Many learning algorithms approximately minimize a risk functional over a predefined function class. In order to establish consistency for such algorithms it is therefore necessary to know whether this function class approximates the Bayes risk. In this work we present necessary and sufficient conditions for the latter. We then apply these results to reproducing kernel Hilbert spaces used in sup...

Candidate selection from n-best lists is a widely used approach in natural language parsing. Instead of attempting to select the most probable candidate, we focus on prediction of a new structure which minimizes an approximation to Bayes risk. Our approach does not place any restrictions on the probabilistic model used. We show how this approach can be applied in both dependency and constituent...

This paper examines two vector quantization algorithms which can combine the tasks of compression and classiication: Bayes risk weighted vector quantization (BRVQ) proposed by Oehler et al., and Optimized Learning Vector Quantization 1 (OLVQ1) proposed by Kohonen et al. BRVQ uses a parameter to control the tradeoo between compression and clas-siication. BRVQ performance is studied for a range o...

A new nearest-neighbor method is described for estimating the Bayes risk of a multiclass pattern claSSification problem from sample data (e.g., a classified training set). Although it is assumed that the classification problem can be accurately described by sufficiently smooth class-conditional distributions, neither these distributions, nor the corresponding prior probabilities of the classes ...

ROVER [1] and its successor voting procedures have been shown to be quite effective in reducing the recognition word error rate (WER). The success of these methods has been attributed to their minimum Bayes-risk (MBR) nature: they produce the hypothesis with the least expected word error. In this paper we develop a general procedure within the MBR framework, called segmental MBR recognition, th...

Speech recognition is the task of converting an acoustic signal, which contains speech, to written text. The error of a speech recognition system is measured in the number of words in which the recognized and the spoken text differ. This work investigates and develops decoding and system combination approaches within the Bayes risk decoding framework with the objective of reducing the number of...

Abstract Naive Bayesian classification algorithm is widely used in big data analysis and other fields because of its simple fast structure. Aiming at the shortcomings naive Bayes algorithm, this paper uses feature weighting Laplace calibration to improve it, obtains improved algorithm. Through numerical simulation, it found that when sample size large, accuracy more than 99%, very stable; attri...

Consider the problem of estimating a multivariate normal mean with a known variance matrix, which is not necessarily proportional to the identity matrix. The coordinates are shrunk directly in proportion to their variances in Efron and Morris’ (J. Amer. Statist. Assoc. 68 (1973) 117–130) empirical Bayes approach, whereas inversely in proportion to their variances in Berger’s (Ann. Statist. 4 (1...