5 research outputs found
Master index
Pla general, del mural cerĂ mic que decora una de les parets del vestĂbul de la Facultat de QuĂmica de la UB. El mural representa diversos sĂmbols relacionats amb la quĂmica
Information Processing Equalities and the Information-Risk Bridge
We introduce two new classes of measures of information for statistical
experiments which generalise and subsume -divergences, integral
probability metrics, -distances (MMD), and
divergences between two or more distributions. This enables us to derive a
simple geometrical relationship between measures of information and the Bayes
risk of a statistical decision problem, thus extending the variational
-divergence representation to multiple distributions in an entirely
symmetric manner. The new families of divergence are closed under the action of
Markov operators which yields an information processing equality which is a
refinement and generalisation of the classical data processing inequality. This
equality gives insight into the significance of the choice of the hypothesis
class in classical risk minimization.Comment: 48 pages; corrected some typos and added a few additional
explanation
Loss functions, complexities, and the Legendre transformation
The paper introduces a way of re-constructing a loss function from predictive complexity. We show that a loss function and expectations of the corresponding predictive complexity w.r.t. the Bernoulli distribution are related through the Legendre transformation. It is shown that if two loss functions specify the same complexity then they are equivalent in a strong sense. The expectations are also related to the so called generalised entropy