observations coming from the same user and provides practical guidance especially when two metrics contradict each other. We propose new estimating methods to…

Unobserved confounding arises when an unmeasured feature influences both the treatment and the outcome, leading to biased causal effect estimates. This issue undermines observational studies in fields like economics, medicine, ecology or…

Applied researchers often find themselves making statistical inferences in settings that would seem to require multiple comparisons adjustments. We challenge the Type I error paradigm that underlies these corrections. Moreover we posit that…

This article provides a thorough meta-analysis of the anomaly detection problem. To accomplish this we first identify approaches to benchmarking anomaly detection algorithms across the literature and produce a large corpus of anomaly…

We introduce a new method for determining the global stability of synchronization in systems of coupled identical maps. The method is based on the study of invariant measures. Besides the simplest non-trivial example, namely two…

To obtain reliable results of expertise, which usually use individual and group expert pairwise comparisons, it is important to summarize (aggregate) expert estimates provided that they are sufficiently consistent. There are several ways to…

Incompatible measurements, i.e., measurements that cannot be simultaneously performed, are necessary to observe nonlocal correlations. It is natural to ask, e.g., how incompatible the measurements have to be to achieve a certain violation…

Benchmarks shape scientific conclusions about model capabilities and steer model development. This creates a feedback loop: stronger benchmarks drive better models, and better models demand more discriminative benchmarks. Ensuring benchmark…

The anomaly detection problem for univariate or multivariate time series is a critical question in many practical applications as industrial processes control, biological measures, engine monitoring, supervision of all kinds of behavior. In…

The abundance of data produced daily from large variety of sources has boosted the need of novel approaches on causal inference analysis from observational data. Observational data often contain noisy or missing entries. Moreover, causal…

Bell's inequalities can be understood in three different ways depending on whether the numbers featuring in the inequalities are interpreted as classical probabilities, classical conditional probabilities, or quantum probabilities. In the…