A ‘nondecimated’ lifting transform

Classical nondecimated wavelet transforms are attractive for many applications. When the data comes from complex or irregular designs, the use of second generation wavelets in nonparametric regression has proved superior to that of classical wavelets. However, the construction of a nondecimated second generation wavelet transform is not obvious. In this paper we propose a new ‘nondecimated’ lifting transform, based on the lifting algorithm which removes one coefficient at a time, and explore its behavior. Our approach also allows for embedding adaptivity in the transform, i.e. wavelet functions can be constructed such that their smoothness adjusts to the local properties of the signal. We address the problem of nonparametric regression and propose an (averaged) estimator obtained by using our nondecimated lifting technique teamed with empirical Bayes shrinkage. Simulations show that our proposed method has higher performance than competing techniques able to work on irregular data. Our construction also opens avenues for generating a ‘best’ representation, which we shall explore.     

论我国部分结婚禁止条件的“解禁”

为规制结婚行为,我国婚姻法设置了禁止直系血亲和三代以内旁系血亲通婚、禁止患有医学上认为不应当结婚的疾病的结婚等禁止性条件。这些规定有的符合婚姻法的契约精神,有的则违背了这种精神,甚至存在着不符合婚姻功能变迁、混淆结婚权和生育权、脱离人们的"道德共识"等问题,因此需要"解禁"。     

“解严”后台湾家族书写的特征与意义

台湾政治“解严”后所形成的多元文化语境使得文学表述及叙事的多样性成为可能,家族书写也以自身的叙事样貌展现了台湾社会文化观念的变迁及文学典律生成与发展的形态。通过分析具体作品,可以发现“解严”后台湾家族书写在讲述家族故事的角度和方式上有其自身的特征,将言说家族的方式放置在文学语境与文化观念的变迁之中考察,则可从更深层面探讨再现家族的意义、叙事价值及家族书写在台湾文化语境中的存在意义。     

日本"井上财政"史论

所谓“井上财政”是指藏相井上准之助所推行的一系列财政政策,其主要措施,一是紧缩通货,推行“产业合理化”,以降低成本,扩大出口;二是解除禁止黄金出口的禁令,恢复金本位制。但世界经济危机迅猛袭来,给日本经济带来莫大冲击,而井上准之助却继续强化“井上财政”政策以应对危机,使日本经济雪上加霜。虽然井上财政没有取得预期效果,却对后来日本经济恢复起到了不可估量的作用,成为日本经济迅速摆脱危机的前提和手段。     

Adaptive lifting for nonparametric regression

Many wavelet shrinkage methods assume that the data are observed on an equally spaced grid of length of the form 2^J for some J. These methods require serious modification or preprocessed data to cope with irregularly spaced data. The lifting scheme is a recent mathematical innovation that obtains a multiscale analysis for irregularly spaced data. A key lifting component is the “predict” step where a prediction of a data point is made. The residual from the prediction is stored and can be thought of as a wavelet coefficient. This article exploits the flexibility of lifting by adaptively choosing the kind of prediction according to a criterion. In this way the smoothness of the underlying ‘wavelet’ can be adapted to the local properties of the function. Multiple observations at a point can readily be handled by lifting through a suitable choice of prediction. We adapt existing shrinkage rules to work with our adaptive lifting methods. We use simulation to demonstrate the improved sparsity of our techniques and improved regression performance when compared to both wavelet and non-wavelet methods suitable for irregular data. We also exhibit the benefits of our adaptive lifting on the real inductance plethysmography and motorcycle data.     

Multiscale methods for data on graphs and irregular multidimensional situations

Summary.  For regularly spaced one-dimensional data, wavelet shrinkage has proven to be a compelling method for non-parametric function estimation. We create three new multiscale methods that provide wavelet-like transforms both for data arising on graphs and for irregularly spaced spatial data in more than one dimension. The concept of scale still exists within these transforms, but as a continuous quantity rather than dyadic levels. Further, we adapt recent empirical Bayesian shrinkage techniques to enable us to perform multiscale shrinkage for function estimation both on graphs and for irregular spatial data. We demonstrate that our methods perform very well when compared with several other methods for spatial regression for both real and simulated data. Although we concentrate on multiscale shrinkage (regression) we present our new 'wavelet transforms' as generic tools intended to be the basis of methods that might benefit from a multiscale representation of data either on graphs or for irregular spatial data.