M-estimator, and D-optimality model construction using orthogonal forward regression

This correspondence introduces a new orthogonal forward regression (OFR) model identification algorithm using D-optimality for model structure selection and is based on an M-estimators of parameter estimates. M-estimator is a classical robust parameter estimation technique to tackle bad data conditions such as outliers. Computationally, The M-estimator can be derived using an iterative reweighted least squares (IRLS) algorithm. D-optimality is a model structure robustness criterion in experimental design to tackle ill-conditioning in model Structure. The orthogonal forward regression (OFR), often based on the modified Gram-Schmidt procedure, is an efficient method incorporating structure selection and parameter estimation simultaneously. The basic idea of the proposed approach is to incorporate an IRLS inner loop into the modified Gram-Schmidt procedure. In this manner, the OFR algorithm for parsimonious model structure determination is extended to bad data conditions with improved performance via the derivation of parameter M-estimators with inherent robustness to outliers. Numerical examples are included to demonstrate the effectiveness of the proposed algorithm.

A-optimality orthogonal forward regression algorithm using branch and bound

In this brief, we propose an orthogonal forward regression (OFR) algorithm based on the principles of the branch and bound (BB) and A-optimality experimental design. At each forward regression step, each candidate from a pool of candidate regressors, referred to as S, is evaluated in turn with three possible decisions: 1) one of these is selected and included into the model; 2) some of these remain in S for evaluation in the next forward regression step; and 3) the rest are permanently eliminated from S. Based on the BB principle in combination with an A-optimality composite cost function for model structure determination, a simple adaptive diagnostics test is proposed to determine the decision boundary between 2) and 3). As such the proposed algorithm can significantly reduce the computational cost in the A-optimality OFR algorithm. Numerical examples are used to demonstrate the effectiveness of the proposed algorithm.

Robust neurofuzzy rule base knowledge extraction and estimation using subspace decomposition combined with regularization and D-optimality

A new robust neurofuzzy model construction algorithm has been introduced for the modeling of a priori unknown dynamical systems from observed finite data sets in the form of a set of fuzzy rules. Based on a Takagi-Sugeno (T-S) inference mechanism a one to one mapping between a fuzzy rule base and a model matrix feature subspace is established. This link enables rule based knowledge to be extracted from matrix subspace to enhance model transparency. In order to achieve maximized model robustness and sparsity, a new robust extended Gram-Schmidt (G-S) method has been introduced via two effective and complementary approaches of regularization and D-optimality experimental design. Model rule bases are decomposed into orthogonal subspaces, so as to enhance model transparency with the capability of interpreting the derived rule base energy level. A locally regularized orthogonal least squares algorithm, combined with a D-optimality used for subspace based rule selection, has been extended for fuzzy rule regularization and subspace based information extraction. By using a weighting for the D-optimality cost function, the entire model construction procedure becomes automatic. Numerical examples are included to demonstrate the effectiveness of the proposed new algorithm.

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.

The consumption of milk and dairy foods and the incidence of vascular disease and diabetes: An overview of the evidence

The health effects of milk and dairy food consumption would best be determined in randomised controlled trials. No adequately powered trial has been reported and none is likely because of the numbers required. The best evidence comes, therefore, from prospective cohort studies with disease events and death as outcomes. Medline was searched for prospective studies of dairy food consumption and incident vascular disease and Type 2 diabetes, based on representative population samples. Reports in which evaluation was in incident disease or death were selected. Meta-analyses of the adjusted estimates of relative risk for disease outcomes in these reports were conducted. Relevant case–control retrospective studies were also identified and the results are summarised in this article. Meta-analyses suggest a reduction in risk in the subjects with the highest dairy consumption relative to those with the lowest intake: 0.87 (0.77, 0.98) for all-cause deaths, 0.92 (0.80, 0.99) for ischaemic heart disease, 0.79 (0.68, 0.91) for stroke and 0.85 (0.75, 0.96) for incident diabetes. The number of cohort studies which give evidence on individual dairy food items is very small, but, again, there is no convincing evidence of harm from consumption of the separate food items. In conclusion, there appears to be an enormous mis-match between the evidence from long-term prospective studies and perceptions of harm from the consumption of dairy food items.

Associations between dairy consumption and body weight: a review of the evidence and underlying mechanisms

As the incidence of obesity is reaching 'epidemic' proportions, there is currently widespread interest in the impact of dietary components on body-weight and food intake regulation. The majority of data available from both epidemiological and intervention studies provide evidence of a negative but modest association between milk and dairy product consumption and BMI and other measures of adiposity, with indications that higher intakes result in increased weight loss and lean tissue maintenance during energy restriction. The purported physiological and molecular mechanisms underlying the impact of dairy constituents on adiposity are incompletely understood but may include effects on lipolysis, lipogeneis and fatty acid absorption. Furthermore, accumulating evidence indicates an impact of dairy constituents, in particular whey protein derivatives, on appetite regulation and food intake. The present review summarises available data and provides an insight into the likely contribution of dairy foods to strategies aimed at appetite regulation, weight loss or the prevention of weight gain.

Nonlinear model structure design and construction using orthogonal least squares and D-optimality design

A very efficient learning algorithm for model subset selection is introduced based on a new composite cost function that simultaneously optimizes the model approximation ability and model robustness and adequacy. The derived model parameters are estimated via forward orthogonal least squares, but the model subset selection cost function includes a D-optimality design criterion that maximizes the determinant of the design matrix of the subset to ensure the model robustness, adequacy, and parsimony of the final model. The proposed approach is based on the forward orthogonal least square (OLS) algorithm, such that new D-optimality-based cost function is constructed based on the orthogonalization process to gain computational advantages and hence to maintain the inherent advantage of computational efficiency associated with the conventional forward OLS approach. Illustrative examples are included to demonstrate the effectiveness of the new approach.

The quantitation of lipoprotein lipase mRNA in biopsies of human adipose tissue, using the polymerase chain reaction, and the effect of increased consumption of n-3 polyunsaturated fatty acids

Objective: To examine the effects of the consumption of fish oils on the gene expression of lipoprotein lipase (LPL, EC 3.1.1.34) in human adipose tissue. In order to measure LPL mRNA in adipose tissue samples obtained by needle biopsy from human volunteers a competitive, reverse transcriptase PCR (RT-PCR) protocol was developed. Design: A randomised controlled, single blind cross over dietary study which compared the effects of a low level n-3 polyunsaturated fatty acids (PUFA) using normal foods enriched with eicosapentaenoic (EPA) and docosahexaenoic (DHA) (test diet), with non-enriched but otherwise identical foods (control). The diets were consumed for a period of 22 d with a wash out period of 5 months between the diets. Setting: Free-living individuals associated with the University of Surrey. Subjects: Six male subjects with a mean (±sd) age of 51.2±3.6 y were recruited. Major Outcome Measures: Pre-and postprandial blood samples were taken for the measurement of triacylglycerol (TAG), postheparin LPL activity and adipose tissue samples for the measurement of LPL mRNA levels. Results: Mean LPL expression values were 4.12´105 molecules of LPL mRNA per ng total RNA on the control diet and 4.60´105 molecules of LPL mRNA per ng total RNA on the n-3 PUFA enriched (test) diet. There was no significant difference between the levels of LPL expression following each diet, consistent with the lack of change in TAG levels in response to increased dietary n-3 PUFA intake. However, the change in LPL expression (Test-Control diet) correlated significantly with the change in fasting TAG levels (P=0.03, R=-0.87 and R2=0.75) and with the total area under the TAG-time response curve (P=0.003, R=-0.96 and R2=0.92) in individuals. Conclusions: These findings, although based on a small number of subjects, suggest that LPL expression may be a determinant of plasma TAG levels. The development of this methodology should allow further elucidation of the effects of dietary manipulation and disease processes on lipid clearance and regulation in human subjects.

A randomised trial to investigate the effects of acute consumption of a blackcurrant juice drink on markers of vascular reactivity and bioavailability of anthocyanins in human subjects

Objective: To study the bioavailability of anthocyanins and the effects of a 20% blackcurrant juice drink on vascular reactivity, plasma antioxidant status and other CVD risk markers. Subjects/Methods: The study was a randomised, cross over, double blind, placebo controlled acute meal study. Twenty healthy volunteers (11 females 9 males) were recruited, and all subjects completed the study. Fasted volunteers consumed a 20% blackcurrant juice drink (250 ml) or a control drink following a low-flavonoid diet for the previous 72 hours. Vascular reactivity was assessed at baseline and 120 mins after juice consumption by Laser Doppler Imaging (LDI). Plasma and urine samples were collected periodically over an 8 hour period for analysis, with a final urine sample collected at 24h. The cross over was performed after a 4-week washout. Results: There were no significant effects of the 20% blackcurrant juice drink on acute measures of vascular reactivity, biomarkers of endothelial function or lipid risk factors. Consumption of the test juice caused increases in plasma vitamin C (P=0.006), and urinary anthocyanins (P<0.001). Delphinidin-3-rutinoside and cyanidin-3-rutinoside were the main anthocyanins excreted in urine with delphinidin-3-glucoside also detected. The yield of anthocyanins in urine was 0.021 ± 0.003% of the dietary intake of delphinidin glycosides and 0.009 ± 0.002 % of the dietary intake of cyanidin glycosides. Conclusions: The juice consumption did not have a significant effect on vascular reactivity. Anthocyanins were present at low concentrations in the urine, and microbial metabolites of flavonoids were detected in plasma after juice consumption.