Tensor regression based on linked multiway parameter analysis

Classical regression methods take vectors as covariates and estimate the corresponding vectors of regression parameters. When addressing regression problems on covariates of more complex form such as multi-dimensional arrays (i.e. tensors), traditional computational models can be severely compromised by ultrahigh dimensionality as well as complex structure. By exploiting the special structure of tensor covariates, the tensor regression model provides a promising solution to reduce the model’s dimensionality to a manageable level, thus leading to efficient estimation. Most of the existing tensor-based methods independently estimate each individual regression problem based on tensor decomposition which allows the simultaneous projections of an input tensor to more than one direction along each mode. As a matter of fact, multi-dimensional data are collected under the same or very similar conditions, so that data share some common latent components but can also have their own independent parameters for each regression task. Therefore, it is beneficial to analyse regression parameters among all the regressions in a linked way. In this paper, we propose a tensor regression model based on Tucker Decomposition, which identifies not only the common components of parameters across all the regression tasks, but also independent factors contributing to each particular regression task simultaneously. Under this paradigm, the number of independent parameters along each mode is constrained by a sparsity-preserving regulariser. Linked multiway parameter analysis and sparsity modeling further reduce the total number of parameters, with lower memory cost than their tensor-based counterparts. The effectiveness of the new method is demonstrated on real data sets.

Sparse kernel density estimator using orthogonal regression based on D-optimality experimental design

A novel sparse kernel density estimator is derived based on a regression approach, which selects a very small subset of significant kernels by means of the D-optimality experimental design criterion using an orthogonal forward selection procedure. The weights of the resulting sparse kernel model are calculated using the multiplicative nonnegative quadratic programming algorithm. The proposed method is computationally attractive, in comparison with many existing kernel density estimation algorithms. Our numerical results also show that the proposed method compares favourably with other existing methods, in terms of both test accuracy and model sparsity, for constructing kernel density estimates.

Regression based D-optimality experimental design for sparse kernel density estimation

This paper derives an efficient algorithm for constructing sparse kernel density (SKD) estimates. The algorithm first selects a very small subset of significant kernels using an orthogonal forward regression (OFR) procedure based on the D-optimality experimental design criterion. The weights of the resulting sparse kernel model are then calculated using a modified multiplicative nonnegative quadratic programming algorithm. Unlike most of the SKD estimators, the proposed D-optimality regression approach is an unsupervised construction algorithm and it does not require an empirical desired response for the kernel selection task. The strength of the D-optimality OFR is owing to the fact that the algorithm automatically selects a small subset of the most significant kernels related to the largest eigenvalues of the kernel design matrix, which counts for the most energy of the kernel training data, and this also guarantees the most accurate kernel weight estimate. The proposed method is also computationally attractive, in comparison with many existing SKD construction algorithms. Extensive numerical investigation demonstrates the ability of this regression-based approach to efficiently construct a very sparse kernel density estimate with excellent test accuracy, and our results show that the proposed method compares favourably with other existing sparse methods, in terms of test accuracy, model sparsity and complexity, for constructing kernel density estimates.

Probability density function estimation using orthogonal forward regression

Using the classical Parzen window estimate as the target function, the kernel density estimation is formulated as a regression problem and the orthogonal forward regression technique is adopted to construct sparse kernel density estimates. The proposed algorithm incrementally minimises a leave-one-out test error score to select a sparse kernel model, and a local regularisation method is incorporated into the density construction process to further enforce sparsity. The kernel weights are finally updated using the multiplicative nonnegative quadratic programming algorithm, which has the ability to reduce the model size further. Except for the kernel width, the proposed algorithm has no other parameters that need tuning, and the user is not required to specify any additional criterion to terminate the density construction procedure. Two examples are used to demonstrate the ability of this regression-based approach to effectively construct a sparse kernel density estimate with comparable accuracy to that of the full-sample optimised Parzen window density estimate.

An orthogonal forward regression technique for sparse kernel density estimation

Using the classical Parzen window (PW) estimate as the desired response, the kernel density estimation is formulated as a regression problem and the orthogonal forward regression technique is adopted to construct sparse kernel density (SKD) estimates. The proposed algorithm incrementally minimises a leave-one-out test score to select a sparse kernel model, and a local regularisation method is incorporated into the density construction process to further enforce sparsity. The kernel weights of the selected sparse model are finally updated using the multiplicative nonnegative quadratic programming algorithm, which ensures the nonnegative and unity constraints for the kernel weights and has the desired ability to reduce the model size further. Except for the kernel width, the proposed method has no other parameters that need tuning, and the user is not required to specify any additional criterion to terminate the density construction procedure. Several examples demonstrate the ability of this simple regression-based approach to effectively construct a SKID estimate with comparable accuracy to that of the full-sample optimised PW density estimate. (c) 2007 Elsevier B.V. All rights reserved.

Orthogonal-least-squares regression: A unified approach for data modelling

A unified approach is proposed for data modelling that includes supervised regression and classification applications as well as unsupervised probability density function estimation. The orthogonal-least-squares regression based on the leave-one-out test criteria is formulated within this unified data-modelling framework to construct sparse kernel models that generalise well. Examples from regression, classification and density estimation applications are used to illustrate the effectiveness of this generic data-modelling approach for constructing parsimonious kernel models with excellent generalisation capability. (C) 2008 Elsevier B.V. All rights reserved.

Rural-urban disparities in child nutrition in Bangladesh and Nepal

Background The persistence of rural-urban disparities in child nutrition outcomes in developing countries alongside rapid urbanisation and increasing incidence of child malnutrition in urban areas raises an important health policy question - whether fundamentally different nutrition policies and interventions are required in rural and urban areas. Addressing this question requires an enhanced understanding of the main drivers of rural-urban disparities in child nutrition outcomes especially for the vulnerable segments of the population. This study applies recently developed statistical methods to quantify the contribution of different socio-economic determinants to rural-urban differences in child nutrition outcomes in two South Asian countries – Bangladesh and Nepal. Methods Using DHS data sets for Bangladesh and Nepal, we apply quantile regression-based counterfactual decomposition methods to quantify the contribution of (1) the differences in levels of socio-economic determinants (covariate effects) and (2) the differences in the strength of association between socio-economic determinants and child nutrition outcomes (co-efficient effects) to the observed rural-urban disparities in child HAZ scores. The methodology employed in the study allows the covariate and coefficient effects to vary across entire distribution of child nutrition outcomes. This is particularly useful in providing specific insights into factors influencing rural-urban disparities at the lower tails of child HAZ score distributions. It also helps assess the importance of individual determinants and how they vary across the distribution of HAZ scores. Results There are no fundamental differences in the characteristics that determine child nutrition outcomes in urban and rural areas. Differences in the levels of a limited number of socio-economic characteristics – maternal education, spouse’s education and the wealth index (incorporating household asset ownership and access to drinking water and sanitation) contribute a major share of rural-urban disparities in the lowest quantiles of child nutrition outcomes. Differences in the strength of association between socio-economic characteristics and child nutrition outcomes account for less than a quarter of rural-urban disparities at the lower end of the HAZ score distribution. Conclusions Public health interventions aimed at overcoming rural-urban disparities in child nutrition outcomes need to focus principally on bridging gaps in socio-economic endowments of rural and urban households and improving the quality of rural infrastructure. Improving child nutrition outcomes in developing countries does not call for fundamentally different approaches to public health interventions in rural and urban areas.

A fast radiative transfer model for the assimilation of water vapor radiances from the Kalpana very high resolution radiometer

A fast radiative transfer model (RTM) to compute emitted infrared radiances for a very high resolution radiometer (VHRR), onboard the operational Indian geostationary satellite Kalpana has been developed and verified. This work is a step towards the assimilation of Kalpana water vapor (WV) radiances into numerical weather prediction models. The fast RTM uses a regression‐based approach to parameterize channel‐specific convolved level to space transmittances. A comparison between the fast RTM and the line‐by‐line RTM demonstrated that the fast RTM can simulate line‐by‐line radiances for the Kalpana WV channel to an accuracy better than the instrument noise, while offering more rapid radiance calculations. A comparison of clear sky radiances of the Kalpana WV channel with the ECMWF model first guess radiances is also presented, aiming to demonstrate the fast RTM performance with the real observations. In order to assimilate the radiances from Kalpana, a simple scheme for bias correction has been suggested.

Modelling seasonally varying data: A case study for sudden infant death syndrome (SIDS)

Many time series are measured monthly, either as averages or totals, and such data often exhibit seasonal variability-the values of the series are consistently larger for some months of the year than for others. A typical series of this type is the number of deaths each month attributed to SIDS (Sudden Infant Death Syndrome). Seasonality can be modelled in a number of ways. This paper describes and discusses various methods for modelling seasonality in SIDS data, though much of the discussion is relevant to other seasonally varying data. There are two main approaches, either fitting a circular probability distribution to the data, or using regression-based techniques to model the mean seasonal behaviour. Both are discussed in this paper.

Do children with Williams syndrome really have good vocabulary knowledge? Methods for comparing cognitive and linguistic abilities in developmental disorders

The comparison of cognitive and linguistic skills in individuals with developmental disorders is fraught with methodological and psychometric difficulties. In this paper, we illustrate some of these issues by comparing the receptive vocabulary knowledge and non-verbal reasoning abilities of 41 children with Williams syndrome, a genetic disorder in which language abilities are often claimed to be relatively strong. Data from this group were compared with data from typically developing children, children with Down syndrome, and children with non-specific learning difficulties using a number of approaches including comparison of age-equivalent scores, matching, analysis of covariance, and regression-based standardization. Across these analyses children with Williams syndrome consistently demonstrated relatively good receptive vocabulary knowledge, although this effect appeared strongest in the oldest children.

Seasonal persistence of midlatitude total ozone anomalies

Temporal autocorrelations of monthly mean total ozone anomalies over the 35–60°S and 35–60°N latitude bands reveal that anomalies established in the wintertime midlatitude ozone buildup persist (with photochemical decay) until the end of the following autumn, and then are rapidly erased once the next winter's buildup begins. The photochemical decay rate is found to be identical between the two hemispheres. High predictability of ozone through late summer exists based on the late-spring values. In the northern hemisphere, extending the 1979–2001 springtime ozone trend to other months through regression based on the seasonal persistence of anomalies captures the seasonality of the ozone trends remarkably well. In the southern hemisphere, the springtime trend only accounts for part of the summertime trends. There is a strong correlation between the ozone anomalies in northern hemisphere spring and those in the subsequent southern hemisphere spring, but not the converse.

Evaluating interval forecasts of high-frequency financial data

A number of methods of evaluating the validity of interval forecasts of financial data are analysed, and illustrated using intraday FTSE100 index futures returns. Some existing interval forecast evaluation techniques, such as the Markov chain approach of Christoffersen (1998), are shown to be inappropriate in the presence of periodic heteroscedasticity. Instead, we consider a regression-based test, and a modified version of Christoffersen's Markov chain test for independence, and analyse their properties when the financial time series exhibit periodic volatility. These approaches lead to different conclusions when interval forecasts of FTSE100 index futures returns generated by various GARCH(1,1) and periodic GARCH(1,1) models are evaluated.

Determinants of fruit and vegetable intake in England: a re-examination based on quantile regression

Objective To examine die sociodemographic determinants of fruit and vegetable (F&V) consumption in England and determine the differential effects of socioeconomic variables at various parts of the intake distribution, with a special focus on severely inadequate intakes Design Quantile regression, expressing F&V intake as a function of sociodemographic variables, is employed. Here, quantile regression flexibly allows variables such as ethnicity to exert effects on F&V intake that. vary depending oil existing levels of intake. Setting The 2003 Health survey of England. Subjects Data were from 11044 adult individuals. Results The influence of particular sociodemographic variables is found to vary significantly across the intake distribution We conclude that women consume more F&V than men, Asians and Hacks mole dian Whites, co-habiting individuals more than single-living ones Increased incomes and education also boost intake However, the key general finding of the present study is that the influence of most variables is relatively weak in the area of greatest concern, i e among those with the most inadequate intakes in any reference group. Conclusions. Our findings emphasise the importance of allowing the effects of socio-economic drivers to vary across the intake distribution The main finding, that variables which exert significant influence on F&V Intake at other parts Of the conditional distribution have a relatively weak influence at the lower tail, is cause for concern. It implies that in any defined group, those consuming the lease F&V are hard to influence using compaigns or policy levers.