Tree-Structured Regression Model Using a Projection Pursuit Approach

In this paper, we propose a new tree-structured regression modelthe projection pursuit regression tree.a new tree-structured regression model—the projection pursuit regression tree—is proposed. It combines the projection pursuit classification tree with the projection pursuit regression. The main advantage of the projection pursuit regression tree is exploring the independent variable space in each range of the dependent variable. Additionally, it retains the main properties of the projection pursuit classification tree. The projection pursuit regression tree provides several methods of assigning values to the final node, which enhances predictability. It shows better performance than CART in most cases and sometimes beats random forest with a single tree. This development makes it possible to find a better explainable model with reasonable predictability.

Physical Activity and Health-Related Quality of Life in Adults With a Neurologically-Related Mobility Disability During the COVID-19 Pandemic: An Exploratory Analysis

Background: During the coronavirus-19 (COVID-19) pandemic various containment strategies were employed. Their impact on individuals with neurological conditions, considered vulnerable to COVID-19 complications, remains to be determined.Objective: To investigate associations between physical activity and health-related quality of life outcomes in individuals with a neurological condition during government mandated COVID-19 restrictions.Methods: An e-survey assessing fear of COVID-19, physical activity level and health-related quality of life outcomes (functional disability and pain, anxiety and depression, loneliness, fatigue, and vitality) was distributed to individuals with a neurologically-related mobility disability living in the United Kingdom. Open-ended questions were also included to contextualize barriers and facilitators to engage in physical activity during the COVID-19 pandemic. Gamma-weighted generalized linear models and tree-structured regression models were employed to determine the associations between physical activity and health-related quality of life.Results: Of 199 responses, 69% reported performing less physical activity compared to pre-pandemic. Tree-structured regression models revealed that lower leisure-time physical activity was significantly associated (p ≤ 0.009) with higher depression and fatigue, but lower vitality. The closure of leisure facilities and organized sport (27%) was the most commonly cited barrier to engage in physical activity, while 31% of participants mentioned concerns around their physical and mental health as a facilitator.Conclusion: Our analysis identified homogenous subgroups for depression, fatigue, and vitality based specifically on leisure-time physical activity cut points, irrespective of additional demographic or situational characteristics. Findings highlight the importance of and need to safely promote leisure-time physical activity during the COVID-19 pandemic in this at-risk population to help support health-related quality of life.

Structured Gaussian Process Regression of Music Mood

Modeling the music mood has wide applications in music categorization, retrieval, and recommendation systems; however, it is challenging to computationally model the affective content of music due to its subjective nature. In this work, a structured regression framework is proposed to model the valence and arousal mood dimensions of music using a single regression model at a linear computational cost. To tackle the subjectivity phenomena, a confidence-interval based estimated consensus is computed by modeling the behavior of various annotators (e.g. biased, adversarial) and is shown to perform better than using the average annotation values. For a compact feature representation of music clips, variational Bayesian inference is used to learn the Gaussian mixture model representation of acoustic features and chord-related features are used to improve the valence estimation by probing the chord progressions between chroma frames. The dimensionality of features is further reduced using an adaptive version of kernel PCA. Using an efficient implementation of twin Gaussian process for structured regression, the proposed work achieves a significant improvement in R2 for arousal and valence dimensions relative to state-of-the-art techniques on two benchmark datasets for music mood estimation.

Evaluating Recurring Traffic Congestion using Change Point Regression and Random Variation Markov Structured Model

This study develops a probabilistic framework that evaluates the dynamic evolution of recurring traffic congestion (RTC) using the random variation Markov structured regression (MSR). This approach integrates the Markov chains assumption and probit regression. The analysis was performed using traffic data from a section of Interstate 295 located in Jacksonville, Florida. These data were aggregated on a 5-minute basis for 1 year (2015). Estimating discrete traffic states to apply the MSR model, this study established a definition of traffic congestion using Bayesian change point regression (BCR), in which the speed–occupancy relationship was explored. The MSR model with flow rate as a covariate was then used to estimate the probability of RTC occurrence. Findings from the BCR model suggest that the morning peak congested state occurs once speed is below 58 miles per hour (mph), whereas the evening peak period occurs at a speed below 55 mph. Evaluating the dynamics of traffic states over time, the Bayesian information criterion confirmed the hypothesis that a first-order Markov chain assumption is sufficient to characterize RTC. Moreover, the flow rate in the MSR model was found to be statistically significant in influencing the transition probability between the traffic regimes at 95% posterior credible interval. The knowledge of RTC transition explained by the approaches presented here will facilitate developing effective intervention strategies for mitigating RTC.

Generalization-Aware Structured Regression towards Balancing Bias and Variance

Attaining the proper balance between underfitting and overfitting is one of the central challenges in machine learning. It has been approached mostly by deriving bounds on generalization risks of learning algorithms. Such bounds are, however, rarely controllable. In this study, a novel bias-variance balancing objective function is introduced in order to improve generalization performance. By utilizing distance correlation, this objective function is able to indirectly control a stability-based upper bound on a model's expected true risk. In addition, the Generalization-Aware Collaborative Ensemble Regressor (GLACER) is developed, a model that bags a crowd of structured regression models, while allowing them to collaborate in a fashion that minimizes the proposed objective function. The experimental results on both synthetic and real-world data indicate that such an objective enhances the overall model's predictive performance. When compared against a broad range of both traditional and structured regression models GLACER was ~10-56% and ~49-99% more accurate for the task of predicting housing prices and hospital readmissions, respectively.

Secretary letter-shapes in County Durham

This paper applies quantitative methods in palaeography. It develops tree-structured regression models of the palaeographical variation found in a synchronic corpus of texts written in orthographically less standardised late Middle English and establishes their accuracy. There are sixteen models, each one relating to a letter-shape known to distinguish the Gothic cursive scripts Anglicana and Secretary. The models predict the presence of the individual letter-shape from one or more of the following variables, in no particular order: (1) localisation of texts’ orthographic variation; (2) text-type; and (3) in-word position. The discussion asks why several Secretary letter-shapes cluster in documents localisable to County Durham and the area further north, given the script’s association with (a) institutions of national administration in the London-Westminster area and (b) orthographic standardisation. It concludes that the linguistics and the palaeography do not co-vary during this period in the history of the English language and suggests that it may illuminate studies of the gradient between Anglicana and Secretary to pay attention to provincial centres, not least Durham.