Related papers: On the Correlation of Increasing Families
Harris's correlation inequality states that any two monotone functions on the Boolean hypercube are positively correlated. Talagrand \cite{Talcorr} started a line of works in search of quantitative versions of this fact by providing a lower…
This paper establishes quantitative correlation inequalities between monotone events and structured threshold objects in both the discrete cube and Gaussian space. We prove that for any increasing balanced family, there exists a linear…
We address a special case of a conjecture of M. Talagrand relating two notions of "threshold" for an increasing family $\mathcal F$ of subsets of a finite set $V$. The full conjecture implies equivalence of the "Fractional…
Talagran's correlation inequality provides quantitative lower bounds on the covariance of two increasing Boolean functions in terms of their coordinate influences, but, in general, a logarithmic loss is necessary. Motivated by a question of…
Quantum correlations typically decrease with increasing noise, although classical correlators (CCors) may rise for a particular class of states with noise. To analyse the behavior of classical correlation (CC) in the presence of local…
This note is concerned with an extension, at second order, of an inequality on the discrete cube $C_n=\{-1,1\}$ (equipped with the uniform measure) due to Talagrand (\cite{TalL1L2}). As an application, the main result of this note is a…
We introduce a new low-noise condition for classification, the Model Margin Noise (MM noise) assumption, and derive enhanced $\mathcal{H}$-consistency bounds under this condition. MM noise is weaker than Tsybakov noise condition: it is…
We prove a lower bound of $\tilde{\Omega}(n^{1/3})$ for the query complexity of any two-sided and adaptive algorithm that tests whether an unknown Boolean function $f:\{0,1\}^n\rightarrow \{0,1\}$ is monotone or far from monotone. This…
We show that classical chaining bounds on the suprema of random processes in terms of entropy numbers can be systematically improved when the underlying set is convex: the entropy numbers need not be computed for the entire set, but only…
A set function can be extended to the unit cube in various ways; the correlation gap measures the ratio between two natural extensions. This quantity has been identified as the performance guarantee in a range of approximation algorithms…
Most correlation inequalities for high-dimensional functions in the literature, such as the Fortuin-Kasteleyn-Ginibre (FKG) inequality and the celebrated Gaussian Correlation Inequality of Royen, are qualitative statements which establish…
Synchronization is a widespread phenomenon observed in physical, biological, and social networks, which persists even under the influence of strong noise. Previous research on oscillators subject to common noise has shown that noise can…
In this paper we consider the possible correlations between two parties using local machines and shared randomness with an additional amount of classical communication. This is a continuation of the work initiated by Bacon and Toner in Ref.…
We consider the problem of releasing a sparse histogram under $(\varepsilon, \delta)$-differential privacy. The stability histogram independently adds noise from a Laplace or Gaussian distribution to the non-zero entries and removes those…
We propose a family of association measures for two-way contingency tables whose latent distribution can be assumed to be bivariate normal. When this assumption holds, the power-divergence measuring departure from independence can be…
Based on the notion of maximal correlation, Kimeldorf, May and Sampson (1980) introduce a measure of correlation between two random variables, called the "concordant monotone correlation" (CMC). We revisit, generalize and prove new…
We derive a new upper bound for the correlations in a heterogeneous one-dimensional Ising model with free boundary conditions. The new upper bound quantifies the simultaneous decay of correlations due to weakness of nearest-neighbor…
Physical principles constrain the way nonlocal correlations can be distributed among distant parties. These constraints are usually expressed by monogamy relations that bound the amount of Bell inequality violation observed among a set of…
Higher criticism is a method for detecting signals that are both sparse and weak. Although first proposed in cases where the noise variables are independent, higher criticism also has reasonable performance in settings where those variables…
The notion of non-classical correlations is a powerful contrivance for explaining phenomena exhibited in quantum systems. It is well known, however, that quantum systems are not free to explore arbitrary correlations---the church of the…