Abstract This work investigates the intersection property of conditional independence. It states that for random variables $$A,B,C$$ and X we have that $$X \bot \bot A{\kern 1pt} {\kern 1pt} |{\kern 1pt} {\kern 1pt} B,C$$ and $$X\, \bot \bot\, B{\kern 1pt} {\kern 1pt} |{\kern 1pt} {\kern 1pt}...

Nearest neighbour classification requires a good distance metric. Previous approaches try to learn a quadratic distance metric learning so that observations of different classes are well separated. For high-dimensional problems, where many uninformative variables are present, it is attractive to...

A frequently encountered challenge in high-dimensional regression is the detection of relevant variables. Variable selection suffers from instability and the power to detect relevant variables is typically low if predictor variables are highly correlated. When taking the multiplicity of the...

We propose probabilistic lower bounds for the number of false null hypotheses when testing multiple hypotheses of association simultaneously. The bounds are valid under general and unknown dependence structures between the test statistics. The power of the proposed estimator to detect the full...

Inspired by the success of the Lasso for regression analysis, it seems attractive to estimate the graph of a multivariate normal distribution by l1-norm penalized likelihood maximization. We examine some properties of the estimator and show that care has to be taken with interpretation of...