Machine Learning (stat.ML)

Abstract: This study investigates the effects of anthropometric attributes, biological sex, and posture on translational body kinematic responses in translational vibrations. In total, 35 participants were recruited. Perturbations were applied on a standard car seat using a motion-based platform with 0.1 to 12.0 Hz random noise signals, with 0.3 m/s2 rms acceleration, for 60 seconds. Multiple linear regression models (three basic models and one advanced model, including interactions between predictors) were created to determine the most influential predictors of peak translational gains in the frequency domain per body segment (pelvis, trunk, and head). The models introduced experimentally manipulated factors (motion direction, posture, measured anthropometric attributes, and biological sex) as predictors. Effects of included predictors on the model fit were estimated. Basic linear regression models could explain over 70% of peak body segments' kinematic body response (where the R2 adjusted was 0.728). The inclusion of additional predictors (posture, body height and weight, and biological sex) did enhance the model fit, but not significantly (R2 adjusted was 0.730). The multiple stepwise linear regression, including interactions between predictors, accounted for the data well with an adjusted R2 of 0.907. The present study shows that perturbation direction and body segment kinematics are crucial factors influencing peak translational gains. Besides the body segments' response, perturbation direction was the strongest predictor. Adopted postures and biological sex do not significantly affect kinematic responses.

Abstract: In this paper, we present new high-probability PAC-Bayes bounds for different types of losses. Firstly, for losses with a bounded range, we present a strengthened version of Catoni's bound that holds uniformly for all parameter values. This leads to new fast rate and mixed rate bounds that are interpretable and tighter than previous bounds in the literature. Secondly, for losses with more general tail behaviors, we introduce two new parameter-free bounds: a PAC-Bayes Chernoff analogue when the loss' cumulative generating function is bounded, and a bound when the loss' second moment is bounded. These two bounds are obtained using a new technique based on a discretization of the space of possible events for the "in probability" parameter optimization problem. Finally, we extend all previous results to anytime-valid bounds using a simple technique applicable to any existing bound.