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Functional dependencies (FDs) are basic constraints in relational databases and are used for many data management tasks. Most FD discovery algorithms find all valid dependencies, but this causes two problems. First, the computational cost…
The analysis of contingency tables is a powerful statistical tool used in experiments with categorical variables. This study improves parts of the theory underlying the use of contingency tables. Specifically, the linkage disequilibrium…
Redundancy of experimental data is the basic statistic from which the complexity of a natural phenomenon and the proper number of experiments needed for its exploration can be estimated. The redundancy is expressed by the entropy of…
Big data and machine learning tools have jointly empowered humans in making data-driven decisions. However, many of them capture empirical associations that might be spurious due to confounding factors and subgroup heterogeneity. The famous…
Principal component analysis is a useful dimension reduction and data visualization method. However, in high dimension, low sample size asymptotic contexts, where the sample size is fixed and the dimension goes to infinity,a paradox has…
We present theoretical analysis and a suite of tests and procedures for addressing a broad class of redundant and misleading association rules we call \emph{specious rules}. Specious dependencies, also known as \emph{spurious},…
We present a theoretical framework that extends classical information theory to finite and structured systems by redefining redundancy as a fundamental property of information organization rather than inefficiency. In this framework,…
The Rashomon effect -- the existence of multiple, distinct models that achieve nearly equivalent predictive performance -- has emerged as a fundamental phenomenon in modern machine learning and statistics. In this paper, we explore the…
The study of inter-human communication requires a more complex framework than Shannon's (1948) mathematical theory of communication because "information" is defined in the latter case as meaningless uncertainty. Assuming that meaning cannot…
Spectral dimensionality reduction algorithms are widely used in numerous domains, including for recognition, segmentation, tracking and visualization. However, despite their popularity, these algorithms suffer from a major limitation known…
There is a growing interest in discovery of internet topology at the interface level. A new generation of highly distributed measurement systems is currently being deployed. Unfortunately, the research community has not examined the problem…
The discrepant posterior phenomenon (DPP) is a counter-intuitive phenomenon that can frequently occur in a Bayesian analysis of multivariate parameters. It refers to the phenomenon that a parameter estimate based on a posterior is more…
There are three principle paradigms of statistics: Bayesian, frequentist and information-based inference. Although these paradigms are in agreement in some contexts, the Lindley paradox describes a class of problems, models of unknown…
In most machine learning tasks, we evaluate a model $M$ on a given data population $S$ by measuring a population-level metric $F(S;M)$. Examples of such evaluation metric $F$ include precision/recall for (binary) recognition, the F1 score…
Dropout represents a typical issue to be addressed when dealing with longitudinal studies. If the mechanism leading to missing information is non-ignorable, inference based on the observed data only may be severely biased. A frequent…
We consider the estimation of densities in multiple subpopulations, where the available sample size in each subpopulation greatly varies. This problem occurs in epidemiology, for example, where different diseases may share similar…
We show that, under a standard hardness assumption, there is no computationally efficient algorithm that given $n$ samples from an unknown distribution can give valid answers to $n^{3+o(1)}$ adaptively chosen statistical queries. A…
The overlapping coefficient is a fundamental measure of similarity between probability distributions. While the case of two distributions has been extensively studied, extending this measure to multiple populations presents both analytical…
The aim of this Lecture Note is to introduce the Signal Processing (SP) community to a powerful yet still under-utilised tool: the semiparametric statistics. In short, the semiparametric framework allows us to estimate or perform hypothesis…
In this work we introduce a statistical framework in order to analyze the spatial redundancy in natural images. This notion of spatial redundancy must be defined locally and thus we give some examples of functions (auto-similarity and…