Related papers: A geometrical perspective on parametric psychometr…
In the era of foundation models and Large Language Models (LLMs), Euclidean space has been the de facto geometric setting for machine learning architectures. However, recent literature has demonstrated that this choice comes with…
The rapid development of large language models (LLMs) has necessitated the creation of benchmarks to evaluate their performance. These benchmarks resemble human tests and surveys, as they consist of sets of questions designed to measure…
In psychophysical experiments time and the limited goodwill of participants is usually a major constraint. This has been the main motivation behind the early development of adaptive methods for the measurements of psychometric thresholds.…
I describe the manifestation of the non-Euclidean geometry in the behavior of collective observables of some complex physical systems. Specifically, I consider the formation of equilibrium shapes of plants and statistics of sparse random…
An adaptive design adjusts dynamically as information is accrued and a consequence of applying an adaptive design is the potential for inducing small-sample bias in estimates. In psychometrics and psychophysics, a common class of studies…
Two of the defining elements of Social Networking Services are the social profile, containing information about the user, and the social graph, containing information about the connections between users. Social Networking Services are used…
We study the geometrical properties of the utility space (the space of expected utilities over a finite set of options), which is commonly used to model the preferences of an agent in a situation of uncertainty. We focus on the case where…
In Mathematics is common to make a mistake and therefore a false conclusion arises. In each case it is important to recognize the mistake in order to avoid a similar one in the future. Geometric figures provide decisive help in order to…
Finite mixture models that allow for a broad range of potentially non-elliptical cluster distributions is an emerging methodological field. Such methods allow for the shape of the clusters to match the natural heterogeneity of the data,…
The manifold of empirical mean values of statistical data ad infinitum has a geometric shape that depends on the probability measure that governs the generating model. Large deviation theory produces entropy functions that depend on both…
Distance correlation is a recent extension of Pearson's correlation, that characterises general statistical independence between Euclidean-space-valued random variables, not only linear relations. This review delves into how and when…
Cognitive diagnosis models have been popularly used in fields such as education, psychology, and social sciences. While parametric likelihood estimation is a prevailing method for fitting cognitive diagnosis models, nonparametric…
Application of the noncommutative geometry to several physical models is considered.
{G}{ustav} Fechner's 1860 delineation of psychophysics, the measurement of sensation in relation to its stimulus, is widely considered to be the advent of modern psychological science. In psychophysics, a researcher parametrically varies…
Quantum mechanics is among the most important and successful mathematical model for describing our physical reality. The traditional formulation of quantum mechanics is linear and algebraic. In contrast classical mechanics is a geometrical…
Fr\'echet regression extends classical regression methods to non-Euclidean metric spaces, enabling the analysis of data relationships on complex structures such as manifolds and graphs. This work establishes a rigorous theoretical analysis…
This report concerns the problem of dimensionality reduction through information geometric methods on statistical manifolds. While there has been considerable work recently presented regarding dimensionality reduction for the purposes of…
The concept of complexity appears in virtually all areas of knowledge. Its intuitive meaning shares similarities across fields, but disagreements between its details hinders a general definition, leading to a plethora of proposed…
We suggest a geometric approach to modeling biochemical processes, aiming at those processes that occur in humans with food sensitivities or chemical sensitivities.
The great behavioral heterogeneity observed between individuals with the same psychiatric disorder and even within one individual over time complicates both clinical practice and biomedical research. However, modern technologies are an…