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Information theory provides ideas for conceptualising information and measuring relationships between objects. It has found wide application in the sciences, but economics and finance have made surprisingly little use of it. We show that…
Despite their widespread utility across domains, basic network models face fundamental limitations when applied to complex biological systems, particularly in neuroscience. This paper critically examines these limitations and explores…
Starting from the working hypothesis that both physics and the corresponding mathematics have to be described by means of discrete concepts on the Planck-scale, one of the many problems one has to face in this enterprise is to find the…
We consider a Gaussian statistical model whose parameter space is given by the variances of random variables. Underlying this model we identify networks by interpreting random variables as sitting on vertices and their correlations as…
Measuring the dependence of data plays a central role in statistics and machine learning. In this work, we summarize and generalize the main idea of existing information-theoretic dependence measures into a higher-level perspective by the…
We propose a novel measure of degree heterogeneity, for unweighted and undirected complex networks, which requires only the degree distribution of the network for its computation. We show that the proposed measure can be applied to all…
In this paper, we extend several approximation theorems, originally formulated in the context of the standard $L^p$ norm, to the more general framework of variable exponent spaces. Our study is motivated by applications in neural networks,…
In recent years, it has become common practice in neuroscience to use networks to summarize relational information in a set of measurements, typically assumed to be reflective of either functional or structural relationships between regions…
In this article, we consider limit theorems for some weighted type random sums (or discrete rough integrals). We introduce a general transfer principle from limit theorems for unweighted sums to limit theorems for weighted sums via rough…
The goal of this paper is to develop methodology for the systematic analysis of asymptotic statistical properties of data driven DRO formulations based on their corresponding non-DRO counterparts. We illustrate our approach in various…
Traditional asymptotic information-theoretic studies of the fundamental limits of wireless communication systems primarily rely on some ideal assumptions, such as infinite blocklength and vanishing error probability. While these assumptions…
Measuring conditional dependencies among the variables of a network is of great interest to many disciplines. This paper studies some shortcomings of the existing dependency measures in detecting direct causal influences or their lack of…
We give simple proofs, under minimal hypotheses, of the Weak Law of Large Numbers and the Central Limit Theorem for independent identically distributed random variables. These proofs use only the elementary calculus, together with the most…
Replicated network data are increasingly available in many research fields. In connectomic applications, inter-connections among brain regions are collected for each patient under study, motivating statistical models which can flexibly…
One of the goals of probabilistic inference is to decide whether an empirically observed distribution is compatible with a candidate Bayesian network. However, Bayesian networks with hidden variables give rise to highly non-trivial…
We present a framework to define a large class of neural networks for which, by construction, training by gradient flow provably reaches arbitrarily low loss when the number of parameters grows. Distinct from the fixed-space global…
One important issue implied by the finite nature of real-world networks regards the identification of their more external (border) and internal nodes. The present work proposes a formal and objective definition of these properties, founded…
Consider d uniformly random permutation matrices on n labels. Consider the sum of these matrices along with their transposes. The total can be interpreted as the adjacency matrix of a random regular graph of degree 2d on n vertices. We…
We develop a statistical mechanics approach for random networks with uncorrelated vertices. We construct equilibrium statistical ensembles of such networks and obtain their partition functions and main characteristics. We find simple…
Theoretical analyses for graph learning methods often assume a complete observation of the input graph. Such an assumption might not be useful for handling any-size graphs due to the scalability issues in practice. In this work, we develop…