Related papers: Strict independence
The monotonic dependence of the outputs of a neural network on some of its inputs is a crucial inductive bias in many scenarios where domain knowledge dictates such behavior. This is especially important for interpretability and fairness…
We consider the problem of bounding large deviations for non-i.i.d. random variables that are allowed to have arbitrary dependencies. Previous works typically assumed a specific dependence structure, namely the existence of independent…
Charge independence and symmetry are approximate symmetries of nature. The observations of the small symmetry breaking effects and the consequences of those effects are reviewed. The effects of the mass difference between up and down quarks…
In this paper, the defining properties of a valid measure of the dependence between two random variables are reviewed and complemented with two original ones, shown to be more fundamental than other usual postulates. While other popular…
We suggest a dependence coefficient between a categorical variable and some general variable taking values in a metric space. We derive important theoretical properties and study the large sample behaviour of our suggested estimator.…
While most fundamental interactions in nature are known to be mediated by quantized fields, the possibility has been raised that gravity may behave differently. Making this concept precise enough to test requires consistent models. Here we…
The law of large numbers is one of the most fundamental results in Probability Theory. In the case of independent sequences, there are some known characterizations; for instance, in the independent and identically distributed setting it is…
We give a universal recipe for constructing nonlinear entanglement witnesses able to detect non-classical correlations in arbitrary systems of distinguishable and/or identical particles for an arbitrary number of constituents. The…
The main contribution of this paper is a strong converse result for $K$-hop distributed hypothesis testing against independence with multiple (intermediate) decision centers under a Markov condition. Our result shows that the set of type-II…
I review recent results regarding the nucleon charge and magnetization densities as well as the shape of the nucleon. First, some phenomenolgical considerations that show that the shape of the proton is not round are discussed. Then model…
We consider theories that modify gravity at cosmological distances, and show that any such theory must exhibit a strong coupling phenomenon, or else it is either inconsistent or is already ruled out by the solar system observations. We show…
We investigate some variants of the splitting, reaping, and independence numbers defined using asymptotic density. Specifically, we give a proof of Con($\mathfrak{i}<\mathfrak{s}_{1/2}$), Con($\mathfrak{r}_{1/2}<\mathfrak{b}$) and…
Based on recent progress in research on copula based dependence measures, we review the original Renyi's axioms on symmetric measures and propose a new set of axioms that applies to nonsymmetric measures. We show that nonsymmetric measures…
This paper introduces a new method for testing the statistical significance of estimated parameters in predictive regressions. The approach features a new family of test statistics that are robust to the degree of persistence of the…
In this expository note we show that the learning parities with noise (LPN) assumption is robust to weak dependencies in the noise distribution of small batches of samples. This provides a partial converse to the linearization technique of…
We study constrained versions of the Ingleton inequality in the entropic setting and quantify its stability under small violations of conditional independence. Although the classical Ingleton inequality fails for general entropy profiles,…
We discuss properties of distributions that are multivariate totally positive of order two (MTP2) related to conditional independence. In particular, we show that any independence model generated by an MTP2 distribution is a compositional…
Credal networks are graph-based statistical models whose parameters take values in a set, instead of being sharply specified as in traditional statistical models (e.g., Bayesian networks). The computational complexity of inferences on such…
We seek to create tools for a model-theoretic analysis of types in algebraically closed valued fields (ACVF). We give evidence to show that a notion of 'domination by stable part' plays a key role. In Part A, we develop a general theory of…
Bifurcation theory and continuation methods are well-established tools for the analysis of nonlinear mechanical systems subject to periodic forcing. We illustrate the added value and the complementary information provided by singularity…