arXiv subjects

Inés Samengo

Publications and source records attributed to Inés Samengo.

15 recordsLinked to original sources

arXiv2026

Condensation Transition in Entropy-Constrained Probability Spaces

Probability spaces are known to undergo a concentration of measure in high dimensions. In particular, if a $K$-dimensional probability distribution is sampled from a $(K-1)$-dimensional simplex with uniform measure, with high probability its empirical distribution of components is logarithmic. Here, we extend this result to the subset of distributions populating level sets of de simplex defined by a fixed Shannon entropy $H_0$. We show that the empirical distribution of components of the large majority of sampled distributions undergoes a phase transition. A critical entropy $H_c \approx \log K - 1 + \gamma $ exists, below which the overwhelming majority of sampled distributions are found in a condensed state, in which a single component captures a macroscopic fraction of the total probability, while the remaining components form a homogeneous incompressible fluid background. We derive the magnitude of the critical entropy, as well as the empirical distribution of components both above and below threshold. These results provide insight into how the level sets of fixed entropy in the simplex are populated.

cond-mat.stat-mech↗

arXiv2026

Modelling time-order effects in haptic perception with a Bayesian dynamical framework

Perceptual judgments of sequential stimuli are systematically biased by prior expectations and by the temporal structure of sensory input. In haptic discrimination tasks, these effects often manifest as time-order asymmetries, whereby the perceived difference between two stimuli depends on their presentation order. Here, we introduce a dynamical Bayesian model that accounts for these biases by combining noisy sensory measurements with an evolving internal representation of stimulus intensity. The model formalizes perception as an inference process in which prior expectations are updated by incoming stimuli and propagate in time between observations. We test the model on psychophysical data from vibrotactile discrimination experiments, in which participants compare pairs of sequential stimuli with varying intensities. With a small number of parameters, the model quantitatively reproduces both the direction and magnitude of time-order effects across subjects, as well as the observed inter-individual variability. The inferred parameters provide a compact description of perceptual biases in terms of prior expectations and noise characteristics. Beyond fitting the data, the model induces a transformation of stimulus space, leading to a subject-dependent geometry of perceived stimuli. In this transformed space, perceptual judgments exhibit approximate symmetries that are absent in the physical stimulus coordinates. These results suggest that temporal biases in perception can be understood as a consequence of dynamical inference, and that they impose non-trivial geometric constraints on perceptual representations.

q-bio.NC↗

arXiv2024

Expansion of net correlations in terms of partial correlations

The marginal correlation between two variables is a measure of their linear dependence. The two original variables need not interact directly, because marginal correlation may arise from the mediation of other variables in the system. The underlying network of direct interactions can be captured by a weighted graphical model. The connection between two variables can be weighted by their partial correlation, defined as the residual correlation left after accounting for the linear effects of mediating variables. While matrix inversion can be used to obtain marginal correlations from partial correlations, in large systems this approach does not reveal how the former emerge from the latter. Here we present an expansion of marginal correlations in terms of partial correlations, which shows that the effect of mediating variables can be quantified by the weight of the paths in the graphical model that connect the original pair of variables. The expansion is proved to converge for arbitrary probability distributions. The graphical interpretation reveals a close connection between the topology of the graph and the marginal correlations. Moreover, the expansion shows how marginal correlations change when some variables are severed from the graph, and how partial correlations change when some variables are marginalised out from the description. It also establishes the minimum number of latent variables required to replicate the exact effect of a collection of variables that are marginalised out, ensuring that the partial and marginal correlations of the remaining variables remain unchanged. Notably, the number of latent variables may be significantly smaller than the number of variables that they effectively replicate. Finally, for Gaussian variables, marginal correlations are shown to be related to the efficacy with which information propagates along the paths in the graph.

stat.ME↗

arXiv2024

The Emergence of the Normal Distribution in Deterministic Chaotic Maps

The Central Limit Theorem states that, in the limit of a large number of terms, an appropriately scaled sum of independent random variables yields another random variable whose probability distribution tends to a stable distribution. The condition of independence, however, only holds in real systems as an approximation. To extend the theorem to more general situations, previous studies have derived a version of the Central Limit Theorem that also holds for variables that are not independent. Here, we present numerical results that characterize how convergence is attained when the variables being summed are deterministically related to one another by the recurrent application of an ergodic mapping. In all the explored cases, the convergence to the limit distribution is slower than for random sampling. Yet, the speed at which convergence is attained varies substantially from system to system, and these variations imply differences in the way information about the deterministic nature of the dynamics is progressively lost as the number of summands increases. Some of the identified factors in shaping the convergence process are the strength of mixing induced by the mapping and the shape of the marginal distribution of each variable, most particularly, the presence of divergences or fat tails.

physics.data-an↗

arXiv2021

Bridging physiological and perceptual views of autism by means of sampling-based Bayesian inference

Theories for autism spectrum disorder (ASD) have been formulated at different levels: ranging from physiological observations to perceptual and behavioral descriptions. Understanding the physiological underpinnings of perceptual traits in ASD remains a significant challenge in the field. Here we show how a recurrent neural circuit model which was optimized to perform sampling-based inference and displays characteristic features of cortical dynamics can help bridge this gap. The model was able to establish a mechanistic link between two descriptive levels for ASD: a physiological level, in terms of inhibitory dysfunction, neural variability and oscillations, and a perceptual level, in terms of hypopriors in Bayesian computations. We took two parallel paths: inducing hypopriors in the probabilistic model, and an inhibitory dysfunction in the network model, which lead to consistent results in terms of the represented posteriors, providing support for the view that both descriptions might constitute two sides of the same coin.

q-bio.NC↗

arXiv2021

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.

physics.data-an↗

arXiv2021

Perceptual spaces and their symmetries: The geometry of color space

Our sensory systems transform external signals into neural activity, thereby producing percepts. We are endowed with an intuitive notion of similarity between percepts, that need not reflect the proximity of the physical properties of the corresponding external stimuli. The quantitative characterization of the geometry of percepts is therefore an endeavour that must be accomplished behaviorally. Here we characterized the geometry of color space using discrimination and matching experiments. We proposed an individually tailored metric defined in terms of the minimal chromatic difference required for each observer to differentiate a stimulus from its surround. Next, we showed that this perceptual metric was particularly adequate to describe two additional experiments, since it revealed the natural symmetry of perceptual computations. In one of the experiments, observers were required to discriminate two stimuli surrounded by a chromaticity that differed from that of the tested stimuli. In the perceptual coordinates, the change in discrimination thresholds induced by the surround followed a simple law that only depended on the perceptual distance between the surround and each of the two compared stimuli. In the other experiment, subjects were asked to match the color of two stimuli surrounded by two different chromaticities. Again, in the perceptual coordinates the induction effect produced by surrounds followed a simple, symmetric law. We conclude that the individually-tailored notion of perceptual distance reveals the symmetry of the laws governing perceptual computations.

q-bio.NC↗

arXiv2021

Statistical properties of color matching functions

In trichromats, color vision entails the projection of an infinite-dimensional space (the one containing all possible electromagnetic power spectra) onto the 3-dimensional space that modulates the activity of the three types of cones. This drastic reduction in dimensionality gives rise to metamerism, that is, the perceptual chromatic equivalence between two different light spectra. The classes of equivalence of metamerism are revealed by color-matching experiments, in which observers adjust the intensity of three monochromatic light beams of three pre-set wavelengths (the primaries) to produce a mixture that is perceptually equal to a given monochromatic target stimulus. Here we use the linear relation between the color matching functions and the absorption probabilities of each type of cone to find particularly useful triplets of primaries. As a second goal, we also derive an analytical description of the trial-to-trial variability and the correlations of color matching functions stemming from Poissonian noise in photon capture. We analyze how the statistical properties of the responses to color-matching experiments vary with the retinal composition and the wavelengths of peak absorption probability, and compare them with experimental data on subject-to-subject variability obtained previously.

q-bio.NC↗

arXiv2020

Time- and frequency-resolved covariance analysis for detection and characterization of seizures from intracraneal EEG recordings

The amount of power in different frequency bands of the electroencephalogram (EEG) carries information about the behavioral state of a subject. Hence, neurologists treating epileptic patients monitor the temporal evolution of the different bands. We propose a covariance-based method to detect and characterize epileptic seizures operating on the band-filtered EEG signal. The algorithm is unsupervised, and performs a principal component analysis of intra-cranial EEG recordings, detecting transient fluctuations of the power in each frequency band. Its simplicity makes it suitable for online implementation. Good sampling of the non-ictal periods is required, while no demands are imposed on the amount of data during ictal activity. We tested the method with 32 seizures registered in 5 patients. The area below the resulting receiver-operating characteristic curves was 87\% for the detection of seizures and 91\% for the detection of recruited electrodes. To identify the behaviorally relevant correlates of the physiological signal, we identified transient changes in the variance of each band that were correlated with the degree of loss of consciousness, the latter assessed by the so-called Consciousness Seizure Scale, summarizing the performance of the subject in a number of behavioral tests requested during seizures. We concluded that those crisis with maximal impairment of consciousness tended to exhibit an increase of variance approximately 40 seconds after seizure onset, with predominant power in the theta and alpha bands, and reduced delta and beta activity.

q-bio.NC↗

arXiv2019

Estimating the Mutual Information between two Discrete, Asymmetric Variables with Limited Samples

Determining the strength of non-linear statistical dependencies between two variables is a crucial matter in many research fields. The established measure for quantifying such relations is the mutual information. However, estimating mutual information from limited samples is a challenging task. Since the mutual information is the difference of two entropies, the existing Bayesian estimators of entropy may be used to estimate information. This procedure, however, is still biased in the severely under-sampled regime. Here we propose an alternative estimator that is applicable to those cases in which the marginal distribution of one of the two variables---the one with minimal entropy---is well sampled. The other variable, as well as the joint and conditional distributions, can be severely undersampled. We obtain an estimator that presents very low bias, outperforming previous methods even when the sampled data contain few coincidences. As with other Bayesian estimators, our proposal focuses on the strength of the interaction between two discrete variables, without seeking to model the specific way in which the variables are related. A distinctive property of our method is that the main data statistics determining the amount of mutual information is the inhomogeneity of the conditional distribution of the low-entropy variable in those states (typically few) in which the large-entropy variable registers coincidences.

physics.data-an↗

arXiv2015

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.

cs.CL↗

arXiv2015

Effects of spike-triggered negative feedback on receptive-field properties

Sensory neurons are often described in terms of a receptive field, that is, a linear kernel through which stimuli are filtered before they are further processed. If information transmission is assumed to proceed in a feedforward cascade, the receptive field may be interpreted as the external stimulus' profile maximizing neuronal output. The nervous system, however, contains many feedback loops, and sensory neurons filter more currents than the ones representing the transduced external stimulus. Some of the additional currents are generated by the output activity of the neuron itself, and therefore constitute feedback signals. By means of a time-frequency analysis of the input/output transformation, here we show how feedback modifies the receptive field. The model is applicable to various types of feedback processes, from spike triggered intrinsic conductances to inhibitory synaptic inputs from nearby neurons. We distinguish between the intrinsic receptive field (filtering all input currents) and the effective receptive field (filtering only external stimuli). Whereas the intrinsic receptive field summarizes the biophysical properties of the neuron associated to subthreshold integration and spike generation, only the effective receptive field can be interpreted as the external stimulus' profile maximizing neuronal output. We demonstrate that spike-triggered feedback shifts low-pass filtering towards band-pass processing, transforming integrator neurons into resonators. For strong feedback, a sharp resonance in the spectral neuronal selectivity may appear. Our results provide a unified framework to interpret a collection of previous experimental studies where specific feedback mechanisms were shown to modify the filtering properties of neurons.

q-bio.NC↗

arXiv2013

Linking dynamical and functional properties of intrinsically bursting neurons

Several studies have shown that bursting neurons can encode information in the number of spikes per burst: As the stimulus varies, so does the length of individual bursts. The represented stimuli, however, vary substantially among different sensory modalities and different neurons. The goal of this paper is to determine which kind of stimulus features can be encoded in burst length, and how those features depend on the mathematical properties of the underlying dynamical system. We show that the initiation and termination of each burst is triggered by specific stimulus features whose temporal characteristsics are determined by the types of bifurcations that initiate and terminate firing in each burst. As only a few bifurcations are possible, only a restricted number of encoded features exists. Here we focus specifically on describing parabolic, square-wave and elliptic bursters. We find that parabolic bursters, whose firing is initiated and terminated by saddle-node bifurcations, behave as prototypical integrators: Firing is triggered by depolarizing stimuli, and lasts for as long as excitation is prolonged. Elliptic bursters, contrastingly, constitute prototypical resonators, since both the initiating and terminating bifurcations possess well-defined oscillation time scales. Firing is therefore triggered by stimulus stretches of matching frequency and terminated by a phase-inversion in the oscillation. The behavior of square-wave bursters is somewhat intermediate, since they are triggered by a fold bifurcation of cycles of well-defined frequency but are terminated by a homoclinic bifurcation lacking an oscillating time scale. These correspondences show that stimulus selectivity is determined by the type of bifurcations. We also demonstrate that additional biological properties that do not modify the bifurcation structure play a minor role in stimulus encoding.

q-bio.NC↗

arXiv2010

Time and category information in pattern-based codes

Sensory stimuli are usually composed of different features (the what) appearing at irregular times (the when). Neural responses often use spike patterns to represent sensory information. The what is hypothesized to be encoded in the identity of the elicited patterns (the pattern categories), and the when, in the time positions of patterns (the pattern timing). However, this standard view is oversimplified. In the real world, the what and the when might not be separable concepts, for instance, if they are correlated in the stimulus. In addition, neuronal dynamics can condition the pattern timing to be correlated with the pattern categories. Hence, timing and categories of patterns may not constitute independent channels of information. In this paper, we assess the role of spike patterns in the neural code, irrespective of the nature of the patterns. We first define information-theoretical quantities that allow us to quantify the information encoded by different aspects of the neural response. We also introduce the notion of synergy/redundancy between time positions and categories of patterns. We subsequently establish the relation between the what and the when in the stimulus with the timing and the categories of patterns. To that aim, we quantify the mutual information between different aspects of the stimulus and different aspects of the response. This formal framework allows us to determine the precise conditions under which the standard view holds, as well as the departures from this simple case. Finally, we study the capability of different response aspects to represent the what and the when in the neural response.

q-bio.NC↗

arXiv2008

Type I and type II neuron models are selectively driven by differential stimulus features

Neurons in the nervous system exhibit an outstanding variety of morphological and physiological properties. However, close to threshold, this remarkable richness may be grouped succinctly into two basic types of excitability, often referred to as type I and type II. The dynamical traits of these two neuron types have been extensively characterized. It would be interesting, however, to understand the information-processing consequences of their dynamical properties. To that end, here we determine the differences between the stimulus features inducing firing in type I and in type II neurons. We work both with realistic conductance-based models and minimal normal forms. We conclude that type I neurons fire in response to scale-free depolarizing stimuli. Type II neurons, instead, are most efficiently driven by input stimuli containing both depolarizing and hyperpolarizing phases, with significant power in the frequency band corresponding to the intrinsic frequencies of the cell.

q-bio.NC↗