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In several decision-making problems, alternatives should be ranked on the basis of paired comparisons between them. We present an axiomatic approach for the universal ranking problem with arbitrary preference intensities, incomplete and…
Information Theory provides a fundamental basis for analysis, and for a variety of subsequent methodological approaches, in relation to uncertainty quantification. The transversal character of concepts and derived results justifies its…
Information is a valuable asset for agents in socio-economic systems, a significant part of the information being entailed into the very network of connections between agents. The different interlinkages patterns that agents establish may,…
Real-world applications of machine learning tools in high-stakes domains are often regulated to be fair, in the sense that the predicted target should satisfy some quantitative notion of parity with respect to a protected attribute.…
Shannon entropy was defined for probability distributions and then its using was expanded to measure the uncertainty of knowledge for systems with complete information. In this article, it is proposed to extend the using of Shannon entropy…
One of the benefits of belief networks and influence diagrams is that so much knowledge is captured in the graphical structure. In particular, statements of conditional irrelevance (or independence) can be verified in time linear in the…
Researchers often misinterpret and misrepresent statistical outputs. This abuse has led to a large literature on modification or replacement of testing thresholds and $P$-values with confidence intervals, Bayes factors, and other devices.…
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…
Misinformation is still a major societal problem and the arrival of Large Language Models (LLMs) only added to it. This paper analyzes synthetic, false, and genuine information in the form of text from spectral analysis, visualization, and…
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…
Probabilistic programming methods have revolutionised Bayesian inference, making it easier than ever for practitioners to perform Markov-chain-Monte-Carlo sampling from non-conjugate posterior distributions. Here we focus on Stan, arguably…
Filter selection techniques are known for their simplicity and efficiency. However this kind of methods doesn't take into consideration the features inter-redundancy. Consequently the un-removed redundant features remain in the final…
This article is a survey of results concerning an inequality, which may be seen as a versatile tool to solve problems in the domain of Applied Probability. The inequality, which we call BRS-inequality, gives a convenient upper bound for the…
We consider the problem of decision-making with side information and unbounded loss functions. Inspired by probably approximately correct learning model, we use a slightly different model that incorporates the notion of side information in…
Ordinal user-provided ratings across multiple items are frequently encountered in both scientific and commercial applications. Whilst recommender systems are known to do well on these type of data from a predictive point of view, their…
The wide application of estimation techniques in system analysis enable us to best determine and understand the history of system states. This paper attempts to delineate the theory behind linear and non-linear estimation with a suitable…
Latent variable models are popularly used to measure latent factors (e.g., abilities and personalities) from large-scale assessment data. Beyond understanding these latent factors, the covariate effect on responses controlling for latent…
Information theory provides a mathematical foundation to measure uncertainty in belief. Belief is represented by a probability distribution that captures our understanding of an outcome's plausibility. Information measures based on…
Monte Carlo is a versatile and frequently used tool in statistical physics and beyond. Correspondingly, the number of algorithms and variants reported in the literature is vast, and an overview is not easy to achieve. In this pedagogical…
Feedforward neural networks (FNNs) are typically viewed as pure prediction algorithms, and their strong predictive performance has led to their use in many machine-learning applications. However, their flexibility comes with an…