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Damián G. Hernández

Damián G. Hernández appears in the imported research catalog. Authorship, coauthor and topic links are available while profile ownership is still unclaimed.

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cond-mat.stat-mech math-ph physics.data-an Quantitative Methods Biological Physics Computation and Language math.MP physics.soc-ph Populations and Evolution

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preprint2026arXiv

Condensation Transition in Entropy-Constrained Probability Spaces

The organization of high-dimensional probability spaces is a fundamental problem at the intersection of statistical physics and information theory. Here, we analyze the distributions populating level surfaces of the probability simplex $Δ_{K-1}$ defined by a fixed Shannon entropy. We introduce a discretization strategy that assigns equal statistical weight to distinct microstate distributions and enables a combinatorial analysis of the simplex. A condensation phase transition is shown to take place below a critical entropy that scales as $H_c \simeq \log K - 1 + γ$ in the thermodynamic limit. For entropy values $H_0 < H_c$, the overwhelming majority of distributions are found in a condensed state, in which a single component captures a macroscopic fraction of the total probability mass while the remaining components form a homogeneous fluid background. These results provide a framework for understanding phenomena such as overconfident predictions in machine learning and the emergence of dominant species in ecology, and suggest that sparsity can arise naturally from entropic constraints in high-dimensional manifolds.

preprint2021arXiv

Inferring a property of a large system from a small number of samples

Inferring the value of a property of a large stochastic system is a difficult task when the number of samples is insufficient to reliably estimate the probability distribution. The Bayesian estimator of the property of interest requires the knowledge of the prior distribution, and in many situations, it is not clear which prior should be used. Several estimators have been developed so far, in which the proposed prior was individually tailored for each property of interest; such is the case, for example, for the entropy, the amount of mutual information, or the correlation between pairs of variables. In this paper we propose a general framework to select priors, valid for arbitrary properties. We first demonstrate that only certain aspects of the prior distribution actually affect the inference process. We then expand the sought prior as a linear combination of a one-dimensional family of indexed priors, each of which is obtained through a maximum entropy approach with constrained mean value of the property under study. In many cases of interest, only one or very few components of the expansion turn out to contribute to the Bayesian estimator, so it is often valid to only keep a single component. The relevant component is selected by the data, so no handcrafted priors are required. We test the performance of this approximation with a few paradigmatic examples, and show that it performs well in comparison to the ad-hoc methods previously proposed in the literature. Our method highlights the connection between Bayesian inference and equilibrium statistical mechanics, since the most relevant component of the expansion can be argued to be the one with the right temperature.

preprint2020arXiv

A framework for studying behavioral evolution by reconstructing ancestral repertoires

Although extensive behavioral changes often exist between closely related animal species, our understanding of the genetic basis underlying the evolution of behavior has remained limited. Here, we propose a new framework to study behavioral evolution by computational estimation of ancestral behavioral repertoires. We measured the behaviors of individuals from six species of fruit flies using unsupervised techniques and identified suites of stereotyped movements exhibited by each species. We then fit a Generalized Linear Mixed Model to estimate the suites of behaviors exhibited by ancestral species, as well as the intra- and inter-species behavioral covariances. We found that much of intraspecific behavioral variation is explained by differences between individuals in the status of their behavioral hidden states, what might be called their "mood." Lastly, we propose a method to identify groups of behaviors that appear to have evolved together, illustrating how sets of behaviors, rather than individual behaviors, likely evolved. Our approach provides a new framework for identifying co-evolving behaviors and may provide new opportunities to study the genetic basis of behavioral evolution.

preprint2015arXiv

Information-theoretical analysis of the statistical dependencies among three variables: Applications to written language

We develop the information-theoretical concepts required to study the statistical dependencies among three variables. Some of such dependencies are pure triple interactions, in the sense that they cannot be explained in terms of a combination of pairwise correlations. We derive bounds for triple dependencies, and characterize the shape of the joint probability distribution of three binary variables with high triple interaction. The analysis also allows us to quantify the amount of redundancy in the mutual information between pairs of variables, and to assess whether the information between two variables is or is not mediated by a third variable. These concepts are applied to the analysis of written texts. We find that the probability that a given word is found in a particular location within the text is not only modulated by the presence or absence of other nearby words, but also, on the presence or absence of nearby pairs of words. We identify the words enclosing the key semantic concepts of the text, the triplets of words with high pairwise and triple interactions, and the words that mediate the pairwise interactions between other words.