arXiv subjects

Mario Angelelli

Publications and source records attributed to Mario Angelelli.

10 recordsLinked to original sources

arXiv2025

Human- vs. AI-generated tests: dimensionality and information accuracy in latent trait evaluation

Artificial Intelligence (AI) and large language models (LLMs) are increasingly used in social and psychological research. Among potential applications, LLMs can be used to generate, customise, or adapt measurement instruments. This study presents a preliminary investigation of AI-generated questionnaires by comparing two ChatGPT-based adaptations of the Body Awareness Questionnaire (BAQ) with the validated human-developed version. The AI instruments were designed with different levels of explicitness in content and instructions on construct facets, and their psychometric properties were assessed using a Bayesian Graded Response Model. Results show that although surface wording between AI and original items was similar, differences emerged in dimensionality and in the distribution of item and test information across latent traits. These findings illustrate the importance of applying statistical measures of accuracy to ensure the validity and interpretability of AI-driven tools.

cs.HC↗

arXiv2023

A robust statistical framework for cyber-vulnerability prioritisation under partial information in threat intelligence

Proactive cyber-risk assessment is gaining momentum due to the wide range of sectors that can benefit from the prevention of cyber-incidents by preserving integrity, confidentiality, and the availability of data. The rising attention to cybersecurity also results from the increasing connectivity of cyber-physical systems, which generates multiple sources of uncertainty about emerging cyber-vulnerabilities. This work introduces a robust statistical framework for quantitative and qualitative reasoning under uncertainty about cyber-vulnerabilities and their prioritisation. Specifically, we take advantage of mid-quantile regression to deal with ordinal risk assessments, and we compare it to current alternatives for cyber-risk ranking and graded responses. For this purpose, we identify a novel accuracy measure suited for rank invariance under partial knowledge of the whole set of existing vulnerabilities. The model is tested on both simulated and real data from selected databases that support the evaluation, exploitation, or response to cyber-vulnerabilities in realistic contexts. Such datasets allow us to compare multiple models and accuracy measures, discussing the implications of partial knowledge about cyber-vulnerabilities on threat intelligence and decision-making in operational scenarios.

stat.ME↗

arXiv2022

Extended Tetrad Analysis in Factor Modelling: Separability and Uncertainty from Multidimensional Dependence Structures

Geometric representations provide a principled framework for structuring the description of latent constructs and clarifying sources of uncertainty in their dimensional characterisation. We introduce a novel geometric representation of factor models via two subspaces spanned by paired matrices, where determinantal expressions explicitly quantify the contributions of different dimension subsets to the factor structure. This formulation refines rank-based conditions relevant to understanding factor score indeterminacy and the implications of non-uniqueness in instrumental variable estimation for over-identified models. By weighting these multidimensional contributions to encode sensitivity to their variation, we extend the definition of tetrads into an algebraic procedure that establishes conditions for identifying variability components attributable to individual dimensions. Focusing on cases where one factor encodes structural information, we derive minimal conditions-expressed through graph planarity-that ensure such dimension-specific identifiability. The proofs yield both formal verification tools and constructive methods for generating counterexamples where these conditions fail. These counterexamples reveal a type of ambiguity, termed contextuality, in which the comparison of dimensional contributions depends on the choice of remaining reference dimensions, violating well-established axioms of order-theoretic consistency. We relate these findings to specific forms of uncertainty examined in the psychometric literature.

math.CO↗

arXiv2021

Representations of epistemic uncertainty and awareness in data-driven strategies

The diffusion of AI and big data is reshaping decision-making processes by increasing the amount of information that supports decisions while reducing direct interaction with data and empirical evidence. This paradigm shift introduces new sources of uncertainty, as limited data observability results in ambiguity and a lack of interpretability. The need for the proper analysis of data-driven strategies motivates the search for new models that can describe this type of bounded access to knowledge. This contribution presents a novel theoretical model for uncertainty in knowledge representation and its transfer mediated by agents. We provide a dynamical description of knowledge states by endowing our model with a structure to compare and combine them. Specifically, an update is represented through combinations, and its explainability is based on its consistency in different dimensional representations. We look at inequivalent knowledge representations in terms of multiplicity of inferences, preference relations, and information measures. Furthermore, we define a formal analogy with two scenarios that illustrate non-classical uncertainty in terms of ambiguity (Ellsberg's model) and reasoning about knowledge mediated by other agents observing data (Wigner's friend). Finally, we discuss some implications of the proposed model for data-driven strategies, with special attention to reasoning under uncertainty about business value dimensions and the design of measurement tools for their assessment.

cs.AI↗

arXiv2021

Combinatorial Reduction of Set Functions and Matroid Permutations through Minor Product Assignment

We introduce an algebraic model, based on the determinantal expansion of the product of two matrices, to test combinatorial reductions of set functions. Each term of the determinantal expansion is deformed through a monomial factor in d indeterminates, whose exponents define a $\mathbb{Z}^{d}$-valued set function. By combining the Grassmann-Pl\"{u}cker relations for the two matrices, we derive a family of sparse polynomials, whose factorisation properties in a Laurent polynomial ring are studied and related to information-theoretic notions. Under a given genericity condition, we prove the equivalence between combinatorial reductions and determinantal expansions with invertible minor products; specifically, a deformation returns a determinantal expansion if and only if it is induced by a diagonal matrix of units in $\mathbb{C}(\mathbf{t})$ acting as a kernel in the original determinant expression. This characterisation supports the definition of a new method for checking and recovering combinatorial reductions for matroid permutations.

math.AC↗

arXiv2020

Entropy driven transformations of statistical hypersurfaces

Deformations of geometric characteristics of statistical hypersurfaces governed by the law of growth of entropy are studied. Both general and special cases of deformations are considered. The basic structure of the statistical hypersurface is explored through a differential relation for the variables, and connections with the replicator dynamics for Gibbs' weights are highlighted. Ideal and super-ideal cases are analysed, also considering their integral characteristics.

math-ph↗

arXiv2020

Streaming Generalized Cross Entropy

We propose a new method to combine adaptive processes with a class of entropy estimators for the case of streams of data. Starting from a first estimation obtained from a batch of initial data, model parameters are estimated at each step by combining the prior knowledge with the new observation (or a block of observations). This allows to extend the maximum entropy technique to a dynamical setting, also distinguishing between entropic contributions of the signal and the error. Furthermore, it provides a suitable approximation of standard GME problems when the exacted solutions are hard to evaluate. We test this method by performing numerical simulations at various sample sizes and batch dimensions. Moreover, we extend this analysis exploring intermediate cases between streaming GCE and standard GCE, i.e. considering blocks of observations of different sizes to update the estimates, and incorporating collinearity effects as well. The role of time in the balance between entropic contributions of signal and errors is further explored considering a variation of the Streaming GCE algorithm, namely, Weighted Streaming GCE. Finally, we discuss the results: in particular, we highlight the main characteristics of this method, the range of application, and future perspectives.

eess.SP↗

arXiv2018

Signatures of partition functions and their complexity reduction through the KP II equation

A statistical amoeba arises from a real-valued partition function when the positivity condition for pre-exponential terms is relaxed, and families of signatures are taken into account. This notion lets us explore special types of constraints when we focus on those signatures that preserve particular properties. Specifically, we look at sums of determinantal type, and main attention is paid to a distinguished class of soliton solutions of the Kadomtsev-Petviashvili (KP) II equation. A characterization of the signatures preserving the determinantal form, as well as the signatures compatible with the KP II equation, is provided: both of them are reduced to choices of signs for columns and rows of a coefficient matrix, and they satisfy the whole KP hierarchy. Interpretations in term of information-theoretic properties, geometric characteristics, and the relation with tropical limits are discussed.

math-ph↗

arXiv2018

Tropical limit and the micro-macro correspondence

Tropical mathematics is used to establish a correspondence between certain microscopic and macroscopic objects in statistical models. Tropical algebra gives a common framework for macrosystems (subsets) and their elementary constituents (elements) that is well-behaved with respect to composition. This kind of connection is studied with maps that preserve a monoid structure. The approach highlights an underlying order relation that is explored through the concepts of filter and ideal. Particular attention is paid to asymmetry and duality between max- and min-criteria. Physical implementations are presented through simple examples in thermodynamics and non-equilibrium physics. The phenomenon of ultrametricity, the notion of tropical equilibrium and the role of ground energy in non-equilibrium models are discussed. Tropical symmetry, i.e. idempotence, is investigated.

math-ph↗

arXiv2016

Geometry of the basic statistical physics mapping

Geometry of hypersurfaces defined by the relation which generalizes classical formula for free energy in terms of microstates is studied. Induced metric, Riemann curvature tensor, Gauss-Kronecker curvature and associated entropy are calculated. Special class of ideal statistical hypersurfaces is analyzed in details. Non-ideal hypersurfaces and their singularities similar to those of the phase transitions are considered. Tropical limit of statistical hypersurfaces and double scaling tropical limit are discussed too.

math-ph↗