A loss function approach to model specification testing and its relative efficiency

The generalized likelihood ratio (GLR) test proposed by Fan, Zhang and Zhang [Ann. Statist. 29 (2001) 153-193] and Fan and Yao [Nonlinear Time Series: Nonparametric and Parametric Methods (2003) Springer] is a generally applicable nonparametric inference procedure. In this paper, we show that although it inherits many advantages of the parametric maximum likelihood ratio (LR) test, the GLR test does not have the optimal power property. We propose a generally applicable test based on loss functions, which measure discrepancies between the null and nonparametric alternative models and are more relevant to decision-making under uncertainty. The new test is asymptotically more powerful than the GLR test in terms of Pitman's efficiency criterion. This efficiency gain holds no matter what smoothing parameter and kernel function are used and even when the true likelihood function is available for the GLR test.Comment: Published in at http://dx.doi.org/10.1214/13-AOS1099 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Bridging the Gap Between Training and Inference for Spatio-Temporal Forecasting

Spatio-temporal sequence forecasting is one of the fundamental tasks in spatio-temporal data mining. It facilitates many real world applications such as precipitation nowcasting, citywide crowd flow prediction and air pollution forecasting. Recently, a few Seq2Seq based approaches have been proposed, but one of the drawbacks of Seq2Seq models is that, small errors can accumulate quickly along the generated sequence at the inference stage due to the different distributions of training and inference phase. That is because Seq2Seq models minimise single step errors only during training, however the entire sequence has to be generated during the inference phase which generates a discrepancy between training and inference. In this work, we propose a novel curriculum learning based strategy named Temporal Progressive Growing Sampling to effectively bridge the gap between training and inference for spatio-temporal sequence forecasting, by transforming the training process from a fully-supervised manner which utilises all available previous ground-truth values to a less-supervised manner which replaces some of the ground-truth context with generated predictions. To do that we sample the target sequence from midway outputs from intermediate models trained with bigger timescales through a carefully designed decaying strategy. Experimental results demonstrate that our proposed method better models long term dependencies and outperforms baseline approaches on two competitive datasets.Comment: ECAI 2020 Accepted, preprin

Isospin particle on S2S^{2} with arbitrary number of supersymmetries

We study the supersymmetric quantum mechanics of an isospin particle in the background of spherically symmetric Yang-Mills gauge field. We show that on $S^{2}$ the number of supersymmetries can be made arbitrarily large for a specific choice of the spherically symmetric SU(2) gauge field. However, the symmetry algebra containing the supercharges becomes nonlinear if the number of fermions is greater than two. We present the exact energy spectra and eigenfunctions, which can be written as the product of monopole harmonics and a certain isospin state. We also find that the supersymmetry is spontaneously broken if the number of supersymmetries is even.Comment: 6 page

BRST symmetries in SU(3) linear sigma model

We study the BRST symmetries in the SU(3) linear sigma model which is constructed through introduction of a novel matrix for the Goldstone boson fields satisfying geometrical constraints embedded in SU(2) subgroup. To treat these constraints we exploit the improved Dirac quantization scheme. We also discuss phenomenological aspacts in the mean field approach to this model.Comment: 17 pages, no figur