We uncover a fairly general principle in online learning: If regret can be (approximately) expressed as a function of certain “sufficient statistics” for the data sequence, then there exists a special Burkholder function that 1) can be used algorithmically to achieve the regret bound and 2) only depends on these sufficient statistics, not the entire data sequence, so that the online strategy is...

Generative score spaces provide a principled method to exploit generative information, e.g., data distribution and hidden variables, in discriminative classifiers. The underlying methodology is to derive measures or score functions from generative models. The derived score functions, spanning the so-called score space, provide features of a fixed dimension for discriminative classification. In ...

We find asymptotically sufficient statistics that could help simplify inference in nonparametric regression problems with correlated errors. These statistics are derived from a wavelet decomposition that is used to whiten the noise process and to effectively separate high resolution and low resolution components. The lower resolution components contain nearly all the available information about...

Based on the empirical or theoretical qualitative information about the relationship between response variable and covariates, we propose a new approach to model polynomial regression using a shape restricted regression after estimating the direction by sufficient dimension reduction. The purpose of this paper is to illustrate that in the absence of prior information other than the shape constr...

Correlation structure contains important information about longitudinal data. Existing sufficient dimension reduction approaches assuming independence may lead to substantial loss of efficiency. We apply the quadratic inference function to incorporate the correlation information and apply the transformation method to recover the central subspace. The proposed estimators are shown to be consiste...

MOTIVATION Measuring evolutionary conservation is a routine step in the identification of functional elements in genome sequences. Although a number of studies have proposed methods that use the continuous time Markov models (CTMMs) to find evolutionarily constrained elements, their probabilistic structures have been less frequently investigated. RESULTS In this article, we investigate a suff...

The problem of superposition of two corresponding vector sets by minimizing their sum-of-squares error under orthogonal transformation is a fundamental task in many areas of science, notably structural molecular biology. This problem can be solved exactly using an algorithm whose time complexity grows linearly with the number of correspondences. This efficient solution has facilitated the wides...