Noise-cleaning the precision matrix of fMRI time series

We present a comparison between various algorithms of inference of covariance and precision matrices in small datasets of real vectors, of the typical length and dimension of human brain activity time series retrieved by functional Magnetic Resonance Imaging (fMRI). Assuming a Gaussian model underlying the neural activity, the problem consists in denoising the empirically observed matrices in order to obtain a better estimator of the true precision and covariance matrices. We consider several standard noise-cleaning algorithms and compare them on two types of datasets. The first type are time series of fMRI brain activity of human subjects at rest. The second type are synthetic time series sampled from a generative Gaussian model of which we can vary the fraction of dimensions per sample q = N/T and the strength of off-diagonal correlations. The reliability of each algorithm is assessed in terms of test-set likelihood and, in the case of synthetic data, of the distance from the true precision matrix. We observe that the so called Optimal Rotationally Invariant Estimator, based on Random Matrix Theory, leads to a significantly lower distance from the true precision matrix in synthetic data, and higher test likelihood in natural fMRI data. We propose a variant of the Optimal Rotationally Invariant Estimator in which one of its parameters is optimised by cross-validation. In the severe undersampling regime (large q) typical of fMRI series, it outperforms all the other estimators. We furthermore propose a simple algorithm based on an iterative likelihood gradient ascent, providing an accurate estimation for weakly correlated datasets.

Unsupervised inference approach to facial attractiveness

The perception of facial beauty is a complex phenomenon depending on many, detailed and global facial features influencing each other. In the machine learning community this problem is typically tackled as a problem of supervised inference. However, it has been conjectured that this approach does not capture the complexity of the phenomenon. A recent original experiment (Ib\'a\~nez-Berganza et al., Scientific Reports 9, 8364, 2019) allowed different human subjects to navigate the face-space and "sculpt" their preferred modification of a reference facial portrait. Here we present an unsupervised inference study of the set of sculpted facial vectors in that experiment. We first infer minimal, interpretable, and faithful probabilistic models (through Maximum Entropy and artificial neural networks) of the preferred facial variations, that capture the origin of the observed inter-subject diversity in the sculpted faces. The application of such generative models to the supervised classification of the gender of the sculpting subjects, reveals an astonishingly high prediction accuracy. This result suggests that much relevant information regarding the subjects may influence (and be elicited from) her/his facial preference criteria, in agreement with the multiple motive theory of attractiveness proposed in previous works.

Subjectivity and complexity of facial attractiveness

The origin and meaning of facial beauty represent a longstanding puzzle. Despite the profuse literature devoted to facial attractiveness, its very nature, its determinants and the nature of inter-person differences remain controversial issues. Here we tackle such questions proposing a novel experimental approach in which human subjects, instead of rating natural faces, are allowed to efficiently explore the face-space and "sculpt" their favorite variation of a reference facial image. The results reveal that different subjects prefer distinguishable regions of the face-space, highlighting the essential subjectivity of the phenomenon. The different sculpted facial vectors exhibit strong correlations among pairs of facial distances, characterizing the underlying universality and complexity of the cognitive processes, leading to the observed subjectivity.