The case-only design, which requires only diseased subjects, allows for estimation of multiplicative interactions between factors known to be independent in the study population. The design is being used as an alternative to the case-control design to study gene-environment interactions. Estimates of gene-environment interactions have been shown to be very efficient relative to estimates obtain...

An important aspect of multiple hypothesis testing is controlling the significance level, or the level of Type I error. When the test statistics are not independent it can be particularly challenging to deal with this problem, without resorting to very conservative procedures. In this paper we show that, in the context of contemporary multiple testing problems, where the number of tests is ofte...

In many applications, independence of event occurrences is assumed, even if there is evidence for dependence. Capturing dependence leads to complex models, and even if the complex models were superior, they fail to beat the simplicity and scalability of the independence assumption. Therefore, many models assume independence and apply heuristics to improve results. Theoretical explanations of th...

We establish several results yielding linear independence of the affine system generated by ψ in exchange for conditions on the space V (ψ) of negative dilates. A typical assumption yielding linear independence is that the space V (ψ) is shift-invariant. In particular, the affine system generated by a Parseval wavelet is linearly independent. As an illustration of our techniques, we give an alt...

In this paper, we propose a novel test of independence based on the concept of correntropy. We explore correntropy from a statistical perspective and discuss its properties in the context of testing independence. We introduce the novel concept of parametric correntropy and design a test of independence based on it. We further discuss how the proposed test relaxes the assumption of Gaussianity. ...

In this paper, we show that generative classifiers are capable of learning non-linear decision boundaries and that non-linear generative models can outperform a number of linear classifiers on some text categorization tasks. We first prove that 3-layer multinomial hierarchical generative (Bayesian) classifiers, under a particular independence assumption, can only learn the same linear decision ...

Many models of recognition are derived from models originally applied to perception tasks, which assume that decisions from trial to trial are independent. While the independence assumption is violated for many perception tasks, we present the results of several experiments intended to relate memory and perception by exploring sequential dependencies in recognition. The findings from these expe...