Monitoring tools for robust estimation of cluster weighted models

In a robust approach to model fitting for the cluster weighted model, many choices are to be made by the statistician: specifying the shape of the clusters in the explanatory variables, assuming (or not) equal variance for the errors in the re- gression lines, and setting hyper-parameter values for the robust estimation to be protected from outliers and contamination. The most delicate hyper-parameter to specify is perhaps the percentage of trimming, or the amount of data to be excluded from the estimate, to ensure reliable inference. In this work we introduce diagnos- tic tools to help the professional, or the scientist who needs to group the data, to make an educated choice about this hyper-parameter, after a first exploration of the resulting model space

Group-wise penalized estimation schemes in model-based clustering

Gaussian mixture models provide a probabilistically sound clustering approach. However, their tendency to be over-parameterized endangers their utility in high dimensions. To induce sparsity, penalized model-based clustering strategies have been explored. Some of these approaches, exploiting the link between Gaussian graphical models and mixtures, allow to handle large precision matrices, encoding variables relationships. By assuming similar components sparsity levels, these methods fall short when the dependence structures are group-dependent. Our proposal, by penalizing group-specific transformations of the precision matrices, automatically handles situations where under or over-connectivity between variables is witnessed. The performances of the method are shown via a real data experimen

Penalized Model-Based Clustering with Group-Dependent Shrinkage Estimation

Gaussian mixture models (GMM) are the most-widely employed approach to perform model-based clustering of continuous features. Grievously, with the increasing availability of high-dimensional datasets, their direct applicability is put at stake: GMMs suffer from the curse of dimensionality issue, as the number of parameters grows quadratically with the number of variables. To this extent, a methodological link between Gaussian mixtures and Gaussian graphical models has recently been established in order to provide a framework for performing penalized model-based clustering in presence of large precision matrices. Notwithstanding, current methodologies do not account for the fact that groups may be under or over-connected, thus implicitly assuming similar levels of sparsity across clusters. We overcome this limitation by defining data-driven and component specific penalty factors, automatically accounting for different degrees of connections within groups. A real data experiment on handwritten digits recognition showcases the validity of our proposal

Soft tissue displacement over pelvic anatomical landmarks during 3-D hip movements

The position, in a pelvis-embedded anatomical coordinate system, of skin points located over the following anatomical landmarks (AL) was determined while the hip assumed different spatial postures: right and left anterior superior and posterior superior iliac spines, and the sacrum. Postures were selected as occurring during walking and during a flexion-extension and circumduction movement, as used to determine the hip joint centre position (star-arc movement). Five volunteers, characterised by a wide range of body mass indices (22-37), were investigated. Subject-specific MRI pelvis digital bone models were obtained. For each posture, the pose of the pelvis-embedded anatomical coordinate system was determined by registering this bone model with points digitised over bony prominences of the pelvis, using a wand carrying a marker-cluster and stereophotogrammetry. The knowledge of how the position of the skin points varies as a function of the hip posture provided information regarding the soft tissue artefact (STA) that would affect skin markers located over those points during stereophotogrammetric movement analysis. The STA was described in terms of amplitude (relative to the position of the AL during an orthostatic posture), diameter (distance between the positions of the AL which were farthest away from each other), and pelvis orientation. The STA amplitude, exhibited, over all postures, a median [inter-quartile] value of 9[6] and 16[11]. mm, for normal and overweight volunteers, respectively. STA diameters were larger for the star-arc than for the walking postures, and the direction was predominantly upwards. Consequent errors in pelvic orientation were in the range 1-9 and 4-11 degrees, for the two groups respectively

Mixed-effects high-dimensional multivariate regression via group-lasso regularization

Linear mixed modeling is a well-established technique widely employed when observations possess a grouping structure. Nonetheless, this standard methodology is no longer applicable when the learning framework encompasses a multivariate response and high-dimensional predictors. To overcome these issues, in the present paper a penalized estimation procedure for multivariate linear mixed-effects models (MLMM) is introduced. In details, we propose to regularize the likelihood via a group-lasso penalty, forcing only a subset of the estimated parameters to be preserved across all components of the multivariate response. The methodology is employed to develop novel surrogate biomarkers for cardiovascular risk factors, such as lipids and blood pressure, from whole-genome DNA methylation data in a multi-center study. The described methodology performs better than current stateof- art alternatives in predicting a multivariate continuous outcome

Foot kinematics in patients with two patterns of pathological plantar hyperkeratosis

Background: The Root paradigm of foot function continues to underpin the majority of clinical foot biomechanics practice and foot orthotic therapy. There are great number of assumptions in this popular paradigm, most of which have not been thoroughly tested. One component supposes that patterns of plantar pressure and associated hyperkeratosis lesions should be associated with distinct rearfoot, mid foot, first metatarsal and hallux kinematic patterns. Our aim was to investigate the extent to which this was true. Methods: Twenty-seven subjects with planter pathological hyperkeratosis were recruited into one of two groups. Group 1 displayed pathological plantar hyperkeratosis only under metatarsal heads 2, 3 and 4 (n = 14). Group 2 displayed pathological plantar hyperkeratosis only under the 1st and 5th metatarsal heads (n = 13). Foot kinematics were measured using reflective markers on the leg, heel, midfoot, first metatarsal and hallux. Results: The kinematic data failed to identify distinct differences between these two groups of subjects, however there were several subtle (generally <3°) differences in kinematic data between these groups. Group 1 displayed a less everted heel, a less abducted heel and a more plantarflexed heel compared to group 2, which is contrary to the Root paradigm. Conclusions: There was some evidence of small differences between planter pathological hyperkeratosis groups. Nevertheless, there was too much similarity between the kinematic data displayed in each group to classify them as distinct foot types as the current clinical paradigm proposes

A mathematical model of interleukin-6 dynamics during exercise

Physical exercise is known to reduce the chronic inflammatory status that leads to Type 2 Diabetes. Its beneficial effects seem to be exerted trough a primary production of the cytokine Interleukin-6 (IL-6) which triggers a cascade of anti-inflammatory cytokines. Consequently, IL-6 has a central role in the description of the metabolic effects of exercise. The aim of this study was to develop a model of IL-6 dynamics during exercise. A model constituted by two non-linear differential equations is proposed. Since IL-6 production seems to be dependent not only on exercise duration but also on exercise intensity, input to the model is represented by heart rate, which is known to correlate well with exercise intensity. Model implementation in a Matlab-based parametric identification procedure allowed optimization of adjustable characteristic coefficients of IL-6 dynamics during exercise. From the reported results, it can be concluded that this model is a suitable tool to reproduce IL-6 time course during the execution of a physical exercise. This model was the first step of a project aimed at describing the complete immune system response to exercise and at giving a comprehensive sight of the effects that exercise has on the metabolic system

To what extent is joint and muscle mechanics predicted by musculoskeletal models sensitive to soft tissue artefacts?

Musculoskeletal models are widely used to estimate joint kinematics, intersegmental loads, and muscle and joint contact forces during movement. These estimates can be heavily affected by the soft tissue artefact (STA) when input positional data are obtained using stereophotogrammetry, but this aspect has not yet been fully characterised for muscle and joint forces. This study aims to assess the sensitivity to the STA of three open-source musculoskeletal models, implemented in OpenSim. A baseline dataset of marker trajectories was created for each model from experimental data of one healthy volunteer. Five hundred STA realizations were then statistically generated using a markerdependent model of the pelvis and lower limb artefact and added to the baseline data. The STA's impact on the musculoskeletal model estimates was finally quantified using a Monte Carlo analysis. The modelled STA distributions were in line with the literature. Observed output variations were comparable across the three models, and sensitivity to the STA was evident for most investigated quantities. Shape, magnitude and timing of the joint angle and moment time histories were not significantly affected throughout the entire gait cycle, whereas magnitude variations were observed for muscle and joint forces. Ranges of contact force variations differed between joints, with hip variations up to 1.8 times body weight observed. Variations of more than 30% were observed for some of the muscle forces. In conclusion, musculoskeletal simulations using stereophotogrammetry may be safely run when only interested in overall output patterns. Caution should be paid when more accurate estimated values are needed

Monitoring Tools in Robust CWM for the Analysis of Crime Data

Robust inference for the Cluster Weighted Model requires the specification of a few hyper-parameters. Their role is crucial for increasing the quality of the estimators, while arbitrary decisions about their value could severely hamper inferential results. To guide the user in the delicate choice of such parameters, a monitoring approach has been introduced in the recent literature, yielding an adaptive method. The approach is here exemplified, via the analysis of a dataset on the effect of punishment regimes on crime rates