Related papers: Some Counterexamples Concerning Maximal Correlatio…
Linear regression is a fundamental modeling tool in statistics and related fields. In this paper, we study an important variant of linear regression in which the predictor-response pairs are partially mismatched. We use an optimization…
Correlations and other collective phenomena in a schematic model of heterogeneous binary agents (individual spin-glass samples) are considered on the complete graph and also on 2d and 3d regular lattices. The system's stochastic dynamics is…
In this paper we study the correlations that arise when two separated parties perform measurements on systems they hold locally. We restrict ourselves to those correlations with which arbitrarily fast transmission of information is…
We revisit the problem of the existence of the maximum likelihood estimate for multi-class logistic regression. We show that one method of ensuring its existence is by assigning positive probability to every class in the sample dataset. The…
The maximal (or Hilbertian) correlation coefficient between two random variables X and Y, denoted by \{X:Y\}, is the supremum of the |Corr(f(X),g(Y))| for real measurable functions f, g, where "Corr" denotes Pearson's correlation…
Maximum Variance Unfolding is one of the main methods for (nonlinear) dimensionality reduction. We study its large sample limit, providing specific rates of convergence under standard assumptions. We find that it is consistent when the…
Logistic regression is widely used in many areas of knowledge. Several works compare the performance of lasso and maximum likelihood estimation in logistic regression. However, part of these works do not perform simulation studies and the…
The inverse problem of statistical mechanics involves finding the minimal Hamiltonian that is consistent with some observed set of correlation functions. This problem has received renewed interest in the analysis of biological networks; in…
We provide a survey on relational models. Relational models describe complete networked {domains by taking into account global dependencies in the data}. Relational models can lead to more accurate predictions if compared to non-relational…
We generalize the classical probability frame by adopting a wider family of random variables that includes nondeterministic ones. The frame that emerges is known to host a ''classical'' extension of quantum mechanics. We discuss the notion…
We give exponential upper bounds for $P(S \le k)$, in particular $P(S=0)$, where $S$ is a sum of indicator random variables that are positively associated. These bounds allow, in particular, a comparison with the independent case. We give…
We suggest novel correlation coefficients which equal the maximum correlation for a class of bivariate Lancaster distributions while being only slightly smaller than maximum correlation for a variety of further bivariate distributions. In…
Collective behaviour in biological systems is often accompanied by strong correlations. The question has therefore arisen of whether correlation is amplified by the vicinity to some critical point in the parameters space. Biological…
We propose a method that infers whether linear relations between two high-dimensional variables X and Y are due to a causal influence from X to Y or from Y to X. The earlier proposed so-called Trace Method is extended to the regime where…
Improving the detection of relevant variables using a new bivariate measure could importantly impact variable selection and large network inference methods. In this paper, we propose a new statistical coefficient that we call the rank…
Although a system is described by a well-known set of equations leading to a deterministic behavior, in the real world the value of a measurand obtained by an experiment will mostly scatter. Accordingly, an uncertainty is associated with…
Empirical economic research frequently applies maximum likelihood estimation in cases where the likelihood function is analytically intractable. Most of the theoretical literature focuses on maximum simulated likelihood (MSL) estimators,…
The machine learning community has recently devoted much attention to the problem of inferring causal relationships from statistical data. Most of this work has focused on uncovering connections among scalar random variables. We generalize…
A scalar-response functional model describes the association between a scalar response and a set of functional covariates. An important problem in the functional data literature is to test the nullity or linearity of the effect of the…
It is clear that conventional statistical inference protocols need to be revised to deal correctly with the high-dimensional data that are now common. Most recent studies aimed at achieving this revision rely on powerful approximation…