相关论文: A comparison of Euclidean metrics and their applic…
A main goal in the field of statistical shape analysis is to define computable and informative metrics on spaces of immersed manifolds, such as the space of curves in a Euclidean space. The approach taken in the elastic shape analysis…
Measures of multiple spike train synchrony are essential in order to study issues such as spike timing reliability, network synchronization, and neuronal coding. These measures can broadly be divided in multivariate measures and averages…
Phylogenetic inference-the derivation of a hypothesis for the common evolutionary history of a group of species- is an active area of research at the intersection of biology, computer science, mathematics, and statistics. One assumes the…
Transformer models learn to encode and decode an input text, and produce contextual token embeddings as a side-effect. The mapping from language into the embedding space maps words expressing similar concepts onto points that are close in…
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…
Simultaneous recordings from many neurons hide important information and the connections characterizing the network remain generally undiscovered despite the progresses of statistical and machine learning techniques. Discerning the presence…
In many animal sensory pathways, the transformation from external stimuli to spike trains is essentially deterministic. In this context, a new mathematical framework for coding and reconstruction, based on a biologically plausible model of…
We develop an inferential toolkit for analyzing object-valued responses, which correspond to data situated in general metric spaces, paired with Euclidean predictors within the conformal framework. To this end we introduce conditional…
Empirically, Deep Learning (DL) has demonstrated unprecedented success in practical applications. However, DL remains by and large a mysterious "black-box", spurring recent theoretical research to build its mathematical foundations. In this…
Characterising the representation of sensory stimuli in the brain is a fundamental scientific endeavor, which can illuminate principles of information coding. Most characterizations reduce the dimensionality of neural data by converting…
Representing, comparing, and measuring the distance between probability distributions is a key task in computational statistics and machine learning. The choice of representation and the associated distance determine properties of the…
Accurate statistical models of neural spike responses can characterize the information carried by neural populations. But the limited samples of spike counts during recording usually result in model overfitting. Besides, current models…
Our knowledge of the sensory world is encoded by neurons in sequences of discrete, identical pulses termed action potentials or spikes. There is persistent controversy about the extent to which the precise timing of these spikes is relevant…
This article provides an overview on the statistical modeling of complex data as increasingly encountered in modern data analysis. It is argued that such data can often be described as elements of a metric space that satisfies certain…
An essential step toward understanding neural circuits is linking their structure and their dynamics. In general, this relationship can be almost arbitrarily complex. Recent theoretical work has, however, begun to identify some broad…
It has been demonstrated many times that the behavior of the human visual system is connected to the statistics of natural images. Since machine learning relies on the statistics of training data as well, the above connection has…
Quantification of information content and its temporal variation in intracellular calcium spike trains in neurons helps one understand functions such as memory, learning, and cognition. Such quantification could also reveal pathological…
Many scientific fields study data with an underlying structure that is a non-Euclidean space. Some examples include social networks in computational social sciences, sensor networks in communications, functional networks in brain imaging,…
We wish to discriminate spike sequences based on the degree of irregularity. For this purpose, we search for a rational expressions of quadratic functions of consecutive interspike intervals that efficiently measures spiking irregularity.…
Image similarity is a core concept in Image Analysis due to its extensive application in computer vision, image processing, and pattern recognition. The objective of our study is to evaluate Quasi-Euclidean metric as an image similarity…