The deviance information criterion (DIC) is widely used for Bayesian model comparison, despite the lack of a clear theoretical foundation. DIC is shown to be an approximation to a penalized loss function based on the deviance, with a penalty derived from a cross-validation argument. This approximation is valid only when the effective number of parameters in the model is much smaller than the nu...

The goal of binary classification is to estimate a discriminant function γ from observations of covariate vectors and corresponding binary labels. We consider an elaboration of this problem in which the covariates are not available directly, but are transformed by a dimensionality-reducing quantizer Q. We present conditions on loss functions such that empirical risk minimization yields Bayes co...

In this extended abstract, we provide an overview of our recent work on the connection between information divergence measures and convex surrogate loss functions used in statistical machine learning. Further details can be found in the technical report [7] and conference paper [6]. The class of f -divergences, introduced independently by Csiszar [4] and Ali and Silvey [1], arise in many areas ...

This paper establishes minimax rates for online regression with arbitrary classes of functions and general losses.1 We show that below a certain threshold for the complexity of the function class, the minimax rates depend on both the curvature of the loss function and the sequential complexities of the class. Above this threshold, the curvature of the loss does not affect the rates. Furthermore...

In this paper we develop an algorithm for structured prediction that optimizes against complex performance measures, those which are a function of false positive and false negative counts. The approach can be directly applied to performance measures such as Fβ score (natural language processing), intersection over union (image segmentation), Precision/Recall at k (search engines) and ROC area (...

Efficient online learning with pairwise loss functions is a crucial component in building largescale learning system that maximizes the area under the Receiver Operator Characteristic (ROC) curve. In this paper we investigate the generalization performance of online learning algorithms with pairwise loss functions. We show that the existing proof techniques for generalization bounds of online a...

In this work, fundamental properties of Bayes decision rule using general loss functions are derived analytically and are verified experimentally for automatic speech recognition. It is shown that, for maximum posterior probabilities larger than 1/2, Bayes decision rule with a metric loss function always decides on the posterior maximizing class independent of the specific choice of (metric) lo...

We introduce and empirically evaluate two novel online gradientbased reinforcement learning algorithms with function approximation – one model based, and the other model free. These algorithms come with the possibility of having non-squared loss functions which is novel in reinforcement learning, and seems to come with empirical advantages. We further extend a previous gradient based algorithm ...

This paper discusses the role of loss functions in Bayesian image classification, object recognition and identification, and reviews the use of a particular loss function which produces visually attractive estimates.

The loss complexity for nonlogarithmic loss functions is defined analogously to the stochastic complexity for logarithmic loss functions such that its mean provides an achievable lower bound for estimation, the mean taken with respect to the worst case data generating distribution. The loss complexity also provides a lower bound for the worst case mean prediction error for all predictors. For t...