Robust Kalman tracking and smoothing with propagating and non-propagating outliers

A common situation in filtering where classical Kalman filtering does not perform particularly well is tracking in the presence of propagating outliers. This calls for robustness understood in a distributional sense, i.e.; we enlarge the distribution assumptions made in the ideal model by suitable neighborhoods. Based on optimality results for distributional-robust Kalman filtering from Ruckdeschel[01,10], we propose new robust recursive filters and smoothers designed for this purpose as well as specialized versions for non-propagating outliers. We apply these procedures in the context of a GPS problem arising in the car industry. To better understand these filters, we study their behavior at stylized outlier patterns (for which they are not designed) and compare them to other approaches for the tracking problem. Finally, in a simulation study we discuss efficiency of our procedures in comparison to competitors.Comment: 27 pages, 12 figures, 2 table

Just Another Gibbs Additive Modeller: Interfacing JAGS and mgcv

The BUGS language offers a very flexible way of specifying complex statistical models for the purposes of Gibbs sampling, while its JAGS variant offers very convenient R integration via the rjags package. However, including smoothers in JAGS models can involve some quite tedious coding, especially for multivariate or adaptive smoothers. Further, if an additive smooth structure is required then some care is needed, in order to centre smooths appropriately, and to find appropriate starting values. R package mgcv implements a wide range of smoothers, all in a manner appropriate for inclusion in JAGS code, and automates centring and other smooth setup tasks. The purpose of this note is to describe an interface between mgcv and JAGS, based around an R function, `jagam', which takes a generalized additive model (GAM) as specified in mgcv and automatically generates the JAGS model code and data required for inference about the model via Gibbs sampling. Although the auto-generated JAGS code can be run as is, the expectation is that the user would wish to modify it in order to add complex stochastic model components readily specified in JAGS. A simple interface is also provided for visualisation and further inference about the estimated smooth components using standard mgcv functionality. The methods described here will be un-necessarily inefficient if all that is required is fully Bayesian inference about a standard GAM, rather than the full flexibility of JAGS. In that case the BayesX package would be more efficient.Comment: Submitted to the Journal of Statistical Softwar

On multi-view learning with additive models

In many scientific settings data can be naturally partitioned into variable groupings called views. Common examples include environmental (1st view) and genetic information (2nd view) in ecological applications, chemical (1st view) and biological (2nd view) data in drug discovery. Multi-view data also occur in text analysis and proteomics applications where one view consists of a graph with observations as the vertices and a weighted measure of pairwise similarity between observations as the edges. Further, in several of these applications the observations can be partitioned into two sets, one where the response is observed (labeled) and the other where the response is not (unlabeled). The problem for simultaneously addressing viewed data and incorporating unlabeled observations in training is referred to as multi-view transductive learning. In this work we introduce and study a comprehensive generalized fixed point additive modeling framework for multi-view transductive learning, where any view is represented by a linear smoother. The problem of view selection is discussed using a generalized Akaike Information Criterion, which provides an approach for testing the contribution of each view. An efficient implementation is provided for fitting these models with both backfitting and local-scoring type algorithms adjusted to semi-supervised graph-based learning. The proposed technique is assessed on both synthetic and real data sets and is shown to be competitive to state-of-the-art co-training and graph-based techniques.Comment: Published in at http://dx.doi.org/10.1214/08-AOAS202 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Approximation of fuzzy numbers by convolution method

In this paper we consider how to use the convolution method to construct approximations, which consist of fuzzy numbers sequences with good properties, for a general fuzzy number. It shows that this convolution method can generate differentiable approximations in finite steps for fuzzy numbers which have finite non-differentiable points. In the previous work, this convolution method only can be used to construct differentiable approximations for continuous fuzzy numbers whose possible non-differentiable points are the two endpoints of 1-cut. The constructing of smoothers is a key step in the construction process of approximations. It further points out that, if appropriately choose the smoothers, then one can use the convolution method to provide approximations which are differentiable, Lipschitz and preserve the core at the same time.Comment: Submitted to Fuzzy Sets and System at Sep 18 201