Of numerous proposals to improve the accuracy of naive Bayes by weakening its attribute independence assumption, both LBR and TAN have demonstrated remarkable error performance. However, both techniques obtain this outcome at a considerable computational cost. We present a new approach to weakening the attribute independence assumption by averaging all of a constrained class of classifiers. In ...

UNLABELLED Most decisions that we make build upon multiple streams of sensory evidence and control mechanisms are needed to filter out irrelevant information. Sequential sampling models of perceptual decision making have recently been enriched by attentional mechanisms that weight sensory evidence in a dynamic and goal-directed way. However, the framework retains the longstanding hypothesis tha...

We examine the Bayesian approach to the discovery of directed acyclic causal models and compare it to the constraint-based approach. Both approaches rely on the Causal Markov assumption, but the two di er signi cantly in theory and practice. An important di erence between the approaches is that the constraint-based approach uses categorical information about conditional-independence constraints...

Peter P. Wakker has forcefully shown the importance for decision theory of a condition that he called “Cardinal Coordinate Independence”. Indeed, when the outcome space is rich, he proved that, for continuous weak orders, this condition fully characterizes the Subjective Expected Utility model with a finite number of states. He has furthermore explored in depth how this condition can be weakene...

Peter P. Wakker has forcefully shown the importance for decision theory of a condition that he called “Cardinal Coordinate Independence”. Indeed, when the outcome space is rich, he proved that, for continuous weak orders, this condition fully characterizes the Subjective Expected Utility model with a finite number of states. He has furthermore explored in depth how this condition can be weakene...

When making a comparison between two or more traits across taxa, the assumption of phylogenetic independence must be tested. Empirically determining the validity of this assumption before and after applying a phylogenetically based comparative method (PCM) can provide researchers with a rigorous methodological approach for analysing comparative data. This approach can help resolve current debat...

Widely used convolutions and deconvolutions techniques traditionally rely on the assumption of independence, an assumption often criticized as being very strong. We observe that independence is, in fact, not necessary for the convolution theorem to hold. Instead, a much weaker notion, known as subindependence, is the appropriate necessary and sufficient condition. We motivate the usefulness of ...

Bell’s theorem requires the assumption that hidden variables are independent of future measurement settings. This independence assumption rests on surprisingly shaky ground. In particular, it is puzzlingly time-asymmetric. The paper begins with a summary of the case for considering hidden variable models which, in abandoning this independence assumption, allow a degree of ‘backward causation’. ...

Latent class analysis is based on the assumption that within each class the observed class indicator variables are independent of each other. We explore a new Bayesian approach that relaxes this assumption to an assumption of approximate independence. Instead of using a correlation matrix with correlations fixed to zero we use a correlation matrix where all correlations are estimated using an i...