In Random Forests [2] several trees are constructed from bootstrapor subsamples of the original data. Random Forests have become very popular, e.g., in the fields of genetics and bioinformatics, because they can deal with high-dimensional problems including complex interaction effects. Conditional Inference Forests [8] provide an implementation of Random Forests with unbiased variable selection...

Bayesian networks, and especially their structures, are powerful tools for representing conditional independencies and dependencies between random variables. In applications where related variables form a priori known groups, chosen to represent different “views” to or aspects of the same entities, one may be more interested in modeling dependencies between groups of variables rather than betwe...

We consider random design nonparametric regression when the response variable is subject to right censoring. Following the work of Fan and Gijbels (1994), a common approach to this problem is to apply what has been termed a censoring unbiased transformation to the data to obtain surrogate responses, and then enter these surrogate responses with covariate data into standard smoothing algorithms....

We consider axiomatically the problem of estimating the strength of a conditional dependence relationship PY |X from a random variables X to a random variable Y . This has applications in determining the strength of a known causal relationship, where the strength depends only on the conditional distribution of the effect given the cause (and not on the driving distribution of the cause). Shanno...

We investigate conditions for the existence of the limiting conditional distribution of a bivariate random vector when one component becomes large. We revisit the existing literature on the topic, and present some new sufficient conditions. We concentrate on the case where the conditioning variable belongs to the maximum domain of attraction of the Gumbel law, and we study geometric conditions ...

We consider axiomatically the problem of estimating the strength of a conditional dependence relationship PY |X from a random variables X to a random variable Y . This has applications in determining the strength of a known causal relationship, where the strength depends only on the conditional distribution of the effect given the cause (and not on the driving distribution of the cause). Shanno...

In Libra, each probabilistic model represents a probability distribution, P (X ), over set of discrete random variables, X = {X1, X2, . . . , Xn}. Libra supports Bayesian networks (BNs), Markov networks (MNs), dependency networks (DNs) [8], sumproduct networks (SPNs) [19], arithmetic circuits (ACs) [6], and mixtures of trees (MT) [17]. BNs and DNs represent a probability distribution as a colle...

We study notions of robustness of Markov kernels and probability distribution of a system that is described by n input random variables and one output random variable. Markov kernels can be expanded in a series of potentials that allow to describe the system’s behaviour after knockouts. Robustness imposes structural constraints on these potentials. Robustness of probability distributions is def...

Motivated by applications to prediction and forecasting, we suggest methods for approximating the conditional distribution function of a random variable Y given a dependent random d-vector X. The idea is to estimate not the distribution of Y |X, but that of Y |θX, where the unit vector θ is selected so that the approximation is optimal under a least-squares criterion. We show that θ may be esti...

We take a closer look at the structure of bivariate dependency induced by a pair of predictor random variables (X1, X2) trying to synergistically, redundantly or uniquely encode a target random variable Y. We evaluate a recently proposed measure of redundancy based on the Gács and Körner's common information (Griffith et al., Entropy 2014, 16, 1985–2000) and show that the measure, in spite of i...