Information geometric measurements of generalisation

Neural networks can be regarded as statistical models, and can be analysed in a Bayesian framework. Generalisation is measured by the performance on independent test data drawn from the same distribution as the training data. Such performance can be quantified by the posterior average of the information divergence between the true and the model distributions. Averaging over the Bayesian posterior guarantees internal coherence; Using information divergence guarantees invariance with respect to representation. The theory generalises the least mean squares theory for linear Gaussian models to general problems of statistical estimation. The main results are: (1)~the ideal optimal estimate is always given by average over the posterior; (2)~the optimal estimate within a computational model is given by the projection of the ideal estimate to the model. This incidentally shows some currently popular methods dealing with hyperpriors are in general unnecessary and misleading. The extension of information divergence to positive normalisable measures reveals a remarkable relation between the dlt dual affine geometry of statistical manifolds and the geometry of the dual pair of Banach spaces Ld and Ldd. It therefore offers conceptual simplification to information geometry. The general conclusion on the issue of evaluating neural network learning rules and other statistical inference methods is that such evaluations are only meaningful under three assumptions: The prior P(p), describing the environment of all the problems; the divergence Dd, specifying the requirement of the task; and the model Q, specifying available computing resources.

A laser induced breakdown spectroscopy quantitative analysis method based on the robust least squares support vector machine regression model

Data fluctuation in multiple measurements of Laser Induced Breakdown Spectroscopy (LIBS) greatly affects the accuracy of quantitative analysis. A new LIBS quantitative analysis method based on the Robust Least Squares Support Vector Machine (RLS-SVM) regression model is proposed. The usual way to enhance the analysis accuracy is to improve the quality and consistency of the emission signal, such as by averaging the spectral signals or spectrum standardization over a number of laser shots. The proposed method focuses more on how to enhance the robustness of the quantitative analysis regression model. The proposed RLS-SVM regression model originates from the Weighted Least Squares Support Vector Machine (WLS-SVM) but has an improved segmented weighting function and residual error calculation according to the statistical distribution of measured spectral data. Through the improved segmented weighting function, the information on the spectral data in the normal distribution will be retained in the regression model while the information on the outliers will be restrained or removed. Copper elemental concentration analysis experiments of 16 certified standard brass samples were carried out. The average value of relative standard deviation obtained from the RLS-SVM model was 3.06% and the root mean square error was 1.537%. The experimental results showed that the proposed method achieved better prediction accuracy and better modeling robustness compared with the quantitative analysis methods based on Partial Least Squares (PLS) regression, standard Support Vector Machine (SVM) and WLS-SVM. It was also demonstrated that the improved weighting function had better comprehensive performance in model robustness and convergence speed, compared with the four known weighting functions.

Artefactual structure from least squares multidimensional scaling

We consider the problem of illusory or artefactual structure from the visualisation of high-dimensional structureless data. In particular we examine the role of the distance metric in the use of topographic mappings based on the statistical field of multidimensional scaling. We show that the use of a squared Euclidean metric (i.e. the SSTRESs measure) gives rise to an annular structure when the input data is drawn from a high-dimensional isotropic distribution, and we provide a theoretical justification for this observation.

Response-based segmentation using Finite Mixture Partial Least Squares: theoretical foundations and an application to American Customer Satisfaction Index Data

When applying multivariate analysis techniques in information systems and social science disciplines, such as management information systems (MIS) and marketing, the assumption that the empirical data originate from a single homogeneous population is often unrealistic. When applying a causal modeling approach, such as partial least squares (PLS) path modeling, segmentation is a key issue in coping with the problem of heterogeneity in estimated cause-and-effect relationships. This chapter presents a new PLS path modeling approach which classifies units on the basis of the heterogeneity of the estimates in the inner model. If unobserved heterogeneity significantly affects the estimated path model relationships on the aggregate data level, the methodology will allow homogenous groups of observations to be created that exhibit distinctive path model estimates. The approach will, thus, provide differentiated analytical outcomes that permit more precise interpretations of each segment formed. An application on a large data set in an example of the American customer satisfaction index (ACSI) substantiates the methodology’s effectiveness in evaluating PLS path modeling results.

Quantification of hydroxycinnamic acids and lignin in perennial forage and energy grasses by Fourier-transform infrared spectroscopy and partial least squares regression

Levels of lignin and hydroxycinnamic acid wall components in three genera of forage grasses (Lolium,Festuca and Dactylis) have been accurately predicted by Fourier-transform infrared spectroscopy using partial least squares models correlated to analytical measurements. Different models were derived that predicted the concentrations of acid detergent lignin, total hydroxycinnamic acids, total ferulate monomers plus dimers, p-coumarate and ferulate dimers in independent spectral test data from methanol extracted samples of perennial forage grass with accuracies of 92.8%, 86.5%, 86.1%, 59.7% and 84.7% respectively, and analysis of model projection scores showed that the models relied generally on spectral features that are known absorptions of these compounds. Acid detergent lignin was predicted in samples of two species of energy grass, (Phalaris arundinacea and Pancium virgatum) with an accuracy of 84.5%.

Toward prediction of class II mouse major histocompatibility complex peptide binding affinity:in silico bioinformatic evaluation using partial least squares, a robust multivariate statistical technique

The accurate identification of T-cell epitopes remains a principal goal of bioinformatics within immunology. As the immunogenicity of peptide epitopes is dependent on their binding to major histocompatibility complex (MHC) molecules, the prediction of binding affinity is a prerequisite to the reliable prediction of epitopes. The iterative self-consistent (ISC) partial-least-squares (PLS)-based additive method is a recently developed bioinformatic approach for predicting class II peptide−MHC binding affinity. The ISC−PLS method overcomes many of the conceptual difficulties inherent in the prediction of class II peptide−MHC affinity, such as the binding of a mixed population of peptide lengths due to the open-ended class II binding site. The method has applications in both the accurate prediction of class II epitopes and the manipulation of affinity for heteroclitic and competitor peptides. The method is applied here to six class II mouse alleles (I-Ab, I-Ad, I-Ak, I-As, I-Ed, and I-Ek) and included peptides up to 25 amino acids in length. A series of regression equations highlighting the quantitative contributions of individual amino acids at each peptide position was established. The initial model for each allele exhibited only moderate predictivity. Once the set of selected peptide subsequences had converged, the final models exhibited a satisfactory predictive power. Convergence was reached between the 4th and 17th iterations, and the leave-one-out cross-validation statistical terms - q2, SEP, and NC - ranged between 0.732 and 0.925, 0.418 and 0.816, and 1 and 6, respectively. The non-cross-validated statistical terms r2 and SEE ranged between 0.98 and 0.995 and 0.089 and 0.180, respectively. The peptides used in this study are available from the AntiJen database (http://www.jenner.ac.uk/AntiJen). The PLS method is available commercially in the SYBYL molecular modeling software package. The resulting models, which can be used for accurate T-cell epitope prediction, will be made freely available online (http://www.jenner.ac.uk/MHCPred).

Towards the in silico identification of class II restricted T-cell epitopes:a partial least squares iterative self-consistent algorithm for affinity prediction

Motivation: The immunogenicity of peptides depends on their ability to bind to MHC molecules. MHC binding affinity prediction methods can save significant amounts of experimental work. The class II MHC binding site is open at both ends, making epitope prediction difficult because of the multiple binding ability of long peptides. Results: An iterative self-consistent partial least squares (PLS)-based additive method was applied to a set of 66 pep- tides no longer than 16 amino acids, binding to DRB1*0401. A regression equation containing the quantitative contributions of the amino acids at each of the nine positions was generated. Its predictability was tested using two external test sets which gave r pred =0.593 and r pred=0.655, respectively. Furthermore, it was benchmarked using 25 known T-cell epitopes restricted by DRB1*0401 and we compared our results with four other online predictive methods. The additive method showed the best result finding 24 of the 25 T-cell epitopes. Availability: Peptides used in the study are available from http://www.jenner.ac.uk/JenPep. The PLS method is available commercially in the SYBYL molecular modelling software package. The final model for affinity prediction of peptides binding to DRB1*0401 molecule is available at http://www.jenner.ac.uk/MHCPred. Models developed for DRB1*0101 and DRB1*0701 also are available in MHC- Pred

Consistent reduction of postprandial glucagon and insulin by lixisenatide in the GetGoal clinical trial programme

Background and aims: Glucagon-like peptide-1 (GLP-1) receptor agonists improve islet function and delay gastric emptying in subjects with type 2 diabetes mellitus. We evaluated 2-hour glucose, glucagon and insulin changes following a standardized mixed-meal tolerance test before and after 24 weeks of treatment with the once-daily prandial GLP-1 receptor agonist lixisenatide (approved for a therapeutic dose of 20 μg once daily) in six randomized, placebo-controlled studies within the lixisenatide Phase III GetGoal programme. In the studies, the mixed-meal test was conducted before and after: (1) lixisenatide treatment in patients insufficiently controlled despite diet and exercise (GetGoal-Mono), (2) lixisenatide treatment in combination with oral antidiabetic drugs (OADs) (GetGoal-M and GetGoal-S), or (3) lixisenatide treatment in combination with basal insulin ± OAD (GetGoal-Duo 1, GetGoal-L and GetGoal-L-Asia).Materials and methods: A meta-analysis was performed (lixisenatide n=1124 vs placebo n=707) combining ANCOVA least squares (LS) mean values using an inverse variance weighted analysis. Results: Lixisenatide significantly reduced 2-hour postprandial glucose from baseline (LS mean difference vs placebo: -4.9 mmol/L, p<0.0001, Figure) and glucose excursions (LS mean difference vs placebo: -4.5 mmol/L, p<0.0001). As measured in two studies, lixisenatide also reduced postprandial glucagon (LS mean difference vs placebo: -19.0 ng/L, p<0.0001) and insulin (LS mean difference vs placebo: -64.8 pmol/L, p<0.0001), although the glucagon/insulin ratio was increased (LS mean difference vs placebo: 0.15, p=0.02) compared with placebo. Conclusion: The results show that lixisenatide potently reduces the glucose excursion after meal ingestion in subjects with type 2 diabetes, in association with marked reductions in glucagon and insulin levels. It is suggested that diminished glucagon secretion and slower gastric emptying contribute to reduced hepatic glucose production and delayed glucose absorption, enabling postprandial glycaemia to be controlled with less demand on beta-cell insulin secretion. Clinical Trial Registration Number: NCT00688701; NCT00712673; NCT00713830; NCT00975286; NCT00715624; NCT00866658 Supported by: Sanofi