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In classification, feature selection is an essential pre-processing step that selects a small subset of features to improve classification performance. Existing feature selection approaches can be divided into three main approaches: wrapper approaches, filter approaches, and embedded approaches. In comparison with two other approaches, embedded approaches usually have better trade-off between classification performance and computation time. One of the most well-known embedded approaches is sparsity regularisation-based feature selection which generates sparse solutions for feature selection. Despite its good performance, sparsity regularisation-based feature selection outputs only a feature ranking which requires the number of selected features to be predefined. More importantly, the ranking mechanism introduces a risk of ignoring feature interactions which leads to the fact that many top-ranked but redundant features are selected. This work addresses the above problems by proposing a new representation that considers the interactions between features and can automatically determine an appropriate number of selected features. The proposed representation is used in a differential evolutionary (DE) algorithm to optimise the feature subset. In addition, a novel initialisation mechanism is proposed to let DE consider various numbers of selected features at the beginning. The proposed algorithm is examined on both synthetic and real-world datasets. The results on the synthetic dataset show that the proposed algorithm can select complementary features while existing sparsity regularisation-based feature selection algorithms are at risk of selecting redundant features. The results on real-world datasets show that the proposed algorithm achieves better classification performance than well-known wrapper, filter, and embedded approaches. The algorithm is also as efficient as filter feature selection approaches.

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In many biomedical applications, we are more interested in the predicted probability that a numerical outcome is above a threshold than in the predicted value of the outcome. For example, it might be known that antibody levels above a certain threshold provide immunity against a disease, or a threshold for a disease severity score might reflect conversion from the presymptomatic to the symptomatic disease stage. Accordingly, biomedical researchers often convert numerical to binary outcomes (loss of information) to conduct logistic regression (probabilistic interpretation). We address this bad statistical practice by modelling the binary outcome with logistic regression, modelling the numerical outcome with linear regression, transforming the predicted values from linear regression to predicted probabilities, and combining the predicted probabilities from logistic and linear regression. Analysing high-dimensional simulated and experimental data, namely clinical data for predicting cognitive impairment, we obtain significantly improved predictions of dichotomised outcomes. Thus, the proposed approach effectively combines binary with numerical outcomes to improve binary classification in high-dimensional settings. An implementation is available in the R package cornet on GitHub (https://github.com/rauschenberger/cornet) and CRAN (https://CRAN.R-project.org/package=cornet).

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BACKGROUND: Risk-adjustment (RA) models are used to account for severity of illness in comparing patient outcomes across hospitals. Researchers specify covariates as main effects, but they often ignore interactions or use stratification to account for effect modification, despite limitations due to rare events and sparse data. Three Agency for Healthcare Research and Quality (AHRQ) hospital-level Quality Indicators currently use stratified models, but their variable performance and limited interpretability motivated the design of better models. METHODS: We analysed patient discharge de-identified data from 14 State Inpatient Databases, AHRQ Healthcare Cost and Utilization Project, California Department of Health Care Access and Information, and New York State Department of Health. We used hierarchical group lasso regularisation (HGLR) to identify first-order interactions in several AHRQ inpatient quality indicators (IQI) - IQI 09 (Pancreatic Resection Mortality Rate), IQI 11 (Abdominal Aortic Aneurysm Repair Mortality Rate), and Patient Safety Indicator 14 (Postoperative Wound Dehiscence Rate). These models were compared with stratum-specific and composite main effects models with covariates selected by least absolute shrinkage and selection operator (LASSO). RESULTS: HGLR identified clinically meaningful interactions for all models. Synergistic IQI 11 interactions, such as between hypertension and respiratory failure, suggest patients who merit special attention in perioperative care. Antagonistic IQI 11 interactions, such as between shock and chronic comorbidities, illustrate that naïve main effects models overestimate risk in key subpopulations. Interactions for PSI 14 suggest key subpopulations for whom the risk of wound dehiscence is similar between open and laparoscopic approaches, whereas laparoscopic approach is safer for other groups. Model performance was similar or superior for composite models with HGLR-selected features, compared to those with LASSO-selected features. CONCLUSIONS: In this application to high-profile, high-stakes risk-adjustment models, HGLR selected interactions that maintained or improved model performance in populations with heterogeneous risk, while identifying clinically important interactions. The HGLR package is scalable to handle a large number of covariates and their interactions and is customisable to use multiple CPU cores to reduce analysis time. The HGLR method will allow scholars to avoid creating stratified models on sparse data, improve model calibration, and reduce bias. Future work involves testing using other combinations of risk factors, such as vital signs and laboratory values. Our study focuses on a real-world problem of considerable importance to hospitals and policy-makers who must use RA models for statutorily mandated public reporting and payment programmes.

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Supervised deep learning models can be optimised by applying regularisation techniques to reduce overfitting, which can prove difficult when fine tuning the associated hyperparameters. Not all hyperparameters are equal, and understanding the effect each hyperparameter and regularisation technique has on the performance of a given model is of paramount importance in research. We present the first comprehensive, large-scale ablation study for an encoder-only transformer to model sign language using the improved Word-level American Sign Language dataset (WLASL-alt) and human pose estimation keypoint data, with a view to put constraints on the potential to optimise the task. We measure the impact a range of model parameter regularisation and data augmentation techniques have on sign classification accuracy. We demonstrate that within the quoted uncertainties, other than ℓ2 parameter regularisation, none of the regularisation techniques we employ have an appreciable positive impact on performance, which we find to be in contradiction to results reported by other similar, albeit smaller scale, studies. We also demonstrate that the model architecture is bounded by the small dataset size for this task over finding an appropriate set of model parameter regularisation and common or basic dataset augmentation techniques. Furthermore, using the base model configuration, we report a new maximum top-1 classification accuracy of 84% on 100 signs, thereby improving on the previous benchmark result for this model architecture and dataset.

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Material models are required to solve continuum mechanical problems. These models contain parameters that are usually determined by application-specific test setups. In general, the theoretically developed models and, thus, the parameters to be determined become increasingly complex, e.g., incorporating higher-order motion derivatives, such as the strain or strain rate. Therefore, the strain rate behaviour needs to be extracted from experimental data. Using image data, the most-common way in solid experimental mechanics to do so is digital image correlation. Alternatively, optical flow methods, which allow an adaption to the underlying motion estimation problem, can be applied. In order to robustly estimate the strain rate fields, an optical flow approach implementing higher-order spatial and trajectorial regularisation is proposed. Compared to using a purely spatial variational approach of higher order, the proposed approach is capable of calculating more accurate displacement and strain rate fields. The procedure is finally demonstrated on experimental data of a shear cutting experiment, which exhibited complex deformation patterns under difficult optical conditions.

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Sleep restriction therapy is a central component of cognitive behavioural therapy for insomnia, but can lead to excessive sleepiness, which may impede treatment adherence. Sleep compression therapy has been suggested as a possibly gentler alternative. The aim of this study was to compare the effects of sleep restriction therapy and sleep compression therapy on objective measures of sleep, with a focus on magnitude and timing of effects. From a larger study of participants with insomnia, a sub-sample of 36 underwent polysomnographic recordings, before being randomised to either sleep restriction (n = 19) or sleep compression (n = 17) and receiving online treatment for 10 weeks. Assessments with polysomnography were also carried out after 2, 5, and 10 weeks of treatment. Data were analysed with multilevel linear mixed effect modelling. As per treatment instructions, participants in sleep restriction initially spent shorter time in bed compared with sleep compression. Participants in sleep restriction also showed an initial decrease of total sleep time, which was not seen in the sleep compression group. Both treatments led to improvements in sleep continuity variables, with a tendency for the improvements to come earlier during treatment in sleep restriction. No substantial differences were found between the two treatments 10 weeks after the treatment start. The results indicate that homeostatic sleep pressure may not be as important as a mechanism in sleep compression therapy as in sleep restriction therapy, and an investigation of other mechanisms is needed. In conclusion, the treatments led to similar changes in objective sleep at a somewhat different pace, and possibly through different mechanisms.

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The motor imagery brain-computer interface (MI-BCI) provides an interactive control channel for spinal cord injury patients. However, the limitations of feature extraction algorithms may lead to low accuracy and instability in decoding electroencephalogram (EEG) signals. In this study, we examined the classification performance of an MI-BCI system by focusing on the distinction of the left and right foot kinaesthetic motor imagery tasks in five subjects. Feature extraction was performed using the common space pattern (CSP) and the Tikhonov regularisation CSP (TRCSP) spatial filters. TRCSP overcomes the CSP problems of noise sensitivity and overfitting. Moreover, support vector machine (SVM) and linear discriminant analysis (LDA) were used for classification and recognition. We constructed four combined classification methods (TRCSP-SVM, TRCSP-LDA, CSP-SVM, and CSP-LDA) and evaluated them by comparing their accuracies, kappa coefficients, and receiver operating characteristic (ROC) curves. The results showed that the TRCSP-SVM method performed significantly better than others (average accuracy 97%, average kappa coefficient 0.91, and average area under ROC curve (AUC) 0.98). Using TRCSP instead of standard CSP improved accuracy by up to 10%. This study provides insights into the classification of EEG signals. The results of this study can aid lower limb MI-BCI systems in rehabilitation training.

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Impact force is the most common form of load which acts on engineering structures and presents a great hidden risk to the healthy operation of machinery. Therefore, the identification or monitoring of impact forces is a significant issue in structural health monitoring. The conventional optimisation scheme based on inversion techniques requires a significant amount of time to identify random impact forces (impact force localisation and time history reconstruction) and is not suitable for engineering applications. Recently, a pattern recognition method combined with the similarity metric, PRMCSM, has been proposed, which exhibits rapidity in practical engineering applications. This study proposes a novel scheme for identifying unknown random impact forces which hybridises two existing methods and combines the advantages of both. The experimental results indicate that the localisation accuracy of the proposed algorithm (100%) is higher than that of PRMCSM (92%), and the calculation time of the hybrid algorithm (179 s) for 25 validation cases is approximately one nineteenth of the traditional optimisation strategy (3446 s).

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I reconsider Bleichrodt, Pinto Prades and Wakker's (BPW) 2001 paper about eliciting utility measures from stated preference surveys. That paper pioneers a method that is now widely used in behavioural economics to correct individuals' 'biases' and to recover their 'true preferences'. However, BPW propose this method as way of dealing with inconsistent responses to stated preference surveys, in contrast to more recent applications which aim to help individuals to avoid supposed mistakes in their private choices. I argue that the concepts of true preference and bias are empirically ungrounded, but that BPW's approach can be interpreted as not invoking those concepts. By 'regularising' preferences revealed in actual choice, this approach constructs measures of individual welfare that are broadly aligned with actual preferences and consistent with normative standards of rationality that are appropriate for public decision-making. Public decision-makers' normative judgements are made explicit, rather than being disguised as apparently empirical claims about true preferences.

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Cancer cell mutations occur when cells undergo multiple cell divisions, and these mutations can be spontaneous or environmentally-induced. The mechanisms that promote and sustain these mutations are still not fully understood. This study deals with the identification (or reconstruction) of the usually unknown cancer cell mutation law, which lead to the transformation of a primary tumour cell population into a secondary, more aggressive cell population. We focus on local and nonlocal mathematical models for cell dynamics and movement, and identify these mutation laws from macroscopic tumour snapshot data collected at some later stage in the tumour evolution. In a local cancer invasion model, we first reconstruct the mutation law when we assume that the mutations depend only on the surrounding cancer cells (i.e., the ECM plays no role in mutations). Second, we assume that the mutations depend on the ECM only, and we reconstruct the mutation law in this case. Third, we reconstruct the mutation when we assume that there is no prior knowledge about the mutations. Finally, for the nonlocal cancer invasion model, we reconstruct the mutation law that depends on the cancer cells and on the ECM. For these numerical reconstructions, our approximations are based on the finite difference method combined with the finite elements method. As the inverse problem is ill-posed, we use the Tikhonov regularisation technique in order to regularise the solution. Stability of the solution is examined by adding additive noise into the measurements.

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In electrocardiography, the "classic" inverse problem is the reconstruction of electric potentials at a surface enclosing the heart from remote recordings at the body surface and an accurate description of the anatomy. The latter being affected by noise and obtained with limited resolution due to clinical constraints, a possibly large uncertainty may be perpetuated in the inverse reconstruction. The purpose of this work is to study the effect of shape uncertainty on the forward and the inverse problem of electrocardiography. To this aim, the problem is first recast into a boundary integral formulation and then discretised with a collocation method to achieve high convergence rates and a fast time to solution. The shape uncertainty of the domain is represented by a random deformation field defined on a reference configuration. We propose a periodic-in-time covariance kernel for the random field and approximate the Karhunen-Loève expansion using low-rank techniques for fast sampling. The space-time uncertainty in the expected potential and its variance is evaluated with an anisotropic sparse quadrature approach and validated by a quasi-Monte Carlo method. We present several numerical experiments on a simplified but physiologically grounded two-dimensional geometry to illustrate the validity of the approach. The tested parametric dimension ranged from 100 up to 600. For the forward problem, the sparse quadrature is very effective. In the inverse problem, the sparse quadrature and the quasi-Monte Carlo method perform as expected, except for the total variation regularisation, where convergence is limited by lack of regularity. We finally investigate an H1/2 regularisation, which naturally stems from the boundary integral formulation, and compare it to more classical approaches.

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In recent years the use of convolutional layers to encode an inductive bias (translational equivariance) in neural networks has proven to be a very fruitful idea. The successes of this approach have motivated a line of research into incorporating other symmetries into deep learning methods, in the form of group equivariant convolutional neural networks. Much of this work has been focused on roto-translational symmetry of R d , but other examples are the scaling symmetry of R d and rotational symmetry of the sphere. In this work, we demonstrate that group equivariant convolutional operations can naturally be incorporated into learned reconstruction methods for inverse problems that are motivated by the variational regularisation approach. Indeed, if the regularisation functional is invariant under a group symmetry, the corresponding proximal operator will satisfy an equivariance property with respect to the same group symmetry. As a result of this observation, we design learned iterative methods in which the proximal operators are modelled as group equivariant convolutional neural networks. We use roto-translationally equivariant operations in the proposed methodology and apply it to the problems of low-dose computerised tomography reconstruction and subsampled magnetic resonance imaging reconstruction. The proposed methodology is demonstrated to improve the reconstruction quality of a learned reconstruction method with a little extra computational cost at training time but without any extra cost at test time.

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BACKGROUND: Genome-wide association studies (GWAS) were successful in identifying SNPs showing association with disease, but their individual effect sizes are small and require large sample sizes to achieve statistical significance. Methods of post-GWAS analysis, including gene-based, gene-set and polygenic risk scores, combine the SNP effect sizes in an attempt to boost the power of the analyses. To avoid giving undue weight to SNPs in linkage disequilibrium (LD), the LD needs to be taken into account in these analyses. OBJECTIVES: We review methods that attempt to adjust the effect sizes (ß-coefficients) of summary statistics, instead of simple LD pruning. METHODS: We subject LD adjustment approaches to a mathematical analysis, recognising Tikhonov regularisation as a framework for comparison. RESULTS: Observing the similarity of the processes involved with the more straightforward Tikhonov-regularised ordinary least squares estimate for multivariate regression coefficients, we note that current methods based on a Bayesian model for the effect sizes effectively provide an implicit choice of the regularisation parameter, which is convenient, but at the price of reduced transparency and, especially in smaller LD blocks, a risk of incomplete LD correction. CONCLUSIONS: There is no simple answer to the question which method is best, but where interpretability of the LD adjustment is essential, as in research aiming at identifying the genomic aetiology of disorders, our study suggests that a more direct choice of mild regularisation in the correction of effect sizes may be preferable.

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Little attention has been paid in Mexico to species' geographical distribution, particularly documenting geographic ranges, as a tool to estimate their conservation status. The objective of this study was to review known species distribution and propose potential and conservation status for Salvia species in Michoacán sState using Ecological Niche Models (ENM). We reviewed taxonomic studies for Salvia in Michoacán to compile an initial species checklist, built upon with recently-described species; all the specimens deposited in the National Herbarium were reviewed. The collection data allowed us to build niche models of Salvia species reported for Michoacán. ENM were generated for the species listed using Maxent. In order to minimise collinearity, environmental variables were selected using a Pearson correlation test. Individual models were statistically evaluated and the potential distribution models for each individual species were stacked to obtain the map of richness potential distribution in the State. A total of 66 species of Salvia are listed for Michoacán; however, ENM could only be constructed for 42 of those with ≥ 5 specimens. The environmental variable that most strongly contributed to the models was annual average temperature. The models estimated that Salvia species occupy an area of 23,541 km2 in the State, 72% in the Trans-Mexican Volcanic Belt and a second richest ecoregion is the Sierra Madre del Sur. Although only 3% of the potential distribution area for Salvia in Michoacán is within Protected Areas (PAs), nonetheless, no PA includes rare species. It will therefore be necessary to consider new protection areas or expand existing ones in order to adequately conserve Salvia richness and rarity in the State.

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Accurate mapping of the functional interactions between remote brain areas with resting-state functional magnetic resonance imaging requires the quantification of their underlying dynamics. In conventional methodological pipelines, a spatial scale of interest is first selected and dynamic analysis then proceeds at this hypothesised level of complexity. If large-scale functional networks or states are studied, more local regional rearrangements are then not described, potentially missing important neurobiological information. Here, we propose a novel mathematical framework that jointly estimates resting-state functional networks and spatially more localised cross-regional modulations. To do so, the changes in activity of each brain region are modelled by a logistic regression including co-activation coefficients (reflective of network assignment, as they highlight simultaneous activations across areas) and causal interplays (denoting finer regional cross-talks, when one region active at timetmodulates thettot + 1 transition likelihood of another area). A two-parameterℓ1regularisation scheme is used to make these two sets of coefficients sparse: one controls overall sparsity, while the other governs the trade-off between co-activations and causal interplays, enabling to properly fit the data despite the yet unknown balance between both types of couplings. Across a range of simulation settings, we show that the framework successfully retrieves the two types of cross-regional interactions at once. Performance across noise and sample size settings was globally on par with that of other existing methods, with the potential to reveal more precise information missed by alternative approaches. Preliminary application to experimental data revealed that in the resting brain, co-activations and causal modulations co-exist with a varying balance across regions. Our methodological pipeline offers a conceptually elegant alternative for the assessment of functional brain dynamics and can be downloaded athttps://c4science.ch/source/Sparse_logistic_regression.git.

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Nonlinear registration is critical to many aspects of Neuroimaging research. It facilitates averaging and comparisons across multiple subjects, as well as reporting of data in a common anatomical frame of reference. It is, however, a fundamentally ill-posed problem, with many possible solutions which minimise a given dissimilarity metric equally well. We present a regularisation method capable of selectively driving solutions towards those which would be considered anatomically plausible by penalising unlikely lineal, areal and volumetric deformations. This penalty is symmetric in the sense that geometric expansions and contractions are penalised equally, which encourages inverse-consistency. We demonstrate that this method is able to significantly reduce local volume changes and shape distortions compared to state-of-the-art elastic (FNIRT) and plastic (ANTs) registration frameworks. Crucially, this is achieved whilst simultaneously matching or exceeding the registration quality of these methods, as measured by overlap scores of labelled cortical regions. Extensive leveraging of GPU parallelisation has allowed us to solve this highly computationally intensive optimisation problem while maintaining reasonable run times of under half an hour.

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In genomic analysis, it is significant though challenging to identify markers associated with cancer outcomes or phenotypes. Based on the biological mechanisms of cancers and the characteristics of datasets, we propose a novel integrative interaction approach under a semiparametric model, in which genetic and environmental factors are included as the parametric and nonparametric components, respectively. The goal of this approach is to identify the genetic factors and gene-gene interactions associated with cancer outcomes, while estimating the nonlinear effects of environmental factors. The proposed approach is based on the threshold gradient-directed regularisation technique. Simulation studies indicate that the proposed approach outperforms alternative methods at identifying the main effects and interactions, and has favourable estimation and prediction accuracy. We analysed non-small-cell lung carcinoma datasets from the Cancer Genome Atlas, and the results demonstrate that the proposed approach can identify markers with important implications and that it performs favourably in terms of prediction accuracy, identification stability, and computation cost.

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A novel pulsed neutron imaging technique based on the finite element method is used to reconstruct the residual strain within a polycrystalline material from Bragg edge strain images. This technique offers the possibility of a nondestructive analysis of strain fields with a high spatial resolution. The finite element approach used to reconstruct the strain uses the least square method constrained by the conditions of equilibrium. This inclusion of equilibrium makes the problem well-posed. The procedure is developed and verified by validating for a cantilevered beam problem. It is subsequently demonstrated by reconstructing the strain from experimental data for a ring-and-plug sample, measured at the spallation neutron source RADEN at J-PARC in Japan. The reconstruction is validated by comparison with conventional constant wavelength strain measurements on the KOWARI diffractometer at ANSTO in Australia. It is also shown that the addition of a Tikhonov regularisation scheme further improves the reconstruction.

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The electrical impulses of the heart will generate a tiny magnetic field outside the thorax that is measured as Magnetocardiographic signals. The challenging study is to estimate the cardiac activities in terms of depolarisation and repolarization maps from the measured signals called as inverse problem. This is computed only if one has solved generic or subject- specific prior models using the anatomical structures of the myocardium, the torso and the detectors called as forward problem. In this study, the Discretised heart is priorily assumed as the dipolar sources forming a double layer. The thorax structure modelled with finite element meshes is considered in the forward study. The magnetocardiographic data are simulated using uniform double layer model representing transmembrane distribution on the epicardium and endocardium. Using this data, the activation maps are non-invasively imaged on the heart surface using Tikhonov's regularisation technique. The inverse study is extended to reconstruct the depolarisation sequences of the abnormal cases.

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[This corrects the article DOI: 10.3389/fphys.2019.00050.].