Related papers: Strong Asymptotic Composition Theorems for Mutual …
We consider the problem of recovering the community structure in the stochastic block model with two communities. We aim to describe the mutual information between the observed network and the actual community structure in the sparse…
We show that the mutual information between two symbols, as a function of the number of symbols between the two, decays exponentially in any probabilistic regular grammar, but can decay like a power law for a context-free grammar. This…
The article studies the almost surely asymptotics of extreme values $\bar{\xi}_n = \max_{1\leq i \leq n} \xi_i$, where $ \xi , \xi_1 , \xi_2 , \ldots$ are discrete identically distributed random variables. One of the main results on this…
Information-theoretic quantities have received significant attention as system-independent measures of correlations in many-body quantum systems, e.g., as universal order parameters of synchronization. In this work, we present a method to…
The maximal information coefficient (MIC), which measures the amount of dependence between two variables, is able to detect both linear and non-linear associations. However, computational cost grows rapidly as a function of the dataset…
Motivated by applications to group synchronization and quadratic assignment on random data, we study a general problem of Bayesian inference of an unknown ``signal'' belonging to a high-dimensional compact group, given noisy pairwise…
A recent article on generalised linear mixed model asymptotics, Jiang et al. (2022), derived the rates of convergence for the asymptotic variances of maximum likelihood estimators. If $m$ denotes the number of groups and $n$ is the average…
The finite sample properties of estimators are usually understood or approximated using asymptotic theories. Two main asymptotic constructions have been used to characterize the presence of many instruments. The first assumes that the…
In random cellular systems, both observation and maximum entropy inference give a specific form to the topological pair correlation: it is bi-affine in the cells number of edges with coefficients depending on the distance between the two…
Linear systems with many degrees of freedom containing multiplicative and additive noise are considered. The steady state probability distribution for equations of this kind is examined. With multiplicative white noise it is shown that…
We investigate the sample complexity of mutual information and conditional mutual information testing. For conditional mutual information testing, given access to independent samples of a triple of random variables $(A, B, C)$ with unknown…
We study the problem of community detection when there is covariate information about the node labels and one observes multiple correlated networks. We provide an asymptotic upper bound on the per-node mutual information as well as a…
When observations are organized into groups where commonalties exist amongst them, the dependent random measures can be an ideal choice for modeling. One of the propositions of the dependent random measures is that the atoms of the…
Consider a random sample $X_1 , X_2 , ..., X_n$ drawn independently and identically distributed from some known sampling distribution $P_X$. Let $X_{(1)} \le X_{(2)} \le ... \le X_{(n)}$ represent the order statistics of the sample. The…
Estimating Mutual Information (MI), a key measure of dependence of random quantities without specific modelling assumptions, is a challenging problem in high dimensions. We propose a novel mutual information estimator based on parametrizing…
We derive high-order terms in the asymptotic expansions of the steady-state voltage potentials in the presence of a finite number of diametrically small inhomogeneities with conductivities different from the background conductivity. Our…
Given two random variables $X$ and $Y$, an operational approach is undertaken to quantify the ``leakage'' of information from $X$ to $Y$. The resulting measure $\mathcal{L}(X \!\! \to \!\! Y)$ is called \emph{maximal leakage}, and is…
We derive a nonparametric higher-order asymptotic expansion for small-time changes of conditional characteristic functions of It\^o semimartingale increments. The asymptotics setup is of joint type: both the length of the time interval of…
Superpositions of Ornstein-Uhlenbeck processes allow a flexible dependence structure, including long range dependence for OU-type processes. Their complex asymptotics are governed by three effects: the behavior of the L\'evy measure both at…
We discuss the equilibrium of a single collective variable characterizing a finite set of coupled, noisy, bistable systems as the noise strength, the size and the coupling parameter are varied. We identify distinct regions in parameter…