96,216 research outputs found
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 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
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
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